ࡱ>    U@ f bjbj Gv Z llllh I    \~ ^~ ^~ ^~ ^~ ^~ ^~ $Ӂ R% ~ % % % ~    . . . %   \~ . % \~ .  . . .&T d!\6  #yl}( 8 E 0I x & q)  \6 v  \6 4 D   .  L  ~ ~ F($D-  ($ Brockton Public Schools Mathematics Curriculum, Pre-K-8 2006-2007 Brockton Public Schools Mathematics Curriculum, Pre-K-8 2006-2007 Basan Nembirkow, Superintendent Catherine F. Brine, Executive Director, Office of Teaching and Learning, K-6 John J. Jerome, Executive Director of Office of Teaching and Learning, 7-8 Linda A. Santry, Coordinator of Math and Science, K-8 Barbara M. Lee, Coordinator of Early Childhood Education Mary H. Sundstrom, Department Head for Math, Pre-K-8 Mathematics Committee Linda JordanMath CoachCentral OfficeCourtney VasquezTeacher, Brookfield ElementaryMarguerite MassonMath CoachCentral OfficeRichard WebbTeacher, Brookfield ElementaryMaxine RichardsonMath CoachCentral OfficeMichael SheehanTeacher, Hancock ElementaryGlenn YoungMath CoachCentral OfficeAmy SimonTeacher, Hancock ElementaryDavid CournoyerIRS, Arnone ElementaryJoan WhiteTeacher, Hancock ElementaryPatricia MedisIRS, Gilmore ElementaryMichelle BernsteinTeacher, Goddard KindergartenKathleen Flaherty-SitesIRS, Franklin ElementarySusan SilvaTeacher, Kennedy ElementaryKathryn McMenamyTeacher, East Junior HighJoyce MeadenTeacher, East Junior HighJocelyn YoungTeacher, Angelo ElementaryJoan FarringtonIRS, South Junior HighViolet LeMarAsst. Princ., Arnone ElementaryJudith GreenTeacher, South Junior HighDiane TarbetTeacher, Ashfield SchoolDiane BehanTeacher, North Junior HighJennifer GiannarosTeacher, Belmont ElementaryRichard CastleTeacher, West Junior HighChanda LavigneTeacher, Brookfield ElementaryLinda MonkeviczTeacher, South Junior HighMatthew MurphyTeacher, South Junior High Table of Contents Mathematics Program Philosophy1Strand: Patterns, Relations, and Algebra78Best Practices in Mathematics3Strand: Geometry80Pre-Kindergarten MathematicsStrand: Measurement82Number Sense 5Strand: Data Analysis, Statistics, and Probability84Patterns & Relations10Grade 5Shapes and Spatial Sense12Strand: Number Sense and Operations88Measurement15Strand: Patterns, Relations, and Algebra92 Data Analysis, Statistics, and Probability16Strand: Geometry94Kindergarten Strand: Measurement96Strand: Number Sense and Operations18Strand: Data Analysis, Statistics, and Probability98Strand: Patterns, Relations, and Algebra23Grade 6Strand: Geometry26Strand: Number Sense and Operations100Strand: Measurement29Strand: Patterns, Relations, and Algebra108Strand: Data Analysis, Statistics, and Probability30Strand: Geometry111Grade 1 & 2Strand: Measurement115Strand: Number Sense and Operations32Strand: Data Analysis, Statistics, and Probability119Strand: Patterns, Relations, and Algebra41Grade 7Strand: Geometry47Strand: Number Sense and Operations122Strand: Measurement51Strand: Patterns, Relations, and Algebra126Strand: Data Analysis, Statistics, and Probability54Strand: Geometry129Grade 3 Strand: Measurement131Strand: Number Sense and Operations59Strand: Data Analysis, Statistics, and Probability133Strand: Patterns, Relations, and Algebra64Grade 8Strand: Geometry66Strand: Number Sense and Operations135Strand: Measurement68Strand: Patterns, Relations, and Algebra139Strand: Data Analysis, Statistics, and Probability70Strand: Geometry146Grade 4 Strand: Measurement148Strand: Number Sense and Operations72Strand: Data Analysis, Statistics, and Probability150 Program Philosophy The Brockton Public Schools Mathematics Program, PreK-8, will provide all students access to the richness of mathematical and technological resources. Through hands-on learning, students will be able to apply mathematical principles to solve problems in their daily lives. The program goals are to promote excellence in the teaching and learning of mathematics. implement the Massachusetts Mathematics Curriculum Framework. increase awareness and use of technology in the learning process. enhance systemic change in the school district by implementing methodologies and strategies to embrace all learning styles. In mathematics, students concentrate on making connections and using principles of mathematics to communicate, reason, and solve problems. Students engage in projects that require them to apply number systems, operations, and forms in real-world contexts. The use of manipulatives and technology further supports student learning. Brocktons Mathematics Program allows students to explore the world of numbers, algorithms, patterns, shapes, data, and spatial sense. Students engage in activities that require them to make sense of real-world data, use manipulatives as representative objects, conceptualize the symbolic value of numbers in various forms, perform operations with numbers, and articulate and justify solutions to problems. The program emphasizes the need for students to make connections and use mathematical principles to communicate, reason, and solve problems. The Brockton Public Schools Mathematics Program, PreK-8, adopts the vision of the Massachusetts Mathematics Curriculum Framework that all students in the Commonwealth will achieve mathematical power through problem solving, communication, reasoning, and connections. The program also embraces the Frameworks Guiding Principles. Guiding Principles Students will explore mathematical ideas in ways that maintain their enjoyment of and curiosity about mathematics and that help them develop a depth of understanding. Students will also reflect on real world applications of mathematical principles. All students will have access to high quality mathematics programs. Mathematics learning is a lifelong process that begins and continues in the home and extends to school and community settings. Mathematics instruction will connect with other disciplines and move toward integration of mathematical domains. Students will work together in teams and groups to enhance mathematical learning, communicate effectively, and develop social and mathematical skills. Technology will be used as an essential tool for effective mathematics education. Mathematics assessment will monitor student performance, improve instruction, enhance learning, and encourage student self reflection. Students as Active Learners In order to encourage students to take an active role in their mathematics learning, teachers must establish an environment in which students can investigate and experiment with mathematics in authentic ways. Teachers will, therefore, provide students of all ages and learning styles a wide variety of models, materials, activities, demonstrations, games, investigations, interesting problems and conversations in the mathematical content being explored. Thus, students will spend daily-sustained time engaged in authentic mathematical activities. Students will work cooperatively to share ideas, solutions and strategies and confirm that there are multiple ways to solve problems. Learning Centers will be set up accordingly. An appreciation of the importance of learning from one another and the importance of reflection, guided by the teacher, will enhance the learning process. Instructional Groupings In order to achieve the goals of the mathematics curriculum, a multiplicity of grouping strategiesincluding whole group, small group and individual workmust be utilized. Teachers will use a variety of grouping practices, including cooperative and flexible groupings, to meet the differences in their students learning styles and rates. The reconfiguration of groups should be based on teachers ongoing assessment of students needs. Learning Centers will be designed to meet the needs of diverse learners as well as facilitate the mathematics program. Importance of Manipulatives Active learning necessitates the extensive and thoughtful use of physical materials to foster the development of abstract ideas, encouraging less teacher direction and more student involvement. Manipulatives and activity-based lessons are necessary to address the different learning styles of our students. Their use will help connect mathematics to the real world. All students, PreK-8, should have frequent, ongoing opportunities to use manipulatives to develop an understanding of mathematical concepts and content. Assessment and Evaluation Assessment and evaluation are an integral part of the teaching of mathematics and, therefore, should be a daily occurrence within the mathematics classroom. Assessment and evaluation determine instructional decisions and must incorporate teacher observation of the students at work, both individually and in groups. The classroom culture should reinforce the belief that errors are opportunities for learning and that students should be encouraged to take risks without fear of embarrassment or failure. Traditionally, quizzes and tests have been administered at regular intervals to ascertain student mastery. Todays battery of assessment devices will also include the teachers daily observation of student performance. Teachers must look at the strategies students use to solve problems as well as the solutions they generate. Teachers will also develop rubrics and other assessment techniques and tools which are based on current research, the National Council of Teachers of Mathematics Standards and the Massachusetts Mathematics Curriculum Framework. Additional student assessments include interviews, daily journal writing, other forms of writing about mathematics, student/teacher conferencing, student self assessment and work samples. Technology The Brockton Public Schools Five Year Plan for Instructional Technology calls for the phasing in of instructional learning systems and software in all schools. Initially, each student will be assessed to determine an accurate instructional level. Thereafter, students will work on their individualized mathematics programs. Research indicates that students will show significant gain in specific skill areas when the software is used appropriately and consistently. Documentation of student progress provided through this software thus becomes part of each students ongoing assessment as well as that of the Brockton Public Schools Mathematics Program. Calculators will also be used in the mathematics program. Neither calculators nor computers replace the need to learn basic facts, to compute mentally or to do paper and pencil computation. Rather, they enhance the learning process and allow the student the opportunity to use technology intelligently to become a confident and knowledgeable decision maker. Best Practices in Mathematics Teachers at each grade level, K-6, will begin each day with The Every Day Counts calendar program from Houghton Mifflin. In grades 7 and 8 each mathematics class will begin with a dialogue, which will bring the lesson of the day into a real life situation. The core program must be utilized to ensure that prior knowledge, developmental and ongoing assessment options are included in each lesson. In addition, writing about mathematical processes and the use of hands-on, activity-based strategies should be incorporated into lessons to ensure that all learning styles are addressed. Each daily K-8 mathematics lesson should include the following components: objective(s) a stated purpose for achieving the objective core program materials with appropriate page numbers other materials/manipulatives authentic and engaging independent/group work vocabulary/reading/writing strategies assessment, when applicable Students will engage in authentic mathematics activities daily. write daily. participate in small group discussions several times a week. participate in cooperative learning several times a week. engage in group problem solving, negotiation and consensus development several times a week. engage in solving multi-step problems several times a week. engage in hands on learning activities (e.g., lab assignments, manipulatives) several times a week. respond to open-ended and open response questions several times a week. participate in various forms of assessment weekly. use calculators as part of lessons several times a month. take multiple choice/short answer tests several times a month. work on group projects monthly. work on share projects with the rest of the school several times a year. make oral presentations. use computers and other technology as part of lessons. Teachers will directly teach and model mathematics strategies daily. engage students in authentic mathematics activities daily. engage students in solving multi-step problems. function as coach and facilitator daily. emphasize the practical real world application of course materials daily. use interdisciplinary teaching materials. use alternative, performance based assessments weekly. use rubrics as part of all assessments. use portfolios of students work as indicators of student success several times a year. plan and implement strategies to increase parent involvement several times a year. LEARNING GUIDELINESTATE STANDARDPRE-K Progress IndicatorsLEARNING EXPERIENCERESOURCES1. Listen to and say the names of numbers in meaningful contexts.K.N.1 Count by ones to at least 20.Count by ones orally from 1-10.Play games and listen to stories and poems that contain numbers and counting sequences. Use concrete objects to practice one-to-one correspondence (e.g., say the name of objects while placing an object in each space in an egg carton; distributing a musical instrument to each child in a group; putting pegs in each hole of a pegboard). Count concrete objects for a meaningful purpose (e.g., three crackers for snack; two eyes to glue on the bunny; three steps down to the playground). Follow visual or rebus recipes (e.g., for making play dough or cookies). Point to numbers displayed in the preschool setting (e.g., labels on objects, projects, activity areas; children's bus numbers, children's ages) Everyday Counts: September-June Mathematics Their Way: 92-105 Young Children in Action: 232-237 LAP-D Cognitive Counting 15 LAP-D Cognitive Counting: 13, 14, 16, 18, 24 Young Children in Action: 232-237 Young Children in Action: 232-237 Young Children in Action: 232-237 2. Connect many kinds/quantities of concrete objects and actions to numbers. K.N.2 Match quantities up to at least 10 with numerals and words. Create sets of objects to repre-sent quantities from 1-5. Recognize numeric symbols for quantities from 1-5. Arrange and count a variety of different kinds of objects to explore the consistency of quantities (e.g., to build understanding of what "3" looks like, whether you are counting blocks, beads or pinecones). Participate in finger plays and action rhymes that associate number concepts with concrete actions (e.g., Five Little Monkeys Jumping on the Bed). Use concrete objects, actions, or drawings to represent quantities (e.g., jump two times; stack four unit blocks; string three beads, hold up two fingers, get three blocks on request). Everyday Counts: September June Mathematics Their Way: 166-178 Workjobs: 130-179 LAP-D Cognitive Counting: 13, 14 Workjobs: 130-179 LAP-D Cognitive Counting: 15 3. Use positional language and ordinal numbers (first, second, third) in everyday activities.K.N.3 Identify position of objects in sequences (e.g., first, second) up to fifth. Use ordinal numbers 1st, 2nd, 3rd verbally to identify position.Place concrete objects such as nesting or stacking cups, boxes, or dolls in a row and identify their position as first, second, third. Arrange materials in order (seriate) from small to large; short to long, etc Use ordinal numbers and positional words (e.g., before/after; first, second, third) to describe the order of daily activities. Arrange illustrations from a story or photographs of class events or daily routines in sequence. Everyday Counts: January - June Young Children in Action: 222-224 Young Children in Action: 222-224 Everyday Counts January - June Young Children in Action: 222-224 Workjobs: 214. Use concrete objects to solve simple addition and subtraction problems using comparative language (more than, fewer than, same number of). K.N.4 Compare sets of up to at least 10 concrete objects using appropriate language (e.g., none, more than, fewer than, some number of, one more than) and order numbers. K.N.7 Use objects and drawings to model and solve related addition and subtraction problems to ten.Order the numerals 1-5. Determine whether a group of objects being changed is getting more or less.Distribute and compare concrete objects in meaningful ways (e.g., which bucket has more rocks in it; how many more napkins are needed for everyone at the table). Sing songs and do finger plays that involve adding and taking away (e.g., Two Little Blackbirds). Use pictorial recipes and discuss how many more cups of cups of flour need to be added to the cookie dough. Make pictorial menus or shopping lists; identify the amount of money needed to "buy products" in various play areas. Figure out how many blocks they have altogether when they join two sets or how many blocks are needed to make two towers the same size. See and discuss meaningful examples of the concept of "none" (e.g., you have two cookies left, I have none). Everyday Counts: November, December, January, March, June Mathematics Their Way: 116-118 LAP-D Cognitive Concepts 10, 20, 26, 27, 29 LAP-D Cognitive Counting 10 Young Children in Action: 230-232 Mathematics Their Way: 116-118 Mathematics Their Way: 116-118 Mathematics Their Way: 116-118 Mathematics Their Way: 116-1185. Observe and manipulate concrete examples of whole and half. K.N.5 Understand the concepts of whole and half.Identify if something cut into two pieces has created equal parts or fair share.Cut food into two equal parts for snacks. Match whole objects to similar objects that have been broken or cut in half. Divide a set of objects into two equal parts (e.g., two for you and two for me).Everyday Counts: November Everyday Counts: November Everyday Counts: November6. Examine, manipulate, and identify familiar U.S. coins (penny, nickel, dime, quarter) in play activities.K.N.6 Identify U.S. coins by name.Identify pennies and count them by ones, (1-5). Match and label penny, nickel, dime, and quarter. Use the word add as a synonym for getting more. Identify the + sign to indicate getting more. Draw a model to represent simple addition problems to 5.Create a grocery store or shoe store in the dramatic play area and use play money to pay for items. Listen to age appropriate books about money and identify the coins. Separate coins by color and size.Everyday Counts: September February Everyday Counts: September February Everyday Counts: September - February LEARNING GUIDELINESTATE STANDARDPRE-K Progress IndicatorsLEARNING EXPERIENCERESOURCES7. Explore and describe a wide variety of concrete objects by their attributes. K.P.1 Identify the attributes of objects as a foundation for sorting and classifying (e.g., a red truck, a red block, and a red ball share the attributes of being red; a square block, a square cracker, and a square book share the attribute of being square shaped). Identify objects by color, shape, and size that are the same or different. Identify the attributes of objects as a foundation for sorting and classifying (e.g., a red truck, a red block, and a red ball share the attributes of being red; a square block, a square cracker, and a square book share the attribute of being square shaped).Describe the size, shape, color, and texture of everyday materials such as pasta, rocks, shells, unit blocks, attribute blocks, parquetry blocks, and crackers. Play games that include identifying (pointing to, selecting, or naming) a specified object from a group of objects (e.g., lotto, concentration cards). Listen to and use words that describe the characteristics of objects (e.g., big, small, tall, short, narrow, thick, thin, deep, shallow, round, flat, straight, crooked, heavy, light).Everyday Counts: November - June LAP-D Cognitive Counting 4, 7 LAP-D Cognitive Counting 4, 7 8. Sort, categorize, or classify objects by more than one attribute.K.P.2 Sort and classify objects by color, shape, size, number, and other properties.Sort and classify objects, giving reasons why they are alike or different.Sort parquetry blocks or string beads by size, shape, color, or texture (e.g., big circles/small circles; blue squares/blue circles; big yellow squares/ small yellow squares). Everyday Counts: December - June Mathematics Their Way: 60-87 Young Children in Action: 200-2069. Recognize, describe, reproduce, extend, create, and compare repeating patterns of concrete materials. K.P.3 Identify, reproduce, describe, extend, and create color, rhythmic, shape, number, and letter repeating patterns with simple attributes (e.g., ABABAB).Reproduce and extend a color, rhythmic, shape, number, and letter simple repeating pattern (ABAB).Repeat clapping or drumbeat patterns. Use pattern cards to reproduce patterns with concrete objects such as beads, colored cubes, mosaic tiles with pattern cards. Find patterns in their everyday environment (plaid, stripes, checks on clothing, floors or walls). Repeat a pattern/sequence in a variety of ways (e.g., an ABAB pattern with stickers, blocks, or stamps). Manipulate objects in and out of patterns. recognize and predict word patterns in familiar rhythms, music or stories. Note: The ability to recognize and create patterns generally develops over time. The ability to distinguish multiple attributes also grows over time.Everyday Counts: October June Mathematics Their Way: 21-2-42 LAP-D Cognitive Matching 7, 10 Everyday Counts: November, December, April, May June Everyday Counts: November-June Everyday Counts: February, April, June Everyday Counts: November - February  LEARNING GUIDELINESTATE STANDARDPRE-K Progress IndicatorsLEARNING EXPERIENCERESOURCES10. Investigate and identify materials of various shapes, using appropriate language.K.G.1 Name, describe, sort, and draw simple, two-dimensional shapes. K.G.2 Describe the attributes of two-dimensional shapes (e.g., number of sides, number of corners). Name and sort simple two-dimensional shapes. Count the number of sides and corners on a triangle, square, and rectangle.Sort parquetry blocks by one or more attributes. Place unit blocks on top of their silhouettes. Feel and describe parquetry blocks, then try to identify them without looking. Eat snacks cut in various shapes; cut cookie dough into basic shapes. Create/represent shapes (e.g., using popsicle sticks, pipe cleaners, unit blocks). Find examples of basic shapes such as circle, square, triangle, and rectangle in the environment (e.g., go on a "shape walk" indoors or outdoors to find examples of basic shapes in buildings, in the classroom, in nature). Locate individual objects in pictures composed of overlapping shapes or find shapes in magazine illustrations, picture books (e.g., I Spy books).Everyday Counts: September - June Mathematics Their Way: 58-60 LAP-D Cognitive Matching 1, 2, 4 LAP-D Cognitive Counting 5, 16 Everyday Counts: December-April Young Children in Action: 262-266 LAP-D Cognitive Matching 7 Young Children in Action: 262-266 Young Children in Action: 262-266 11. Explore and identify space, direction, movement, relative position, and size using body movement and concrete objects. K. G. 4 Identify positions of objects in space, and use appropriate language (e.g., beside, inside, next to, close to, above, below, apart) to describe and compare their relative positions.Identify positions of objects in space and use appropriate language (e.g., inside, outside, under, over, next to) to describe and compare their relative positions.Illustrate position and relative distance among objects/ locations using classroom materials or outdoor equipment (e.g., up, down, high, low, above, below, in front of, behind, beside, near, far, next to, apart, together). Move their bodies in space by following verbal instructions through an obstacle course (e.g., crawl under the table, walk around the jungle gym; jump over the block). Follow or use directional language related to daily routines and activities or in dance recordings (e.g., "Put your hands up, down, over your head."). Locate objects based on directional words (e.g., it's next to the ball; under the basket). Play with puzzles of increasing complexity as skills develop. Figure out how much space is needed for a task (e.g., to build a construction using large interlocking panels, or whether two children can fit inside a cardboard box). Identify shapes in different orientations (a triangle is still a triangle even though it's turned in different directions). Everyday Counts: September June Everyday Counts: LAP-D Cognitive Counting 2, 9 LAP-D Cognitive Matching 11, 14 Young Children in Action: 248-261 LAP-D Cognitive Counting 2, 9 LAP-D Cognitive Counting 2, 9 Young Children in Action: 248-261 Young Children in Action: 248-261 Young Children in Action: 248-26112. Listen to and use comparative words to describe the relationships of objects to one another. K.M.1 Recognize and compare the attributes of length, volume/capacity, weight, area, and time using appropriate language, e.g., longer, taller, shorter, same length, heavier, lighter, same weight, holds more, holds less, holds the same amount.Use words that describe amounts appropriately, e.g., longer, taller, shorter, same length, heavier, lighter, same weight, holds more, holds, less, holds the same amount.Compare and describe objects according to a single attribute (e.g., which is bigger, smaller, taller, longer, shorter, same length, wider, narrower, thicker, thinner, deeper, shallower, lighter, heavier, holds less, or holds the same amount). Measure sand, water, or rice using variety of containers and compare the amounts. Make objects of play dough and compare their size. Build structures with blocks and compare their length or height. String beads and compare the length of two necklaces. Use simple balance scales to compare the weight of classroom materials. Compare the size of various everyday objects (e.g., put various people's shoes side by side to see which is longest. Note: Younger preschool children should focus on a single attribute at a time.Everyday Counts March Jun Mathematics Their Way: 116-139 LAP-D Cognitive Counting 11 Young Children in Action: 135-136 Mathematics Their Way: 116-139 Young Children in Action: 135-136 Young Children in Action: 135-136 Young Children in Action: 135-136 Young Children in Action: 135-136 Young Children in Action: 135-136 LEARNING GUIDELINESTATE STANDARDPRE-K Progress IndicatorsLEARNING EXPERIENCERESOURCES13. Use estimation in meaningful ways and follow up by verifying the accuracy of estimations. K.M.2 Make and use estimates of measurements from everyday experiences.Make and use estimates of measurements from everyday experiences.Estimate how many steps it will take to cross the room or the sandbox; how many small containers it will take to fill a larger one, how many mosaic tiles it will take to fill the board; which cup contains more beans. Experiment to verify whether their estimates were accurate.Everyday Counts: March June14. Use nonstandard units to measure length, weight, and amount of content in familiar objects. K.M.3 Use non-standard units to measure length, area, weight, and capacity. Use non-standard units to measure length, area, weight, and capacity.Measure the circumference of a pumpkin or watermelon using a piece of string. Measure the length of a table using their hands. Measure the width of the sandbox with footsteps. Measure a child's height using large cardboard blocks. Compare the length of two play dough snakes or the height of two block towers using their hands. Compare the capacity of two different containers in the sand or water table.Everyday Counts: March June LEARNING GUIDELINESTATE STANDARDPRE-K Progress IndicatorsLEARNING EXPERIENCERESOURCES15. Organize and draw conclusions from facts they have collected. K.D.1 Collect, sort, organize, and draw conclusions about data using concrete objects, pictures, numbers, and graphs.Collect and sort concrete objects, pictures, or shapes to create a simple bar graph.Construct simple graphs and charts to describe concrete materials (e.g., after sorting leaves, children create a graph illustrating the various kinds of leaves, marking the number of leaves in each category, and describing how they sorted the leaves). Take part in creating and discussing surveys (e.g., survey children's food preferences to decide what snack to serve, with children placing marks on graphs indicating their choice).Everyday Counts: December June Mathematics Their Way: 142-163 Everyday Counts: December June Mathematics Their Way: 142-163 Everyday Counts: December June Mathematics Their Way: 142-163  Pre Kindergarten Curriculum Resources Every Day Counts: Every Day in Pre-K Math. 2002/Great Source Education Group. LAP-D (Learning Accomplishment Profile) Planning Cards 1996/Kaplan Early Learning Company Mathematics Their Way Barrata-Lorton, Mary. 1995/Dale Seymour Publications Workjobs II: Number Activities for Early Childhood. Barrata-Lorton, Mary 1987/Pearson Learning. Young Children in Action: A Manual for Preschool Educators. Hohman, Mary. 1983/High Scope Press. Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group  Strand: Number Sense and OperationsDOE Standard numberState StandardPre-Kindergarten Progress IndicatorsKindergarten Progress IndicatorsResourcesK.N.1Count by ones to at least 20.Count by ones orally from 1-10.Count by ones orally beginning from any number in the sequence from 0-20.Mathematical Thinking in Kindergarten Investigation 1, 4-2 Investigation 2, 26-39 Collecting, Counting, and Measuring Investigation 1, 2-21 Investigation 2, 22-35 Investigation 3, 36-51, Investigation 4, 52-65 Investigation 5, 66-77 Investigation 6, 78-97 Counting Ourselves and Others Investigation 1, 2-35 Investigation 4, 76-91 How Many In All? Investigation 1, 2-27 Every Day Counts September-June Digi-Blocks Supplement with: - Super Source Snap Cubes Counting Colors p. 18 - Developing Number Sense Book 1, pp. 52-56 K.N.2Match quantities up to at least 10 with numerals and words.Create sets of objects to represent quantities from 1-5. Recognize numeric symbols for quantities from 1-5.Create sets of objects to represent quantities from 0-10. Recognize and write numeric symbols for quantities from 0-10. Represent an empty set with the numeral 0.Mathematical Thinking in Kindergarten Investigation 1, 4-23 Investigation 2, 26-39 Collecting, Counting, and Measuring Investigation 1, 2-21 Investigation 2, 22-35 Investigation 3, 36-51 Investigation 4, 52-65 Investigation 5, 66-77 Investigation 6, 78-97 Counting Ourselves and Others Investigation 1, 2-35 Investigation 4, 76-91 How Many In All? Investigation 1, 2-27 Every Day Counts September-June Digi-Blocks Supplement with: - Super Source Color Tiles Creating Patterns, p. 22 - Developing Number Sense Book 1, pp. 50-52 K.N.3Identify position of objects in sequences (e.g., first, second) up to fifth.Use ordinal numbers 1st, 2nd, 3rd verbally to identify position. Order the numerals 1-5.Use ordinal numbers, 1st, 2nd, 3rd, 4th, and 5th verbally to identify positions. Order the numerals 0-10.Collecting, Counting, and Measuring Investigation 5, 66-77 Investigation 6, 78-97 Every Day Counts September-June Digi-Blocks Supplement with: - Super Source Color Tiles Line Up Four, pg. 62 - Super Source Snap Cubes Make A Copy, pg. 38 K.N.4Compare sets of up to at least 10 concrete objects using appropriate language (e.g., none, more than, fewer than, some number of, one more than) and order numbers.Determine whether a group of objects being changed is getting more or less.Determine whether a group of objects being changed is getting more, less or staying the same. Represent two equal sets containing up to 10. Compare sets of at least 10 objects using appropriate language.Mathematical Thinking in Kindergarten Investigation 4, 54-60 Collecting, Counting, and Measuring Investigation 4, 52-65 Investigation 5, 66-77 Investigation 6, 78-97; Every Day Counts September-June Digi-Blocks Supplement with: - Developing Number Concepts Book 1, pp. 45-46, 48 K.N.5Understand the concepts of whole and half.Identify if something cut into two pieces has created equal parts or fair share.Identify if something cut in 2 pieces has been fairly cut in half. Tell or show how to cut something equally in half.May be used in conjunction with the Making Shapes and Building Blocks Unit Every Day Counts None Supplement with: - Super Source Color Tiles Half and Half, pg. 46 - Super Source Snap Cubes Make A Copy, pg. 38 K.N.6Identify U.S. coins by name.Identify pennies and count them by ones, (1-5) Match and label penny, nickel, dime, and quarter.Identify U.S. coins by name. Match coins to their correct value (i.e. a nickel = 5 cents) See Grade 1 Number Games and Story Problems Investigation 2, p. 69. Every Day Counts February-April Supplement with: - Games for Number Sense pp. S27-S28 - Math By All Means (Gr. 1 & 2), Menu Activities K.N.7Use objects and drawings to model and solve related addition and subtraction problems to ten.Use the word add as a synonym for getting more. Identify the + sign to indicate getting more. Draw a model to represent simple addition problems to 5.Interpret number sentences for addition and subtraction problems using numbers 0-10 with manipulatives (e.g., with number tiles, counters). Create and interpret simple stories that can be solved using addition or subtraction. Use objects and drawings to model and solve related addition and subtraction problems to ten.How Many In All? Investigation 2, 28-51 Investigation 3, 52-73 Investigation 4, 74-95 Every Day Counts February-April Digi-Blocks Supplement with: - Games for Number Sense Domino sums pg. 57 - Super Source Color Tiles Very Busy Animals, pg. 78 K.N.8Estimate the number of objects in a group and verify results.Put sets of objects in order from least to greatest, shortest to longest, etc., using visual clues.Use the strategy of guess and check to estimate with like objects from 0-10 and verify results.Counting Ourselves and Others Investigation 1, 2-35 Every Day Counts None Digi-Blocks Supplement with: - Developing Number Concepts Book 1, pg. 62  Strand: Patterns, Relations, and AlgebraDOE Standard numberState StandardPre-Kindergarten Progress IndicatorsKindergarten Progress IndicatorsResourcesK.P.1Identify the attributes of objects as a foundation for sorting and classifying (e.g., a red truck, a red block, and a red ball share the attributes of being red; a square block, a square cracker, and a square book share the attribute of being square shaped).Given a set of objects, tell how they are all alike (e.g., all red, all round, etc.).Identify objects by color, shape, and size that are the same or different. Identify the attributes of objects as a foundation for sorting and classifying (e.g., a red truck, a red block, and a red ball share the attributes of being red; a square block, a square cracker, and a square book share the attribute of being square shaped).Mathematical Thinking in Kindergarten Investigation 1, 4-23 Pattern Trains and Hopscotch Paths Investigation 1, 2-23 Counting Ourselves and Others Investigation 1, 2-35 Investigation 2, 36-55 Investigation 3, 56-75 Every Day Counts October, December, March Digi-Blocks Supplement with: - Developing Number Concepts Book 1, pg. 65 K.P.2Sort and classify objects by color, shape, size, number, and other properties.Sort objects by matching color, shape, and size.Sort and classify objects, giving reasons why they are alike or different.Mathematical Thinking in Kindergarten Investigation 1, 4-23 Pattern Trains and Hopscotch Paths Investigation 1, 2-23 Counting Ourselves and Others Investigation 1, 2-35 Investigation 2, 36-55 Investigation 3, 56-75 Every Day Counts September-June Digi-Blocks Supplement with: - Developing Number Concepts Book 1, pg. 67 - Games and Number Sense, pp. 46-47 K.P.3Identify, reproduce, describe, extend, and create color, rhythmic, shape, number, and letter repeating patterns with simple attributes (e.g., ABABAB).Reproduce and extend a color, rhythmic, shape, number, and letter simple repeating pattern (ABAB).Identify, reproduce, describe, extend, and create color, rhythmic, shape, number, and letter repeating patterns with simple attributes (e.g., ABABAB).Mathematical Thinking in Kindergarten Investigation 1, 4-23 Pattern Trains and Hopscotch Paths Investigation 1, 2-23 Counting Ourselves and Others Investigation 1, 2-35 Investigation 2, 36-55 Investigation 3, 56-75 Every Day Counts September-June Digi-Blocks Supplement with: - Super Source, Pattern Blocks, Antwalks p.18, Sping to Win p.88, Who Caught the Biggest Fish? p.86 - Developing MathConcepts Book 1, pg. 91-124 - Games and Number Sense, pp. 46-47 K.P.4Count by fives and tens at least up to 50.Count by tens to 50.Count by fives and tens at least up to 50.Mathematical Thinking in Kindergarten Investigation 1, 4-23; Pattern Trains and Hopscotch Paths Investigation 1, 2-23 Counting Ourselves and Others Supplement with: - Games for Number Sense, p.26-27,88-89 Investigation 1, 2-35 Investigation 2, 36-55 Investigation 3, 56-75 Every Day Counts November, February, March May/June Digi-Blocks Strand: GeometryDOE Standard numberState StandardPre-Kindergarten Progress IndicatorsKindergarten Progress IndicatorsResourcesK.G.1Name, describe, sort, and draw simple, two-dimensional shapes.Name and sort simple two-dimensional shapes.Name, describe, sort, and draw simple, two-dimensional shapes (e.g. Square, circle, triangle).Making Shapes and Building Blocks Investigation 1, 2-25 Investigation 2, 26-37 Investigation 3, 38-59 Investigation 4, 60-81 Every Day Counts September, March, April Supplement with: - Math By All Means Geometry Gr. 1&2 Menu Activities - Super Source Geoboards All About squares, p. 18 K.G.2Describe the attributes of two-dimensional shapes (e.g., number of sides, number of corners).Count the number of sides and corners on a triangle, square, and rectangle.Describe the attributes of two-dimensional shapes (e.g., number of sides, number of corners).Mathematical Thinking in Kindergarten Investigation 1, 4-23 Making Shapes and Building Blocks Investigation 1, 2-25 Investigation 2, 26-37 Investigation 3, 38-59 Investigation 4, 60-81 Every Day Counts September, March, April Digi-Blocks Supplement with: - Super Source Geoboards Four in a Row, p. 30 K.G.3Name and compare three-dimensional shapes.Match and sort three-dimensional shapes.Name and compare three-dimensional shapes (e.g., sphere, cube).Mathematical Thinking in Kindergarten Investigation 1, 4-23 Making Shapes and Building Blocks Investigation 1, 2-25 Investigation 2, 26-37 Investigation 3, 38-59 Investigation 4, 60-81 Every Day Counts September, December, May/June Digi-Blocks Supplement with: - Super Source Geoboards Farm Fences, p. 26 K.G.4Identify positions of objects in space, and use appropriate language (e.g., beside, inside, next to, close to, above, below, apart) to describe and compare their relative positions.Identify positions of objects in space and use appropriate language (e.g., inside, outside, under, over, next to) to describe and compare their relative positions. Identify positions of objects in space, and use appropriate language (e.g., beside, inside, next to, close to, above, below, apart) to describe and compare their relative positions. See Math Frameworks, Nov. 2000, p. 37.Mathematical Thinking in Kindergarten Investigation 1, 4-23 Making Shapes and Building Blocks Investigation 1, 2-25 Investigation 2, 26-37 Investigation 3, 38-59 Investigation 4, 60-81 Every Day Counts None Digi-Blocks Supplement with: - Super Source Geoboards Inside, Outside, p. 42 Strand: MeasurementDOE Standard numberState StandardPre-Kindergarten Progress IndicatorsKindergarten Progress IndicatorsResourcesK.M.1Recognize and compare the attributes of length, volume/capacity, weight, area, and time using appropriate language, e.g., longer, taller, shorter, same length, heavier, lighter, same weight, holds more, holds less, holds the same amount.Use words that describe amounts appropriately, e.g., longer, taller, shorter, same length, heavier, lighter, same weight, holds more, holds, less, holds the same amount.Recognize and compare the attributes of length (longer, shorter), of volume or capacity holds (more, less), weight (heavier, lighter), area (more, less), time (yesterday, today, tomorrow), and temperature (hotter, colder).Collecting, Counting, and Measuring Investigation 3, 36-51 How Many In All? Investigation 1, 2-27 Every Day Counts November-June Digi-Blocks Supplement with: - Super Source Geobards - Two Line Design, p. 82 - Path finder, p.50 - Make the Other Half, p. 46K.M.2Make and use estimates of measurements from everyday experiences.Demonstrate a strategy.Make and use estimates of measurements from everyday experiences.Collecting, Counting, and Measuring Investigation 3, 36-51 How Many In All? Investigation 1, 2-27; Every Day Counts November, December, January Digi-Blocks Supplement with: - Super Source Shape Cubes How Long Is It? p. 30 Puzzles, p. 54 - Super Source Geoboards Tell Me About That p. 70 K.M.3Use non-standard units to measure length, area, weight, and capacity.Use non-standard units to measure length, area, weight, and capacity.Use non-standard units to measure length, area, weight, and capacity.Collecting, Counting, and Measuring Investigation 3, 36-51 How Many In All? Investigation 1, 2-27 Every Day Counts November-January Digi-Blocks Supplement with: - Super Source Geoboards From A to Z p. 34  Strand: Data Analysis, Statistics, and ProbabilityDOE Standard numberState StandardPre-Kindergarten Progress IndicatorsKindergarten Progress IndicatorsResourcesK.D.1Collect, sort, organize, and draw conclusions about data using concrete objects, pictures, numbers, and graphs.Collect and sort concrete objects, pictures, or shapes to create a simple bar graph.Use counters to represent data from a simple survey. Sort a variety of objects (fruit, toy animal, etc.) and place them on a graphic mat to create a concrete graph using numbers to 10. Demonstrate an understanding of at least one fact shown by first-hand data (e.g., count the number of students who stand in each line to show their favorite kind of ice cream). Verbally state a reason for the results shown on one part of a pictorial table, chart, or graph. Collect, sort, organize, and draw conclusions about data using concrete objects, pictures, numbers, and graphs.Mathematical Thinking in Kindergarten Investigation 4, 54-64 Counting Ourselves and Others Investigation 2, 36-55 Investigation 3, 56-75 Investigation 4, 76-91 Every Day Counts September-June Digi-Blocks Supplement with: - Math By All means - Probability and Statistics Grades 1 & 2 Menu Activities - Developing Number Sense Book 1 p. 152 - Super Source Geoboards Things that Fly p. 74 - Super Source Color Tiles Counting Colors p. 18 - Super Source Snap Cubes Red or Blue p. 58 The Disappearing Train p. 78 Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group  Strand: Number Sense and OperationsDOE Standard NumberState StandardGrade 1 Progress IndicatorsGrade 2 Progress IndicatorsResources2.N.1Name and write (in numerals) whole numbers to 1000, identify the place values of the digits, and order the numbers.Create and label sets of objects from 0 to100. Demonstrate an understanding of the concepts of tens and ones (e.g., base ten blocks, number lines) using a variety of manipulatives. Recognize dictated numbers from 0-100.Create and label sets of objects from 0 to 1000. Demonstrate an understanding of the concepts of place valueones, tens, and hundreds to 1,000 using manipulatives (e.g., base ten blocks, number lines). Write dictated whole numbers from 0 to 1,000 with correct place value.Grade 1 Mathematical Thinking at Grade 1 Investigation 2, 24-59 Investigation 5, 114-140 Building Number Sense Investigation 1, 2-35 Investigation 3, 92-111 Survey Questions and Secret Rules Investigation 4, 74-99 Investigation 2, 32-53 Number Games and Story Problems Investigation 2, 49-98 Every Day Counts All months Digi-Blocks Grade 2 Mathematical Thinking at Grade 2 Investigation 1, 2-19 Investigation 2, 20-51 Investigation 3, 2-75 Investigation 4, 76-99 Investigation 5, 100-123 Coins, Coupons, and Combinations Investigation 4, 108-124 Every Day Counts All months Digi-Blocks 2.N.2Identify and distinguish among multiple uses of numbers including cardinal (to tell how many) and ordinal (to tell which one in an ordered list), and numbers as labels and as measurement.Distinguish between cardinal (there are 2) and ordinal (its the second one) numbers verbally. Use ordinal numbers (1st-10th). Measure common objects using non-standards units of measure. Measure common objects using a ruler to nearest inch. Identify and distinguish among multiple uses of numbers including cardinal (to tell how many, 1-1000) and ordinal (to tell which one in an ordered list, to 1000th), and numbers as labels and as measurement. Use a standard ruler to measure to nearest half-inch.Grade 1 Mathematical Thinking at Grade 1 Investigation 2, 24-59 Bigger, Taller, Heavier, Smaller Investigation 3, 60-81 Every Day Counts Sept., Oct., Nov., Dec., Feb., March, April, May, June Digi-Blocks CCC Lab Ordinal Numbers Grade 2 Mathematical Thinking at Grade 2 Investigation 1, 2-19 Investigation 2, 20-51 Every Day Counts All months Digi-Blocks 2.N.3Identify and represent common fractions (1/2, 1/3, 1/4) as parts of wholes, parts of groups, and numbers on the number line.Identify fair shares in halves, thirds and fourths. Describe one unit of a fraction as one-half, one-third or one-fourth (1/2, 1/3, 1/4).Identify and represent common fractions (1/2 to 7/8) as parts of wholes, parts of groups, and numbers on the number line. Use the terms numerator or denominator correctly. Add simple fractions with like denominators using manipulatives (1/4 + 2/4 +3/4).Grade 1 Additional resources needed Every Day Counts Feb. CCC Lab - Super Source Pattern Blocks Grade 2 Shapes, Halves, and Symmetry Investigation 3, 72-93 Every Day Counts Oct., March2.N.4Compare whole numbers using terms and symbols (e.g., less than, equal to, greater than [<,=,>]Compare whole numbers to 100 using terms and symbols (e.g. less than, equal to, greater than [<,=,>]Read, write, compare (>, <, =, odd, even), and order whole numbers to 1,000.Grade 1 Readiness: Mathematical Thinking at Grade 1 Investigation 2, 24-59 Investigation 4, 82-113 Investigation 5, 114-135 Survey Questions and Secret Rules Investigation 4, 74-99 Every Day Counts Oct., Nov., April CCC Lab Symbols Grade 2 Every Day Counts Sept. 2.N.5Identify odd and even numbers and determine whether a set of objects has an odd or even number of elements.Identify odd and even numbers and determine whether a set of objects has an odd or even number of elements.Identify odd and even numbers and determine whether a set of objects has an odd or even number of elements. Predict whether a simple addition problem will have an even or odd answer.Grade 1 Number Games and Story Problems Investigation 2, 46-99 Every Day Counts ABAB Patterns in Calendar Grade 2 Coins, Coupons, and Combinations Investigation 1 2-52 Every Day Counts Sept.2.N.6Identify the value of all U.S. coins and $1, $5, $10, and $20 bills. Find the value of a collection of coins and dollar bills and different ways to represent an amount of money up to $.50. Use appropriate notation, e.g., $.69, $1.35.Identify the value of all U.S. coins and $1, $5, $10, and $20 bills. Find the value of a collection of coins and dollar bills and give appropriate ways to represent an amount of money up to $0.50. Use appropriate notation, e.g., $0.69, $1.35.Identify the value of all U.S. coins and $1, $5, $10, and $20 bills. Find the value of a collection of coins and dollar bills and give appropriate ways to represent an amount of money up to $0.50. Use appropriate notation, e.g., $0.69, $1.35.Grade 1 Number Games and Story Problems Investigation 2, 46-99 Every Day Counts Nov., Dec., Feb., March, April CCC Lab Grade 2 Mathematical Thinking at Grade 2 Investigation 4, 76-99 Coins, Coupons, and Combinations Investigation 2, 54-85 Every Day Counts All months 2.N.7Demonstrate an understanding of various meanings of addition and subtraction (e.g., addition as combination [plus combined with, more]; subtraction as comparison [how much less, how much more], equalizing [how many more are needed to make these equal], and separation [how much remaining]).Represent visually presented addition or subtraction problems (acted out or in pictures) (0-20) with a number sentence. Solve addition and subtraction number sentences up to 20 using manipulatives.Write a number sentence to represent visually presented addition or subtraction problems (acted out or in pictures) (0-100s). Use mental math to add and subtract whole numbers to 20. Add or subtract one-, two-, and three-digit numbers using pencil and paper, and an appropriate algorithm (with and without regrouping).Grade 1 Mathematical Thinking at Grade 1 Investigation 2, 24-59 Investigation 4, 82-113 Investigation 5, 114-144 Building Number Sense Investigation 2, 36-79 Investigation 4, 114-171 Number Games and Story Problems Investigation 1, 2-45 Investigation 3, 100-165 Every Day Counts Oct., Nov., Feb., March, April Digi-Blocks Grade 2 Mathematical Thinking at Grade 2 Investigation 2, 20-51 Investigation 4, 76-99 Coins, Coupons, and Combinations Investigation 1, 2-53 Investigation 3, 86-107 Investigation 4, 108-124 Putting Together and Taking Apart Investigation 1, 2-39 Every Day Counts Oct., Dec., Jan., Feb., March, April Digi-Blocks 2.N.8Understand and use the inverse relationship between addition and subtraction (e.g., 8 + 6 = 14 is equivalent to 14 - 6 = 8 and is also equivalent to 14 - 8 = 6) to solve problems and check solutions.Use numbers to solve real problems 0-20. (How many cartons of milk do we need if everyone needs one?) Show a basic understanding of how to reverse a simple addition or subtraction problem.Explain and demonstrate the relationship between addition and subtraction (fact families). Use the appropriate operation (addition or subtraction) to solve single-step problems.Grade 1 Number Games and Story Problems Investigation 1, 2-45 Investigation 3, 100-165 Every Day Counts Oct., Nov., March, April Digi-Blocks Grade 2 Coins, Coupons, and Combinations Investigation 3, 86-107 Putting Together and Taking Apart Investigation 1,2-39 Investigation 5, 104-134 Every Day Counts Oct., Dec., Jan., Feb., April 2.N.9Know addition facts (addends to 10) and related subtraction facts, and use them to solve problems.Know the concepts of addition and subtraction of single digit numbers 0-10.Demonstrate an understanding of addition and subtraction of numbers 10-20. Know addition facts (addends to 10) and related subtraction facts, and use them to solve problems.Grade 1 Mathematical Thinking at Grade 1 Investigation 2, 24-59 Building Number Sense Investigation 2, 36-79 Investigation 3, 80-113 Investigation 4, 114-171 Number Games and Story Problems Investigation 1, 2-45 Investigation 3, 100-165 Every Day Counts Oct., Nov., March, April Grade 2 Mathematical Thinking at Grade 2 Investigation 3, 20-51 Coins, Coupons, and Combinations Investigation 1, 2-53 Investigation 3, 86-107 Investigation 4, 108-124 Putting Together and Taking Apart Investigation 1, 2-39 Investigation 2, 40-71 Investigation 5, 104-134 Every Day Counts Dec., Jan., Feb., March, April 2.N.10 2.N.11 Demonstrate the ability to add and subtract three-digit numbers accurately and efficiently. Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for addition (two 3- digit numbers and three 2digit numbers) and subtraction (two, 3 digit numbers). Combine and separate sets of objects 0-20. Combine and separate sets of objects 0-20. Demonstrate an understanding of the concepts of addition and subtraction of any two- and three-digit numbers 0-999 by adding and subtracting 3 digit numbers accurately (with and without regrouping). Demonstrate an understanding of the concepts of addition and subtraction of any two- and three-digit numbers 0-999 by adding and subtracting 3 digit numbers accurately (with and without regrouping).Grade 1 Readiness: Mathematical Thinking at Grade 1 Investigation 2, 24-59 Investigation 4, 82-113 Building Number Sense Investigation 2, 36-79, Investigation 4, 114-171 Number Games and Story Problems Investigation 1, 2-45 Investigation 3, 100-165 Investigation 2, 49-98 Every Day Counts None Grade 2 Readiness: Mathematical Thinking at Grade 2 Investigation 4, 76-99 Putting Together and Taking Apart Investigation 1, 2-39 Investigation 2, 40-71 Investigation 5, 104-134 Every Day Counts Dec., Jan., Feb., March, April Grade 1 Number Games and Story Problems Investigation 3, p. 102-149 2.N.12 Estimate, calculate, and solve problems involving addition and subtraction of 2-digit numbers. Describe differences between estimates and calculations.  Strand: Patterns, Relations, and AlgebraDOE Standard NumberState StandardGrade 1 Progress IndicatorsGrade 2 Progress IndicatorsResources2.P.1Identify, reproduce, describe, extend, and create simple rhythmic, shape, size, number, color, and letter repeating patterns.Identify, extend, and create a variety of rhythmic, visual, shape, size, color, letter, number, and verbal two- and three-element patterns (e.g., ABBABB, ABCABC, etc.).Identify, extend, and construct a variety of rhythmic, shape, size, color, letter, number, verbal, and visual patterns up to five elements. Identify and extend a two-element numerical pattern up to 100.Grade 1 Mathematical Thinking at Grade 1 Investigation 3, 60-81 Investigation 4, 82-113 Building Number Sense Investigation 3, 80-113 Investigation 4, 163 Quilt Squares and Block Towns Investigation 1, 2-61 Number Games and Story Problems Investigation 2, 46-99 Every Day Counts Sept., Oct., Nov., Dec., Jan., Feb., March, April Digi-Blocks Grade 2 Mathematical Thinking at Grade 2 Investigation 3, 52-75 Coins, Coupons, and Combinations Investigation 1, 2-53 Shapes, Halves, and Symmetry Investigation 3, 72-93 Putting Together and Taking Apart Investigation 2, 40-71 Timelines and Rhythm Patterns Investigation 2, 34-6 Every Day Counts All months Digi-Blocks2.P.2Identify different patterns on the hundreds chart.Describe various simple patterns on a number chart 1 -100.Describe various patterns on a number chart 1 100.Grade 1 Building Number Sense Investigation 3, 80-113 Number Games and Story Problems Investigation 2, 46-99 Every Day Counts Oct., Nov., April Grade 2 Putting Together and Taking Apart Investigation 1, 2-39 Investigation 2, 40-71 Every Day Counts Nov., Dec., Jan., Feb., March, May/June 2.P.3Describe and create addition and subtraction number patterns (e.g., 1, 4, 7, 1, or 25, 23, 21,).Describe and create addition and subtraction number patterns (e.g., 2, 4, 6 or 5, 10, 15, or 100, 90, 80).Describe and create addition and subtraction number patterns (e.g., 1, 4, 7, 10 ; or 25, 23, 21).Grade 1 Mathematical Thinking at Grade 1 Investigation 3, 60-81 Investigation 4, 82-113 Building Number Sense Investigation 3, 80-113 Quilt Squares and Block Towns Investigation 1, 2-61 Number Games and Story Problems Investigation 2, 46-99 Every Day Counts March, April Grade 2 Coins, Coupons, and Combinations Investigation 2, 54-85 Every Day Counts Oct., Dec., Jan.-June 2.P.4Skip count by twos, fives, and tens up to at least 50, starting at any number.Skip count by twos to 50; fives and tens to 100, starting at any number.Skip count by twos, fives, and tens to 100, starting at any number.Grade 1 Number Games and Story Problems Investigation 2, 46-99 Every Day Counts October-June Building Number Sense Investigation 3, 60-81 Grade 2 Mathematical Thinking at Grade 2 Investigation 1, 2-19 Investigation 3, 52-75 Investigation 5, 76-99 Coins, Coupons, and Combinations Investigation 2, 54-85 Putting Together and Taking Apart Investigation 2, 40-71 Every Day Counts Sept., Nov., Jan., Feb., March, May/June 2.P.5Construct and solve open sentences that have variables (e.g., ( + 7 = 100).Construct and solve open sentences that have missing addends and subtrahends (up to 20).Construct and solve open sentences that have missing addends and subtrahends (up to 1,000).Grade 1 Readiness: Building Number Sense Investigation 4, 114-171 Investigation 2, 36-79 Every Day Counts Oct., Nov. Grade 2 Putting Together and Taking Apart Investigation 3, 72-85 Investigation 4, 86-103 Every Day Counts None2.P.6Write number sentences using +, -, <, =, and/or > to represent mathematical relationships in everyday situations. Write number sentences using +, -, <, =, and/or > to represent mathematical relationships in everyday situations ( up to 100 i.e. 22<80).Write number sentences using +, -, <, =, and/or > to represent mathematical relationships in everyday situations (up to 1,000).Grade 1 Building Number Sense Investigation 4, 114-117 Number Games and Story Problems Investigation 1, 5-40 Investigation 3, 102-149 Every Day Counts Oct., Nov. Grade 2 Putting Together and Taking Apart Investigation 5, 104-134 Every Day Counts Oct., Nov., Dec. Jan. March 2.P.7Describe functions related to trading, including coin trades and measurement trades (e.g., five pennies make one nickel or four cups make a quart).Describe functions related to trading, including coin trades (e.g., five pennies make one nickel. ).Describe functions related to trading, including 2c = 1pint, 4 c =1 qt., 1 ft. = 12 in., 4 quarters = $1.00., 7 days = 1 weekGrade 1 Number Games and Story Problems Investigation 2, 46-99 Every Day Counts Sept., Oct., Nov., Dec., Feb., March Grade 2 Putting Together and Taking Apart Investigation 2, 0-71 Every Day Counts April, May/June  Strand: GeometryDOE Standard NumberState StandardGrade 1 Progress IndicatorsGrade 2 Progress IndicatorsResources2.G.1Describe attributes and parts of two- and three-dimensional shapes (e.g., length of sides, and number of corners, edges, faces, and sides).Describe attributes and parts of two- and three-dimensional shapes (e.g., faces and sides).Describe attributes and parts of two- and three-dimensional shapes (e.g., corners, edges, faces and sides).Grade 1 Mathematical Thinking at Grade 1 Investigation 1, 2-23 Survey Questions and Secret Rules Investigation 1, 2-31 Quilt Squares and Block Towns Investigation 1, 2-61 Investigation 2, 62-97 Investigation 3, 98-126 Every Day Counts Oct., Nov., Dec., Jan., Grade 2 Mathematical Thinking at Grade 2 2-19, 52-75 Shapes, Halves, and Symmetry Investigation 1, 2-43 Investigation 2, 36-57 Investigation 3, 72-93 Investigation 4, 94-115 Every Day Counts Oct., Nov., Dec., Jan., March, April, May/June 2.G.2Identify, describe, draw, and compare two-dimensional shapes, including both polygonal (up to six sides) and curved figures such as circles.Identify, describe, draw, and compare two-dimensional shapes including polygons (up to four sides) and circles.Identify, describe, draw, and compare two-dimensional shapes including both polygons (up to six sides) and curved figures, such as circlesGrade 1 Mathematical Thinking at Grade 1 Investigation 1, 2-23 Quilt Squares and Block Towns Investigation 1, 2-61 Investigation 2, 62-97 Investigation 3, 98-126 Every Day Counts Oct., Nov., Jan., Grade 2 Mathematical Thinking at Grade 2 Investigation 3, 52-75 Shapes, Halves, and Symmetry Investigation 1, 2-43 Investigation 2, 36-57 Investigation 3, 72-93 Every Day Counts Oct., Jan., March, April, May/June2.G.3Recognize congruent shapesRecognize congruent shapes (see above). Use the term congruent correctlyRecognize congruent shapes (see above). Use the term congruent correctlyGrade 1 Every Day Counts January Grade 2 Shapes, Halves, and Symmetry Investigation 1, 2-43 Investigation 3, 72-93 Every Day Counts Jan., March, April, May/June 2.G.4Identify shapes that have been rotated (turned), reflected (flipped), translated (slid), and enlarged. Describe direction of translations (e.g., left, right, up, down).Demonstrate flips, slides, and turns with their bodies. Identify shapes that have been turned, flipped, slid, and enlarged. Demonstrate flips, slides, and turns with manipulatives. Identify shapes that have been turned, flipped, slid, and enlarged. Describe the direction (e.g., left, right, up, down).Grade 1 Quilt Squares and Block Towns Investigation 1, 2-61 Every Day Counts January Grade 2 See Grade 1 Quilt Squares and Block Towns 2-61 Every Day Counts None2.G.5Identify symmetry in two-dimensional shapes.Identify horizontal and vertical lines of symmetry in two-dimensional shapes.Identify various forms of symmetry in two-dimensional shapes (e.g. Lines of symmetry, rotational symmetry).Grade 1 Readiness: Quilt Squares and Block Towns Investigation 2-61 (Reading Only) Every Day Counts None Grade 2 Shapes, Halves, and Symmetry Investigation 4, 94-115 Every Day Counts Jan., March, April, May/June 2.G.6Predict the results of putting shapes together and taking them apart.Predict and confirm the results of putting shapes together and taking them apart.Predict and confirm the results of putting shapes together and taking them apart.Grade 1 Quilt Squares and Block Towns Investigation 1, 2-61 Investigation 2, 62-97 Every Day Counts Oct., Nov., Jan. Grade 2 Mathematical Thinking at Grade 2 Investigation 3, 52-75 Shapes, Halves, and Symmetry Investigation 1, 2-43; Investigation 2, 36-57 Every Day Counts None2.G.7Relate geometric ideas to numbers (e.g., seeing rows in an array as a model of repeated addition).Relate geometric ideas to numbers (e.g., seeing rows in an array as a model for addition and subtraction).Relate geometric ideas to numbers (e.g., seeing rows in an array as a model of repeated addition).Grade 1 Every Day Counts None Grade 2 Mathematical Thinking at Grade 2 Investigation 1, 2-19 Shapes, Halves, and Symmetry Investigation 1, 2-43 Investigation 2, 36-57 Every Day Counts None Strand: MeasurementDOE Standard NumberState StandardGrade 1 Progress IndicatorsGrade 2 Progress IndicatorsResources2.M.1 Identify parts of the day (e.g., morning, afternoon, evening), days of the week, and months of the year. Identify dates using a calendar.Identify the use of a calendar and verbally identify the days of the week and months of the year. Identify parts of the day (e.g., morning, afternoon, evening). Identify the four seasonsIdentify parts of the day (e.g., morning, afternoon, evening), days of the week, and months of the year. Identify dates using a calendar. Relate specific months to the seasonsGrade 1 Survey Questions and Secret Rules Investigation 3, 54-73 Every Day Counts All months Grade 2 Timelines and Rhythm Patterns Investigation 1, 2-33 Every Day Counts All months2.M.2Tell time at quarter-hour intervals on analog and digital clocks using a.m. and p.m.Tell and record time to the hour using an analog and digital clock, and using a.m. and p.m.Tell and record time to the half hour, and quarter hour using an analog or digital clock, and using a.m. and p.m.Grade 1 Every Day Counts Sept., Oct., Nov., Dec., Feb., March, May, June Grade 2 Timelines and Rhythm Patterns Investigation 1, 2-33 Every Day Counts March 2.M.3Compare the length, weight, area, and volume of two or more objects by using direct comparison.Compare length and weight of two or more objects by using direct comparison. Identify capacity (which holds more) using direct comparison and containers.Compare length, weight, area, and volume of two or more objects by using direct comparison.Grade 1 Bigger, Taller, Heavier, Smaller Investigation 1, 2-31 Investigation 2, 32-59 Investigation 3, 60-86 Building Number Sense Investigation 3, 92,113 Every Day Counts Nov., May, June Grade 2 How Long? How Far? Investigation 1, 2-43, Investigation 2, 44-81 Every Day Counts Nov., Feb., March, May/June2.M.4Measure and compare common objects using metric and English units of length measurement (e.g., centimeter, and inch).Measure and compare common objects using metric and English units of length measurement (e.g., centimeter, and inch).Measure and compare common objects using metric and English units of length measurement (e.g., 36, 1 m, 100 cm). Measure to the nearest inch and nearest centimeter.Grade 1 Readiness: Bigger, Taller, Heavier, Smaller Investigation 1, 2-3 Investigation 2, 32-59 Investigation 3, 60-86 Every Day Counts May, June Grade 2 Readiness: How Long? How Far? Investigation 1, 2-43, 34-63 Every Day Counts Feb., March, April, May/June2.M.5Select and correctly use the appropriate measurement tools (e.g., ruler, balance scale, thermometer).Select and correctly use the appropriate measurement tools (e.g., ruler, balance scale).Select and correctly use the appropriate measurement tools (e.g., ruler, balance scale, thermometer).Grade 1 Bigger, Taller, Heavier, Smaller Investigation 1, 2-31 Every Day Counts May, June Grade 2 How Long? How Far? Investigation 1, 2-43 Every Day Counts Nov., Jan., Feb., Mar., Apr., May/June2.M.6Make and use estimates of measurement, including time, volume, weight, and area.Make and use estimates of measurement, including time and weight.Make and use estimates of measurement, including time, volume, weight, and area.Grade 1 Bigger, Taller, Heavier, Smaller Investigation 1, 2-31 Investigation 2, 32-59 Every Day Counts Sept., May, June Grade 2 How Long? How Far? Investigation 1, 2-43 Every Day Counts Feb., March, May/June Strand: Data Analysis, Statistics, and probabilityDOE Standard NumberState StandardGrade 1 Progress IndicatorsGrade 2 Progress IndicatorsResources2.D.1Use interviews, surveys, and observations to gather data about themselves and their surroundings.Take a class survey and record information.Use interviews, surveys, and observations to gather data about themselves and their surroundings.Grade 1 Mathematical Thinking at Grade 1 Investigation 5, 114-144 Survey Questions and Secret Rules Investigation 2, 32-53 Investigation 4, 74-99 Investigation 3, 54-73 Every Day Counts Dec., Feb., March Grade 2 Mathematical Thinking at Grade 2, 100-123 Does It Walk, Crawl, or Swim? Investigation 1, 2-35; Investigation 2, 36-57 Investigation 3, 58-69 Investigation 4, 70-85 How Many Pockets? How Many Teeth? Investigation 1, 2-27 Everyday Counts Sept., Oct., Jan. 2.D.2Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams; interpret the representations.Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams; interpret the representations.Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams; interpret the representations.Grade 1 Mathematical Thinking at Grade 1 Investigation 5, 114-144 Survey Questions and Secret Rules Investigation 2, 32-53 Investigation 4, 74-99 Investigation Bigger, Taller, Heavier, Smaller Investigation 2, 32-59 Every Day Counts Dec., Jan., Feb., March, April, May, June Grade 2 Mathematical Thinking at Grade 2 100-123 Does It Walk, Crawl, or Swim? Investigation 1, 2-35 Investigation 2, 36-57 Investigation 3, 58-69 Investigation 4, 70-85 How Many Pockets? How Many Teeth? Investigation 1, 2-27 Investigation 2, 28-59 Investigation 3, 60-73 Every Day Counts Sept., Oct., Jan. April, May/June 2.D.3Formulate inferences (draw conclusions) and make educated guesses (conjectures) about a situation based on information gained from data.Formulate inferences (draw conclusions) and make educated guesses (conjectures) about a situation based on information gained from data.Formulate inferences (draw conclusions) and make educated guesses (conjectures) about a situation based on information gained from data.Grade 1 Mathematical Thinking at Grade 1 Investigation 5, 114-144 Survey Questions and Secret Rules Investigation 2, 32-53 Investigation 4, 74-99 Investigation 3, 54-73 Every Day Counts December Grade 2 Does It Walk, Crawl, or Swim? Investigation 1, 2-35; Investigation 2, 36-57 Investigation 3, 58-69, Investigation 4, 70-85 How Many Pockets? How Many Teeth? Investigation 1, 2-27 Investigation 2, 28-59 Investigation 3, 60-73 Every Day Counts Feb. 2.D.4Decide which outcomes of experiments are most likely.Based on data gathered, decide which outcomes of experiments are most likely.With guided discussion, decide which outcomes of experiments are most likely Grade 1 Every Day Counts December Grade 2 See Grade 3 Things that Come in Groups Investigation 2, 58, Investigation 5, 76, 93-94 Every Day Counts Feb., May/June  Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed CCC Lab Activities Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group  Strand: Number Sense and OperationsDOE Standard NumberState StandardGrade 3 Progress IndicatorsResources3.N.1Exhibit an understanding of the values of the digits in the base-ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999.Exhibit an understanding of the values of the digits in the base-ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999.Mathematical Thinking at Grade 3 Investigation 1, 2-13; Investigation 4, 68-86 Landmarks in the Hundreds Investigation 1, 2-29: Combining and Comparing Investigation 4, 40-57 Exploring Solids and Boxes Investigation 5, 52-62 Every Day Counts, All Digi-Blocks 3.N.2Represent, order, and compare numbers through 9,999. Represent numbers using expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3, and written out in words, e.g., eight hundred fifty-three.Represent, order, and compare numbers through 9,999. Represent numbers using expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3, and written out in words, e.g., eight hundred fifty-three.Mathematical Thinking at Grade 3 Investigation 3, 46-67; Everyday Counts, November Digi-Blocks Every Day Counts- None3.N.3Identify and represent fractions between 0 and 1 with denominators through 10 as parts of unit wholes and parts of groups.Demonstrate an understanding of fractions with denominators through 10 as parts of unit wholes and parts of a group. Measure to the nearest inchMathematical Thinking at Grade 3 Investigation 4, 68-86 Fair Shares Investigation 1, 2-21 Investigation 2, 22-45 Investigation 3, 46-59 Every Day Counts, March 3.N.4Locate on the number line and compare fractions (between 0 and 1) with denominators 2, 3, and 4, e.g., 2/3: and the mixed numbers 1 , 1 , and 1 .Locate on the number line and compare fractions (between 0 and 1) with denominators 2, 3, and 4, e.g., 2/3: and the mixed numbers 1 , 1 , and 1 . Show which fractions are equivalent (using manipulatives)Mathematical Thinking at Grade 3 Investigation 4, 68-86 Fair Shares Investigation 1, 2-2 Investigation 2, 22-45 Investigation 3, 46-59 Every Day Counts, None 3.N.5Recognize classes (odd numbers, even numbers; and multiples of numbers through 10) to which a number may belong, and identify the numbers in those classes, e.g., the class of multiples of 7 between 1 and 29 consist of 7, 14, 21, 28.Recognize classes (in particular, odds, evens; and multiples of a given number) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems. Predict whether an addition or subtraction problem will have an even or odd answer.Mathematical Thinking at Grade 3 Investigation 4, 68-86 Things That Come in Groups Investigation 2, 20-39 Landmarks in the Hundreds Investigation 1, 2-29; Investigation 2, 30-51; Investigation 3, 52-60 Combining and Comparing Investigation 1, 2-12 Every Day Counts All Digi-Blocks 3.N.6Select, use, and explain various meanings and models of multiplication (through 10 x 10). Relate a multiplication problem to a corresponding division problem, e.g., draw a model to represent 5 x 6 and 30 6. Select, use, and explain various meanings and models of multiplication (up to 10 x 10) and division of whole numbers. Understand and use the inverse relationship between the two operations. Model and describe multiplication as repeated addition. Model and describe division as repeated subtraction. Mathematical Thinking at Grade 3 Investigation 2, 14-45 Things That Come in Groups Investigation 1, 4-16 Investigation 3, 40-53 Investigation 4, 56-70 Investigation 5, 74-87 Landmarks in the Hundreds Investigation 1, 2-30 Every Day Counts December, February April-June Digi-Blocks 3.N.7Use the commutative and identify properties of addition and multiplication on whole numbers in computations and problem situations, e.g., 3 + 4 + 7 = 3 + 7 + 4 = 10 + 4Select, use, and explain the commutative, and identity properties of operations on whole numbers, e.g., 3 + 4 + 7 = 3 + 7 + 4 = 10 + 4  Additional Resources Needed 3.N.8 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.Mathematical Thinking at Grade 3 Investigation 2, 14-45; Things That Come in Groups Investigation 1, 2-19 Investigation 4, 56-73 Investigation 5, 74-90 Landmarks in the Hundreds Investigation 2, 30-51 Combining and comparing Investigation 1, 2-12 Investigation 3, 26-35 Investigation 4, 40-53 Up and Down the Number Line Investigation 1, 2-31 Every Day Counts September, October, December-May/June Digi-Blocks3.N.9 Know multiplication facts through 10 x 10 and related division facts, e.g., 9 x 8 = 72 and 72 9 = 8. Use these facts to solve related problems e.g., 3 x 5 is related to 30 x 50.Know multiplication facts through 10 x 10 and related division facts. Use these facts to solve related multiplication problems and compute related problems (e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500). Things That Come in Groups Investigation 1, 2-19 Investigation 4, 56-73 Investigation 5, 74-90 Landmarks in the Hundreds Investigation 2, 30-51 Every Day Counts, February, April-June Digi-Blocks 3.N.10Add and subtract (up to four-digit numbers) and multiply (up to two digit numbers by one digit numbers) accurately and efficiently.Add and subtract (up to four-digit numbers) and multiply one- and two-digit numbers by another one-digit number accurately and efficiently.Mathematical Thinking at Grade 3 Investigation 2, 14-45 Landmarks in the Hundreds Investigation 2, 30-51 Every Day Counts, January, April Digi-Blocks 3.N.11Round whole numbers through 1,000 to the nearest 10, 100, and 1000.Round whole numbers through 1,000 to the nearest 10 and 100, and 1,000.Landmarks in the Hundreds Investigation 2, 30-51 Investigation 3, 52-60 Every Day Counts, February-June Digi-Blocks3.N.12Understand and use the strategies of rounding, and regrouping to estimate quantities, measures, and the results of whole-number computations (addition, subtraction, and multiplication) up to two-digit whole numbers and amounts of money to $100, and to judge the reasonableness of the answer. Select and use a variety of strategies (e.g., rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to two-digit whole numbers and amounts of money to $100, and to judge the reasonableness of the answer.Readiness: Fair Shares Investigation 1, 2-29 Investigation 2, 30-51 Investigation 3, 52-57 Every Day Counts February 3.N.13Use concrete objects and visual models to add and subtract (only when the answer is greater than or equal to zero) common fractions (halves, thirds, fourths, sixths, and eighths) with like denominators.Use concrete objects and visual models to add and subtract common fractions, halves, thirds, fourths, sixths, and eighths (with like denominators)Landmarks in the Hundreds Investigation 2, 30-51 Combining and Comparing Investigation 3, 26-35 Every Day Counts March Digi-Blocks  Strand: Patterns, Relations, and AlgebraDOE Standard NumberState StandardGrade 3 Progress IndicatorsResources3.P.1 Create, describe, extend, and explain symbolic (geometric) patterns and addition and subtraction patterns, e.g., 2, 6, 10, ...; and 50, 45, 40... Create, describe, extend, and explain symbolic (geometric) and addition and subtraction patterns, e.g., 2, 6, 10, ...; and 50, 45, 40...Mathematical Thinking at Grade 3 Investigation 1,2-13 Investigation 2, 14-45 Things That Come in Groups Investigation 2, 20-39 Investigation 5, 74-90 Flips, Turns, and Area Investigation 1, 2-31 Landmarks in the Hundreds Investigation 1, 2-29 Exploring Solids and Boxes, Investigation 4, 38-51 Every Day Counts, September-December, February, April-June Digi-Blocks3.P.2 Determine which symbol (<, >, or =) is appropriate for a given number sentence, e.g., 7 x 8 __ 49 + 6. Determine which symbol (<, >, or =) is appropriate for a given number sentence, e.g., 7 x 8 __ 49 + 6. Write number sentences using <, >, or =.Mathematical Thinking at Grade 3 Investigation 1,2-13 Investigation 2, 14-45 Things That Come in Investigation 2, 20-39; Investigation 5, 74-90; Flips, Turns, and Area Investigation 1, 2-31 Landmarks in the Hundreds Investigation 1, 2-29 Exploring Solids and Boxes, Investigation 4, 38-51 Every Day Counts, None Digi-Blocks3.P.3Determine value of a variable (through 10) in simple equations involving addition, subtraction, or multiplication, e.g., 2 + ( = 9: 5 x ( = 35 Determine values of variables in simple equations (e.g., 106 - ( = 37; 5 = (+ 3 and ( - ( = 3) (up to 1,000).Readiness: Combining and Comparing Investigation 3, 26-39 Investigation 4, 40-57 Investigation 5, 58-70 Every Day Counts, None 3.P.4Write number sentences using + , -, x, , <, =, and/or > to represent mathematical relationships in everyday situations. Write number sentences using + , -, x, , <, =, and/or > to represent mathematical relationships in everyday situations. Mathematical Thinking at Grade 3 Investigation 1, 2-13 Things That Come in Groups Investigation 2, 20-39 Exploring Solids and Boxes Investigation 4, 38-51 Every Day Counts, March Digi-Blocks  STRAND: GEOMETRYDOE Standard NumberState StandardGrade 3 Progress IndicatorResources3.G.1 Compare and analyze attributes and other features (e.g., number of sides, corners, diagonals, and lines of symmetry) of two-dimensional geometric shapes. Compare and analyze attributes and other features (e.g., number of sides, corners, diagonals and lines of symmetry) of two- dimensional geometric shapes. Mathematical Thinking at Grade 3 Investigation 2, 14-45 Turtle Paths, Investigation 2, 28-61 Exploring Solids and Boxes Investigation 1, 2-13 Investigation 2, 14-25 Investigation 3, 26-37 Everyday Counts November, April-June Digi-Blocks Geometry Packet 3.G.2 Describe, model, draw, compare, and classify two- dimensional shapes, e.g., circles, triangles and quadrilaterals. Identify and describe simple three-dimensional shapes, e.g., cubes, spheres, and pyramids Describe, model, draw, compare, and classify two- dimensional shapes, e.g., circles, triangles, squares,. Identify and describe simple three-dimensional shapes, e.g., cubes, spheres, and pyramidsTurtle Paths, Investigation 2, 28-61 Exploring Solids and Boxes Investigation 1, 2-13 Investigation 2, 14-25 Investigation 3, 26-37 Every Day Counts April-May 3.G.3Identify angles as right angles, less than a right angle, and greater than a right angle. Identify angles as right angles. Identify angles less than or greater than right angles. Additional Resources Needed Every Day Counts None Geometry Packet 3.G.4Identify and draw parallel lines, perpendicular lines, and other intersecting lines.Describe and draw parallel, perpendicular, and intersecting lines.Additional Resources Needed Every Day Counts None Geometry Packet 3.G.5Using ordered pairs of whole numbers and/or letters, locate, and identify points on a grid. Using ordered pairs of numbers and/or letters, graph, locate, and identify points on a grid.Turtle Paths, Investigation 1, 2-27; Investigation 2, 28-61 Investigation 3, 62-81 Every Day Counts None Geometry Packet 3.G.6Identify and draw lines symmetry in two-dimensional shapes.Identify and describe line symmetry in two-dimensional shapes.Additional Resources Needed Every Day Counts-April 3.G.7Predict and explain the results of taking apart and combining two-dimensional shapes.Predict and validate the results of partitioning, folding, and combining two-dimensional shapes.Flips, Turns, and Area Investigation 2, 32-52 Every Day Counts None  STRAND: MEASUREMENTDOE Standard NumberState StandardGrade 3 Progress IndicatorsResources3.M.1Demonstrate an understanding of the attributes length, area, and weight, and select the appropriate type of unit for measuring each attribute using both the U. S. Customary (English) and metric systems.Demonstrate an understanding of such attributes as length, area, and weight and select the appropriate type of unit for measuring each attribute. Use metric system for determining above attributes.Things That Come in Groups Investigation 3, 40-55 Flips, Turns, and Area Investigation 1, 2-31 Investigation 2, 32-52 From Paces to Feet Investigation 1, 2-25 Investigation 2, 26-59 Investigation 3, 6-67 Investigation 4, 68-74 Combining and Comparing Investigation 2, 18-25 Turtle Paths, Investigation 1, 2-27 Investigation 3, 62-81 Every Day Counts November, February-June Digi-Blocks 3.M.2Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.).Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.). Combining and Comparing Investigation 3, 74-92 Every Day Counts-Nov., Feb., June  3.M.3 Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time less than one hour using a clock (e.g., minutes since ) and using a calendar (e.g., days since ). Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time less than one hour using a clock (e.g., minutes since ) and using a calendar (e.g., days since ). Combining and Comparing Investigation 4, 40-57 Investigation 5, 58-70 Every Day Counts October, November, April-June 3.M.4Estimate and find area and perimeter of a rectangle using diagrams, models, and grids or by measuring.Estimate and find area and perimeter of a rectangle, using diagrams, models, and grids or by measuring.Things That Come in Groups Investigation 3, 40-55; Flips, Turns, and Area Investigation 2, 32-52 From Paces to Feet Investigation 4, 68-74 Turtle Paths, Investigation 1, 2-27 Every Day Counts, None Digi-Blocks3.M.5Identify and use appropriate metric and U. S. Customary (English) units and tools (e.g., ruler, scale, thermometer, clock) to estimate, measure, and solve problems involving length, area, weight, temperature, and time.Identify and use appropriate metric and English units and tools (e.g., ruler, grids, scales, thermometer, clock) to estimate, measure, and solve problems involving length, area, weight, time, and temperature.Flips, Turns, and Area Investigation 2, 32-52 From Paces to Feet Investigation 2, 26-59 Investigation 3, 60-67 Investigation 4, 68-74 Every Day Counts March-June  DATA ANALYSIS, STATISTICS, AND PROBABILITYDOE Standard NumberState StandardGrade 3 Progress IndicatorsResources3.D.1Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.Collect data to draw simple bar graphs, line graphs, and pictographs, and to compare and explain what is recorded.Mathematical Thinking at Grade 3 Investigation 3, 46-67 Digi-Blocks From Paces to Feet Investigation 3, 60-67 Combining and Comparing Investigation 4, 40-57 Every Day Counts October, December-January, April 3.D.2Match representations of a data set in the form of tables, line plots, pictographs, tallies, or bar graphs with the actual data set. Match representations of a data set such as tables, line plots, or graphs with the actual set of data.Combining and Comparing Investigation 4, 40-57 Every Day Counts December, January, March 3.D.3Construct and draw conclusions from representations of data sets, in the form of tables, line plots, pictographs, tallies, and bar graphs. Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, and tallies.Combining and Comparing Investigation 4, 40-57 Every Day Counts, October, December, January, March-June 3.D.4List and count the number of possible combinations of objects from two sets (e.g., how many different outfits can one make from a set of two sweaters, and a set of three skirts?).List and count the number of possible combinations of objects from two sets.Additional Resources Needed Every Day Counts-None  Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed CCC Lab Activities Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group  NUMBER SENSE AND OPERATIONSDOE Standard NumberState StandardGrade 4 Progress IndicatorsResources4.N.1Exhibit an understanding of the base-ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers.Exhibit an understanding of the base-ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers.Mathematical Thinking at Grade 4 Investigation 1, 2-31 Investigation 2, 32-45 Investigation 3, 46-63 Landmarks in the Thousands Investigation 2, 18-35 Investigation 3, 36-51; Investigation 4, 52-58 Every Day Counts-Sept., Oct., May, June 4.N.2Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3.Represent, order, and compare large numbers (to at least 1,000,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3. Landmarks in the Thousands Investigation 3, 36-51 Investigation 4, 52-58 Every Day Counts- None4.N.3Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line. Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line. Measure on a ruler to the nearest 1/8 inchDifferent Shapes, Equal Pieces Investigation 1, 2-21; Investigation 2, 22-37 Investigation 3, 38-54 Three out of Four Like Spaghetti Investigation 1, 2-25 Everyday Counts-None 4.N.4Select, use, and explain models to relate common fractions and mixed numbers (, S!, , 1/6, 1/8, 1/12, and 1), find equivalent fractions, mixed numbers, and decimals, and order fractions.Select, use, and explain models to relate common fractions and mixed numbers to twelfths, find equivalent fractions, mixed numbers, and decimals, and order fractions. Compare and order fractions and mixed numbers with like denominators up to twelfths. Represent mixed numbers as improper fractions and vice versa Different Shapes, Equal Pieces Investigation 1, 2-21 Investigation 2, 22-37 Investigation 3, 38-54 Money, Miles, and Large Numbers Investigation 2, 30-45 Three out of Four Like Spaghetti Investigation 1, 2-25 Every Day Counts- Nov., Jan., Feb., March, April 4.N.5Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths).Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths). Different Shapes, Equal Pieces Investigation 2, 22-37 Investigation 3, 38-54 Money, Miles, and Large Numbers Investigation 2, 30-45 Combining and Comparing Investigation 1, 2-12 Landmarks Investigation 1, 2, 3 Every Day Counts- None4.N.6Exhibit an understanding of the base-ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths. Exhibit an understanding of the base-ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths. Money, Miles, and Large Numbers Investigation 1, 2-29 Every Day Counts Oct. 4.N.7Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems.Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems. Find common multiples and common factors for sets of numbers. Make predictions about the solutions to problems using an understanding of the classes of numbers (i.e. even x even) Arrays and Shares Investigation 1, 2-11 Landmarks in the Thousands Investigation 1, 2-17 Investigation 2, 18-35 Investigation 3, 36-51 Packages and Groups Investigation 1, 2-1 Investigation 3, 28 62 Every Day Counts- Sept., Nov., Dec., Jan., Feb. March, April, May, June 4.N.8 Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations. Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations. Model and describe multiplication as repeated addition. Model and describe division as repeated subtraction.Arrays and Shares Investigation 2, 12-41 Investigation 3, 42-59 Landmarks in the Thousands Investigation 2, 18-35 Packages and Groups Investigation 1, 2-15 Investigation 2, 16-23 Investigation 3, 28-62 Every Day Counts-None 4.N.9 Select, use, and explain the commutative, associative, and identify properties of operations on whole numbers in problem situations (e.g., 37 x 46 = 46 x 37, [5 x 7] x 2 = 5 x [7 x 2]).Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations (e.g., 37 x 46 = 46 x 37, [5 x 7] x 2 = 5 x [7 x 2]).Arrays and Shares Investigation 2, 12-4 Investigation 3, 42-59 Every Day Counts- None4.N.10Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.Arrays and Shares Investigation 1, 2-11 Investigation 3, 42-59 Landmarks in the Thousands Investigation 1, 2-17 Investigation 2, 18-35 Investigation 3, 36-51 Investigation 4, 52-58 Money, Miles, and Large Numbers Investigation 1, 2-29 Investigation 2, 30-45 Packages and Groups Investigation 2, 16-23 Investigation 3, 28-62 Every Day Counts-All months4.N.11Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems (e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500).Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems (e.g., 3 x 5 is related to 30 x 50, 300 x 5, 30 x 500). Arrays and Shares Investigation 1, 2-11 Packages and Groups Investigation 2, 16-23 Investigation 3, 28-62 Every Day Counts-None4.N.12Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently.Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently.Landmarks in the Thousands Investigation 1, 2-17 Investigation 2, 18-35 Investigation 3, 36-51 Investigation 4, 52-58 Money, Miles, and Large Numbers Investigation 1, 2-29 Packages and Groups Investigation 2, 16-23 Every Day Counts- None4.N.13 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders. Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders as fractions.Arrays and Shares Investigation 2, 12-41 Investigation 3, 42-59 Everyday Counts- None 4.N.14 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits). Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits).Landmarks in the Thousands Investigation 1, 2-17; Investigation 2, 18-3 Investigation 3, 36-51 Investigation 4, 52-58 Packages and Groups Investigation 2, 16-23 Every Day Counts-None 4.N.15Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders).Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders).Arrays and Shares Investigation 2, 12-41 Investigation 3, 42-59 Every Day Counts-None4.N.16Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000.Round whole numbers through 100,000 to the nearest 10, 100, 1,000, 10,000, and 100,000.Mathematical Thinking at Grade 4 Investigation 1, 2-31 Landmarks in the Thousands Investigation 1, 2-17 Investigation 3, 36-51 Money, Miles, and Large Numbers Investigation 1, 2-29 Every Day Counts-None4.N.17Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer.Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer.Readiness: Different Shapes, Equal Pieces Investigation 1, 2-19 Investigation 2, 22-37 Investigation 3, 38-54 Every Day Counts4.N.18Use concrete objects and visual models to add and subtract common fractions.Use concrete objects and visual models to add and subtract common fractions, represent answers in lowest terms.Mathematical Thinking at Grade 4 Investigation 1, 2-31 Every Day Counts- None PATTERNS, RELATIONS, AND ALGEBRADOE Standard NumberState StandardGrade 4 Progress IndicatorsResources4.P.1 Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, . Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, . or 1, 4, 9, 16, 25, ___, ___Mathematical Thinking at Grade 4 Investigation 4, 64-90 Arrays and Shares Investigation 1, 2-11 Investigation 3, 42-59 Packages and Groups Investigation 1, 2-15 Sunken Ships and Grid Patterns Investigation 1, 2-41 Every Day Counts- All months 4.P.2 Use symbol and letter variables (e.g., (, x) to represent unknowns or quantities that vary in expressions and in equations or inequalities (mathematical sentences that use =, <, >). Use symbol and letter variables (e.g., (, x) to represent unknowns or quantities that vary in expressions and in equations or inequalities (mathematical sentences that use =, <, >).Mathematical Thinking at Grade 4 Investigation 4, 64-90 Arrays and Shares Investigation 1, 2-11 Investigation 3, 42-59 Packages and Groups Investigation 1, 2-15 Sunken Ships and Grid Patterns Investigation 1, 2-41 Every Day Counts- All months  4.P.3  Determine values of variables in simple equations (e.g., 4106 - ( = 37; 5 = (+ 3 and ( - ( = 3).  Determine values of variables in simple equations (e.g., 4106 - ( = 37; 5 = (+ 3 and ( - ( = 3) (up to 100,000).  Readiness: Money, Miles, and Large Numbers Investigation 1, 2-29 Every Day Counts- None4.P.4Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships. Use pictures, models, tables, charts, graphs, bar line, circle, words, number sentences, and mathematical notations to interpret mathematical relationships.Mathematical Thinking at Grade 4 Investigation 4, 64-90 The Shape of the Data Investigation 1, 2-19 Investigation 2, 20-49 Investigation 3, 50-64 Money, Miles, and Large Numbers Investigation 2, 30-45 Investigation 3, 46-57 Three out of Four Like Spaghetti Investigation 1, 2-25 Investigation 2, 26-50 Every Day Counts-All months 4.P.5Solve problems involving proportional relationships, including unit pricing (e.g., four apples cost 80, so one apple costs 20) and map interpretation (e.g., one inch represents five miles, so two inches represent ten miles). Solve problems involving proportional relationships, including unit pricing (e.g., five apples cost 0.80, so one apple costs 0.16) and map interpretation (e.g., one inch represents five miles, so inch represent 2 miles).Money, Miles, and Large Numbers Investigation 2, 30-45 Investigation 3, 46-57 Every Day Counts-None4.P.6Determine how change in one variable relates to a change in a second variable (e.g., input-output tables). Determine how change in one variable relates to a change in a second variable (e.g., input-output tables). (i.e. in 7 10 12 (n) out 3 6 8 (n-4)Landmarks in the Thousands, Ten Minute Math 61-62 Every Day Counts- None STRAND: GEOMETRYDOE Standard NumberState StandardGrade 4 Progress IndicatorResources4.G.1 Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes. Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional shapes. Seeing Solids and Silhouettes Investigation 1, 2-13 Investigation 2, 14-41 Investigation 3, 42-49 Investigation 4, 50-62 Every Day Counts-None4.G.2 Describe, model, draw, compare, and classify two- and three-dimensional shapes, e.g., circles, polygonsespecially triangles and quadrilateralscubes, spheres, and pyramids. Describe, model, draw, compare, and classify two- and three-dimensional shapes (e.g., circles, polygonsespecially triangles and quadrilateralscubes, spheres, and pyramids).Seeing Solids and Silhouettes Investigation 1, 2-13 Investigation 2, 14-41 Investigation 3, 42-49 Investigation 4, 50-62 Every Day Counts- April, May, June4.G.3Recognize similar figures. Recognize similar figures. Describe what makes them similar. See Grade 3 Turtle Paths, Investigation 3, 62-81 Every Day Counts-None4.G.4Identify angles as acute, right, or obtuse. Identify angles as acute, right, or obtuse.Additional Resources Needed Every Day Counts-None4.G.5Describe and draw intersecting, parallel, and perpendicular lines. Describe and draw intersecting, parallel, and perpendicular lines. Additional Resources Needed Every Day Counts-None4.G.6Using ordered pairs of numbers and/or letters, graph, locate, and identify points, and describe paths (first quadrant). Using ordered pairs of numbers and/or letters, graph, locate, and identify points, and describe paths (first quadrant). See Math Frameworks, Nov. 2000, p. 41.Sunken Ships and Grid Patterns Investigation 1, 2-41 Investigation 2, 42-86 Every Day Counts-None4.G.7Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent. Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent. Use these terms correctly. Mathematical Thinking at Grade 4 Investigation 4, 64-90 Every Day Counts-None 4.G.8Identify and describe line symmetry in two-dimensional shapes. Identify and describe line symmetry in two-dimensional shapes.Mathematical Thinking at Grade 4 Investigation 4, 64-90 Sunken Ships and Grid Patterns Investigation 2, 42-86 Every Day Counts- None 4.G.9Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes.Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes.Sunken Ships and Grid Patterns Investigation 2, 42-86 Every Day Counts- None STRAND: MEASUREMENTDOE Standard NumberState StandardGrade 4 Progress IndicatorsResources4.M.1Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute.Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute.Seeing Solids and Silhouettes Investigation 1, 2-13 Different Shapes, Equal Pieces Investigation 1, 2-21 Every Day Counts- Nov., Jan., Feb., March, April 4.M.2Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.).Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.). Additional Resources Needed See Grade 5, Measurement Benchmarks, Investigation 3, 74-924.M.3Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since ) and using a calendar (e.g., days since ).Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since ) and using a calendar (e.g., days since ) correctly use a.m. and p.m.Additional Resources Needed Every Day Counts-Oct., Nov., Dec., Feb., March, April, May 4.M.4Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring.Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring. Different Shapes, Equal Pieces Investigation 1, 2-21 Every Day Counts-None4.M.5Identify and use appropriate metric and English units and tools (e.g., ruler, angle, ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature.Identify and use appropriate metric and English units and tools (e.g., ruler, scales, compass, ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature. Seeing Solids and Silhouettes Investigation 1, 2-13 Every Day Counts-Jan., March, April DATA, STATISTICS, AND PROBABILITYDOE Standard NumberState StandardGrade 4 Progress IndicatorsResources4.D.1Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.The Shape of the Data Investigation 1, 2-19 Investigation 2, 20-49 Investigation 3, 50-64 Changes Over Time Investigation 1, 10-29 Investigation 2, 30-45 Investigation 3, 46-57 Three out of Four Like Spaghetti Investigation 1, 2-25 Investigation 2, 26-50 Every Day Counts- Oct., March, May, June 4.D.2Match representations of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data. Match representations of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data.The Shape of the Data Investigation 1, 2-19 Investigation 2, 20-49 Investigation 3, 50-64 Changes Over Time Investigation 1, 10-29 Investigation 2, 30-45 Investigation 3, 46-57 Three out of Four Like Spaghetti Investigation 1, 2-25 Investigation 2, 26-50 Every Day Counts-None 4.D.3Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies. Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies.The Shape of the Data Investigation 1, 2-19 Investigation 2, 20-4 Investigation 3, 50-64 Changes Over Time Investigation 1, 10-29 Investigation 2, 30-45 Investigation 3, 46-57 Three out of Four Like Spaghetti Investigation 2, 26-50 Every Day Counts-Oct., March, May, June 4.D.4Represent the possible outcomes for a simple probability situation (e.g., the probability of drawing a red marble from a bag containing three red marbles and four green marbles). Represent the possible outcomes for a simple probability situation (e.g., the probability of drawing a red marble from a bag containing three red marbles and four green marbles). See Math Frameworks, Nov.2000, p.57. Represent the outcome as a ratio, i.e. )Landmarks in the Thousands Investigation 2, 20 Investigation 5, 59-60 Three out of Four Like Spaghetti Investigation 1, 51-52 Every Day Counts-None4.D.5List and count the number of possible combinations of objects from three sets (e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?). List and count the number of possible combinations of objects from three sets (e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?). Grade 4 Landmarks in the Thousands Investigation 5, 59-60 Every Day Counts-None4.D.6Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners, or coins. Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners, or coins.Landmarks in the Thousands Investigation 2 Investigation 5, 34, 59-60 Money, Miles, and Large Numbers Investigations 1, 13 Investigation 3, 48, 58-59 Three out of Four Like Spaghetti Investigation 1, 17, 51-52 Every Day Counts-None Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group  STRAND: NUMBER SENSE AND OEPRATIONSDOE Standard NumberState StandardGrade 5 Progress IndicatorsResources5.N.1.Demonstrate an understanding of (positive integer) powers of ten, e.g., 102, 105.Identify powers of ten up to 106.Mathematical Thinking at Grade 5 Investigation 3, 48-54 Every Day Counts None5.N.2Demonstrate an understanding of place value through millions and thousandths.Demonstrate an understanding of place value through millions and thousandths.Mathematical Thinking at Grade 5 Investigation 2, 26-47 Name That Portion Investigation 3, 64-82 Building on Numbers You Know Investigation 4, 106-119 Every Day Counts All months5.N.3Represent and compare large (millions) and small (thousandths) positive numbers in various forms, such as expanded notation without exponents, e.g., 9724= 9 x 1000 + 7 x 100 + 2 x 10 + 4. Compare and order decimals to the 1,000ths. Represent and compare millions. Represent whole numbers without exponents in expanded notation.Mathematical Thinking at Grade 5 Investigation 4 Every Day Counts January5.N.4Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on a number line. This standard is intentionally the same as standard 6.N.4. Demonstrate fractions as parts of unit wholes, parts of a collection, and as locations on a number line. Demonstrate fractions as ratios.Name That Portion Investigation 1, 2-3 Investigation 2, 32-63 Every Day Counts All months5.N.5Identify and determine common equivalent fractions and mixed numbers with denominators 2, 4, 5, 10 only, decimals, and percents (through 100%), e.g., =0.75=75%.Recognize commonly used fractions and their decimal equivalents. Recognize the relationship between percents and fractions with denominators of 2, 4, 5, and 10.Name That Portion Investigation 1, 2-31 Investigation 2, 32-63 Every Day Counts All months5.N.6Find and position whole numbers, and positive fractions, positive mixed numbers, and positive decimals on a number line.Find and position whole numbers, positive fractions, mixed numbers, and decimals on a number line.Name That Portion Investigation 1, 2-31 Investigation 2, 32-63 Investigation 3, 64-99 Every Day Counts All Months 5.N.7Compare and order whole numbers, positive fractions, positive mixed numbers, positive decimals, and percents.Compare and order whole numbers, and positive fractions, mixed numbers, decimals, and percents.Mathematical Thinking at Grade 5 Investigation 4, 72-95 Name That Portion Investigation 1, 2-31 Investigation 2, 32-63 Investigation 3, 64-99 Every Day Counts All months 5.N.8Apply the number theory concepts of common factor, common multiple, and divisibility rules for 2, 3, 5 and 10 to the solution of problems. Demonstrate an understanding of the concepts of prime and composite numbers.Demonstrate understanding that a number can be prime or composite and that numbers can be divided into factors. Recognize when one number is a multiple of another. Find the greatest common factor and least common multiple for sets of numbers. Apply divisibility rules for 2, 3, 5,and 10Mathematical Thinking at Grade 5 Investigation 1, 2-25 Investigation 2, 26-47 Investigation 3, 48-71 Investigation 4, 72-95 Building on Numbers You Know Investigation 1, 2-39 Investigation 4, 106-119 Every Day Counts December, January, February5.N.9Solve problems involving multiplication and division of whole numbers, and multiplication of a positive fraction with a whole number.Select the appropriate operations to solve problems. Determine if there is too little or too much information when solving problems. Model real-world problems using numbers other than whole numbers.Mathematical Thinking at Grade 5 Investigation 3, 48-71 Investigation 4, 72-95 Picturing Polygons Investigation 2, 28-79 Name That Portion Investigation 3, 64-99 Building on Numbers You Know Investigation 1, 2-39 Investigation 2, 40-7 Investigation 5, 120-146 Every Day Counts None5.N.10Demonstrate an understanding of how parentheses affect expressions involving addition, subtraction, and multiplication, and use to solve problems, e.g., 3 x (4+2) = 3 x 6 Recognize and demonstrate that addition, subtraction, multiplication and division follow an Order of Operations and that parentheses can affect the order.Building on Numbers You Know - may be used as a springboard for meeting this standard. See Grade 3 Every Day Counts None5.N.11Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems. This standard is intentionally the same as standard 6.N.12. Explain how addition and subtraction, and multiplication and division are related. Building on Numbers You Know Investigation 1, 2-39 Every Day Counts None5.N.12Accurately and efficiently add and subtract whole numbers and positive decimals; multiply and divide (with double-digit divisors) whole numbers; multiply positive decimals with whole numbersUse algorithms to perform division with two-digit divisors. Use algorithms to add and subtract decimal numbers. Demonstrate understanding of multiplication and division of decimals using diagrams and manipulatives.Mathematical Thinking at Grade 5 Investigation 4, 72-95 Building on Numbers You Know Investigation 1, 2-39 Investigation 2, 40-71 Investigation 3, 72-105; Investigation 5, 120-146 Every Day Counts None5.N.13Accurately and efficiently add and subtract positive fractions and mixed numbers with like denominators and with unlike denominators (2, 4, 5, 10 only); multiply positive fractions with whole numbers. Simplify fractions in cases when both the numerator and the denominator have 2, 3, 4, 5, and 10 as a common factor.Use algorithms to perform division with two-digit divisors. Use algorithms to add and subtract decimal numbers. Demonstrate understanding of multiplication and division of decimals using diagrams and manipulatives.Mathematical Thinking at Grade 5 Investigation 4, 72-95 Building on Numbers You Know Investigation 1, 2-39 Investigation 2, 40-71 Investigation 3, 72-105; Investigation 5, 120-146 Every Day Counts None5.N.14Estimate sums and differences of whole numbers, and positive fractions and decimals. Estimate products of whole numbers, and positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer. Add and subtract common fractions with like and unlike denominators. Add and subtract mixed numerals with like denominators. Simplify fractions Readiness: Name That Portion Investigation 1, 2-31 Every Day Counts None STRAND: PATTERNS, RELATIONS, AND ALGEBRADOE Standard NumberState StandardGrade 5 Progress IndicatorsResources5.P.1Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions, e.g., ABBCCC, 1, 5, 9,13.; 3,9,27.Recognize, describe, and extend whole number sequences (e.g., square numbers 1, 4, 9, 16 and Fibonacci Numbers 1, 1, 2, 3, 5). Recognize and extend patterns involving various two-dimensional geometric shapes. Represent patterns with manipulatives by building towers, pyramids, or other patterns.Mathematical Thinking at Grade 5 Investigation 2, 26-47 Building on Numbers You Know Investigation 1, 2-39 Patterns of Change Investigation 1, 2-25 Investigation 3, 54-92 Every Day Counts All months5.P.2Replace variables with given values and evaluate/simplify [e.g., 2(() + 3 when ( = 4]. This standard is essentially the same as standard 6.P.2.Find the missing number in a number sentence. Recognize and describe the concept of variable as the missing number in a number sentence.Additional Resources Needed Every Day Counts None5.P.3Use the properties of equality to solve problems (e.g., if ( + 7 = 13, then ( = 13 - 7, therefore ( = 6; if 3 x ( = 15, then (=15/3, therefore ( = 5.Identify properties of equality with whole numbers in four operations.Mathematical Thinking at Grade 5 Investigation 3, 55-59, 63 Every Day Counts None5.P.4Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols (e.g., input-output tables). This standard is intentionally the same as standard 6.P.4.Analyze and describe the data orally and in writing, commenting on patterns and trends. Organize data logically with a table, chart or other model.Patterns of Change Investigation 1, 2-25 Investigation 3, 54-92 Every Day Counts None5.P.5Solve problems involving proportional relationships using concrete models, tables, graphs, and paper-pencil methods.Find the value of an expression given the replacement value for the variables (e.g., what is 7 - C if C = 3.5?). Solve equations in one variable using concrete objects and guess and check. Patterns of Change Investigation 3, 54-92 Every Day Counts None 5.P.6 Interpret graphs that represent the relationship between two variables in everyday situations. Determine and express simple ratios. Create graphs using data from table of values (examples in Frameworks, Nov. 2000, page 35). Patterns of Change Investigation 1, 2-25 Investigation 3, 54-92 Every Day Counts None  STRAND: GEOEMTRYDOE Standard NumberSTATE STANDARDGRADE 5 Progress IndicatorsRESOURCES5.G.1Identify, describe, and compare special types of triangles (isosceles, equilateral, right) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezoid), e.g., Recognize that all equilateral triangles are isosceles, but not all isosceles triangles are equilateral.Compare and classify acute, right, and obtuse angles. Identify and compare types of triangles (acute, obtuse, right, scalene, isosceles, and equilateral) and quadrilaterals. Identify pentagons, hexagons, and octagons. Draw all acute, right, and obtuse triangles and draw quadrilaterals. Picturing Polygons Investigation 1, 2-27 Investigation 2, 28-79 Investigation 3, 80-111 Every Day Counts November, December, April5.G.2Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces.Identify three-dimensional shapes based on their properties.Containers and Cubes Investigation 1, 2-23 Every Day Counts May, June5.G.3Identify relationships among points, lines, and planes (e.g. intersecting, perpendicular).Identify and describe points, lines, angles, and circles. Draw illustrations of points, lines, angles, and segments. Describe the properties of points and lines. Identify segments of lines. Describe the length of a segment.Picturing Polygons Investigation 2, 28-79 Every Day Counts November, April,5.G.4Using ordered pairs of whole numbers (including zero), graph, locate, and identify points, and describe paths on the Cartesian coordinate plane.Graph points and identify coordinates of points on the Cartesian coordinate plane on the first quadrant.Picturing Polygons Investigation 1, 2-27 Investigation 1, 5-10 Every Day Counts None 5.G.5Describe and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections.Using manipulatives, perform and record simple transformations.Picturing Polygons Investigation 2, 28-79 Investigation 3, 80-111 Every Day Counts None January 5.G.6Identify and describe line symmetry in two-dimensional shapes, including shapes that have multiple lines of symmetry.Using manipulatives, illustrate and record examples/patterns that represent rotational symmetry and line of symmetry.Additional Resources Needed Every Day Counts None5.G.7Determine if two triangles or two quadrilaterals are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions, e.g., translations, rotations, and reflections.Describe properties of congruence. Determine congruence through measurement and transformations.Patterns of Change Investigation 3, 54-92 Every Day Counts May, June STRAND: MEASUREMENTDOE Standard NumberSTATE STANDARDGRADE 5 Progress IndicatorsRESOURCES5.M.1Apply the concepts of perimeter and area to the solution of problems involving triangles and rectangles. Apply formulas where appropriate.Find the area of squares and rectangles. Describe how to find the perimeter of a polygon. Calculate perimeter of a polygon.Picturing Polygons Investigation 3, 80-111 Every Day Counts October, November, December5.M.2Identify, measure, describe, classify, and draw various angles. Draw triangles given two sides and the angle between them, or two angles and the side between them, e.g., Draw a triangle with one right angle and two sides congruent.Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals. (e.g. acute, right, obtuse, equilateral, square, rectangle)Picturing Polygons Investigation 3, 80-111 Every Day Counts February, April, May, June5.M.3Solve problems involving simple unit conversions within a system of measurement.Use a ratio such as 2:1 to create a simple scale drawing or map.Measurement Benchmarks Investigation 1, 2-43 Picturing Polygons Investigation 3, 93-111 Patterns of Change Investigation 2, 26-53 Investigation 3, 54-92 Every Day Counts None5.M.4Find volumes and surface areas of rectangular prisms. This standard is intentionally the same as standard 6.M.6.Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same areas. Picturing Polygons Investigation 3, 80-111 Every Day Counts None5.M.5Find the sum of the measures of the interior angles in triangles with and without measuring the angles.Using sum of angles in a triangle = 180, find sum of simple polygons without measuring. Estimate various angles in simple polygons.Picturing Polygons Investigation 3, 80-111 Every Day Counts None STRAND: DATA ANALYSIS, STATISTICS, AND PROBABILITYDOE Standard NumberSTATE STANDARDGRADE 5 Progress IndicatorsRESOURCES5.D.1Give a set of data, find the median, mean, mode maximum, minimum, and range, and apply to solutions of problems.Using given data, apply the concepts of median, mean, mode, maximum and minimum, and range. Data: Kids, Cats, and Ads Investigation 1, 2-34 Every Day Counts November5.D.2Construct and interpret line plots, line graphs and bar graphs. Interpret and label circle graphs.Construct line plots, line and bar graphs. Interpret line and bar graphs, and interpret and label circle graphs. Data: Kids, Cats, and Ads Investigation 1, 2-34 Every Day Counts November, April5.D.3Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions.Demonstrate a basic understanding of the probability of an event occurring as the likelihood that an event will happen. Conduct an experiment that produces experimental data and compute a ratio to represent the probability. Between Never and Always Investigation 1, 2-45 Investigation 2, 46-70 Data: Kids, Cats, and Ads Investigation 3, 44-67; Investigation 4, 68-81 Every Day Counts None Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group  STRAND: NUMBER SENSE AND OPERATIONSDOE Standard NumberState StandardGrade 6 Progress IndicatorsResources6.N.1Demonstrate an understanding of positive integer exponents.Identify powers of ten up to 106. Identify and evaluate 2nd and 3rd power of small positive integers (e.g. 0,1,2).Prime Time SE: 49 Every Day Counts Jan., Feb., Mar., Apr. 6.N.2Demonstrate an understanding of place value to billions and thousandths.Demonstrate an understanding of place value to billions and hundred thousandths.Bits and Pieces I SE: 43-45, 48-49, 51-52, 55, 63-64 TE: 52c-h, 92, 95 TR: Transparencies: 151, 153 Every Day Counts All months 6.N.3Represent and compare billions and thousandths positive numbers in various forms (e.g., expanded notation).Compare and order decimals to hundred thousandths Represent whole numbers and decimals in expanded notation. (8x102)+(5x101)=3x100)=853 Bits and Pieces I SE: 43-45, 48-49, 51-52, 55, 63-64 TE: 52c-h, 92, 95 TR: Transparencies: 151, 153 Every Day Counts All months 6.N.4Demonstrate an understanding of fractions as a ratio of whole numbers, parts of a collection.Demonstrate an understanding of fractions as ratios of whole numbers, parts of a collection.Bits and Pieces I SE: 5-18, 19-30, 31-38, 39-52, 53-66, 67-83, 84-86 TE: 18a-j, 30a-i, 38a-d, 52a-h, 66a-g, 83a-g, 86-87, 88-89, 90-92, 94-95, 96-97, 98 TR: Labsheets: 125-126 Transparencies: 137-139, 146-151, 153,156, 158, 159, 160-163; Additional Practice: 175, 177-179 How Likely Is It? SE: 5-13, 14-21, 22-28, 29-41, 42-48, 49-56, 57-64, 65-67 TE: 13a, 13b, 13c, 13d, 21a, 21b, 21c, 28a, 28b, 41a, 41b, 41c, 41d, 48a, 48b, 48c, 56a, 56b, 64a, 64b, 64c, 67-68, 69-70, 71-72, 73, 74-77 TR: Labsheets: 90, 91 Transparencies: 95-106 Additional Practice: 112 Bits and Pieces II SE: 11, 13-16, 31-42, 43-53, 54-63 TE: 42a, 42b, 53a, 53b, 53c, 53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 80-81, 82-83, 84-86, 88-90, 91 TR: Labsheets: 108 Transparencies: 118, 119, 120, 121, 122, 123, 124, 125, 127; Additional Practice: 146, 147, 148, 149 Every Day Counts: All Months6.N.5Identify and determine common equivalent fractions, mixed numbers, decimals, and percents.Express common fractions as equivalent fractions, decimals and percents. Investigate and describe the relationship among fractions, decimals, and percents.Bits and Pieces I SE: 40-43, 54-55, 57, 67-78 TE: 52a, 52b, 66a, 66b, 83a, 83b, 83c, 83d, 83e, 83f, 83g, 93 TR: Labsheets: 125-126 Transparencies: 145-151, 155, 157-163 Additional Practice: 176-179 Bits and Pieces II SE: 31-42, 43-53, 54-63 TE: 42a, 42b, 53a, 53b, 53c, 53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 80-81, 82-83, 84-86, 87-90, 91 TR: Transparencies: 122-125, 127 Additional Practice: 146-149 Every Day Counts All months6.N.6Find and position integers, fractions, mixed numbers, and decimals.Find and position both positive and negative integers, fractions, mixed numbers, and decimals on a number line, in an ordered list, or in relation to zero. Bits and Pieces I SE: 22-24, 27-28, 63-64, 82 TE: 30d, 92 TR: Transparencies: 141 Every Day Counts All months6.N.7Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents.Compare whole numbers, fractions, integers (including negative), and decimals using the < and > symbols. Demonstrate knowledge of the structure of sets of numbers including whole numbers, fractions, and integers using Venn Diagrams. Compare fractions, decimals, and percents.Bits and Pieces I SE: 5-18, 19-30, 39-52, 53-66, 67-83, 84-86 TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 18h, 18i, 18j, 30i, 38a, 38b, 38c, 38d, 52a, 52b, 52c, 52d, 52e, 52f, 52g, 52h, 66a, 66b, 66c, 66d, 66e, 66f, 66g, 83a, 83b, 83c, 83d, 83e, 83f, 83g, 86-87, 88-89, 90-92, 94-95, 96-97, 98 TR: Labsheets: 126 Transparencies: 128-141, 152-156, 159-163 Additional Practice: 174-179 Bits and Pieces II SE: 5-17, 18-30, 31-42, 43-53, 54-63, 64-76 TE: 17a, 17b, 17c, 17d, 17e, 30a, 30b, 30c, 30d, 42a, 42b, 53a, 53b, 53c, 53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 76a, 76b, 76c, 76d,76e, 76f, 79, 80-81, 82-83, 84-86, 87-90, 91-92 TR: Labsheets: 106-109 Transparencies: 110-132 Additional Practice: 144-149 Every Day Counts All months 6.N.8Apply number theory conceptsincluding prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10to the solution of problems.Apply number theory conceptsincluding prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10to the solution of problems.Prime Time SE: 6-16, 17-25, 26-35, 36-45, 46-57, 58-64, 65-67 TE: 16a, 16b, 16c, 16d,16e, 25a, 25b, 25c, 25d, 25e, 35a, 35b, 35c, 35d,45a, 45b, 45c, 57a, 57b,57c, 57d, 57e, 57f, 64a, 64b, 68, 69, 70, 71, 72-73, 74-75 TR: Labsheets: 96, 97, 98, 99 Transparencies: 100-115 Additional Practice: 122-127 Bits and Pieces I SE: 5-18, 19-30, 31-38, 39-52, 53-66, 67-83, 84-86 TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 18h, 18i, 18j, 30a, 31b, 30c, 30d, 30e, 30f,30g, 30h, 30i, 38a, 38b, 38c, 38d, 52a, 52b, 52c, 52d, 52e, 52f, 52g, 52h, 66a, 66b, 66c, 66d, 66e, 66f, 66g,83a, 83b, 83c, 83d, 83e, 83f, 83g, 86-87, 88-89, 90-92, 94-95, 96-97, 98 TR: Labsheets: 118, 124 Transparencies: 137-139, 152-154, 156 Additional Practice: 174-175, 178-179 Bits and Pieces II SE: 5-17, 18-30, 31-42, 43-53, 54-63, 64-76 TE: 17a, 17b, 17c, 17d, 17e, 30a, 30b, 30c, 30d, 42a, 42b, 53a, 53b, 53c,53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 76a, 76b, 76c, 76d, 76e, 76f, 79, 80-81, 82-83, 84-86, 8790, 91-92 TR: Transparencies: 127, 129- 131 Additional Practice: 146-147 Every Day Counts Sept., Oct., Nov., Dec., Jan. 6.N.9Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents.Select the appropriate operations to solve problems. Determine if there is too little or too much information when solving problems. Model real-world problems using numbers other than whole numbers.Data About Us SE: 54-66, 70 TE: 67j, 75, 76 TR: Transparencies: 111, 114, 116 Covering and Surrounding SE: 46, 49-52, 59-61, 74, 76-78 TE: 45b, 45c, 55e, 55f, 68d, 68e, 68f, 81c, 81g, 90, 91-92, 93, 96-97, 98-99 TR: Transparencies; 123, 127, 136 Additional Practice: 150, 152-156 How Likely Is It? SE: 36 TE: 71, 75-77 Bits and Pieces II SE: 5-17, 18-30, 31-42, 43-53, 54-63, 64-76 TE: 17a, 17b, 17c, 17d, 17e, 30a, 30b, 30c, 30d, 42a, 42b, 53a, 53b, 53c, 53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 76a, 76b, 76c, 76d, 76e, 76f, 79, 80-81, 82-83, 84-86, 87-90, 91-92 TR: Labsheets: 106, 107, 109; Transparencies: 110-117, 122-128, 130-132 Additional Practice: 144-149 Every Day Counts: Sept.-Feb.6.N.10Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers. Use the number line to model addition and subtraction of subtracting negative integers).Additional Resources Needed Every Day Counts None6.N.11Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ().Apply Order of Operations for all four operations.Covering and Surrounding SE: 30, 46, 49-52, 59-61, 74, 76-78 TE: 34b, 34c, 45b, 45c, 55e, 55f, 68d, 68e, 68f, 81c, 81g, 90, 91-92, 93, 96-97, 98-99 TR: Transparencies; 123, 127, 136; Additional Practice: 150-156 Every Day Counts All months6.N.12Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems. Demonstrate knowledge of identities and inverses for all four operations.Additional Resources Needed Every Day Counts None6.N.13Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals.Add, subtract, multiply, and divide decimals.Bits and Pieces II SE: 5-17, 18-30, 64-76 TE: 17a, 17b, 17c, 17d, 17e, 30a, 30b, 30c, 30d,76a, 76b, 76c, 76d, 76e,76f, 87, 89-90, 91 TR: Labsheets: 106-107,109 Transparencies: 110-113, 116, 128-132 Additional Practice: 144-146, 149 Every Day Counts None6.N.14Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers. Add and subtract mixed numerals with unlike denominators. Multiply and divide fractions and mixed numerals. Simplify fractionsHow Likely Is It? SE: 36 TE: 71, 75-77 Bits and Pieces II SE: 43-53, 54-63 TE: 53a, 53b, 53c, 53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 80-81, 82-83, 84-86, 88-90, 91 TR: Transparencies: 120-127, 132 Additional Practice: 146-149 Every Day Counts All months 6.N.15Add and subtract integers, with the exception of subtracting negative integers.Add and subtract integers without number line, with the exception of subtracting negative integers.Data About Us SE: 54-66, 70 TE: 67j, 75, 76 TR: Transparencies: 111, 114, 116 Every Day Counts None6.N.16Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates.Estimate sums, differences, products, and quotients with whole numbers, fractions, and decimals with reasoned strategies.Bits and Pieces II SE: 4, 31-41, 64-66, 72-73 TE: 42a, 42b, 76a, 76b TR: Labsheets: 106-107 Transparencies: 111, 118-119 Additional Practice: 146 Every Day Counts None STRAND: PATTERNS, RELATIONS, AND ALGEBRADOE Standard NumberState StandardGrade 6 Progress IndicatorsResources6.P.1Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions.Recognize and extend sequences of numbers involving whole numbers, fractions, and decimals. Recognize and extend patterns of various two- and three-dimensional shapes. Extend patterns, organize information, and make tables to solve problems.Prime Time SE: 58-60, 64 TE: 64a, 64b TR: Transparencies: 102, 103, 107 Additional Practice: 127 Data About Us SE: 42-45, 48-49 TE: 52a, 52d, 77, 78 TR: Transparencies: 96-99, 108-110 Additional Practice: 125 How Likely Is It? SE: 43-45 TE: 48a, 48b, 48c Every Day Counts All months6.P.2Replace variables with given values and evaluate/simplify [e.g., 2(() + 3 when ( = 4].Recognize the term variable as used in an equation. Determine the numerical value of an algebraic expression given the value of the variable in the expression.Shapes and Designs SE: 47 TE: 50d, 81 TR: Additional Practice: 135, 137, 138 Covering and Surrounding SE: 49-52, 59-61, 74, 76-78 TE: 55e, 55f, 68d, 68e, 68f, 81c, 81g, 90, 91-92, 93, 96-97, 98-99 TR: Labsheets: 117- 119 Transparencies; 120-141 Additional Practice: 150-156 Every Day Counts All months 6.P.3Use the properties of equality to solve problems (e.g., if ( + 7 = 13, then ( = 13 - 7, therefore ( = 6; if 3 x ( = 15, then S! x 3 x ( = S! x 15, therefore ( = 5). Identify and use the properties of equality to solve problems with whole numbers, fractions and decimals.Additional Resources Needed Every Day Counts None6.P.4Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols (e.g., input-output tables).Construct expressions, equations, and inequalities that describe real-world problems using a symbol to represent the missing number. Collect data from an experiment and express the data in a table of values.Data About Us SE: 42-45, 48-49 TE: 52a, 52d, 77, 78 TR: Transparencies: 108-110 Additional Practice: 125 How Likely Is It? SE: 43-45 TE: 48a, 48b, 48c Every Day Counts All months6.P.5Solve linear equations using concrete models, tables, graphs, and paper-pencil methods.Solve first-degree equations in one variable using manipulatives and guess and check. Solve equations using manipulatives. Recognize variables and solve basic equations with one variable by using properties of equality. Additional Resources Needed Every Day Counts All months 6.P.6Produce and interpret graphs that represent the relationship between two variables in everyday situations.Analyze and describe data in tables and graphs orally and in writing, commenting on patterns and trends. Create a graph using data from a table of values.How Likely Is It? SE: 43-45 TE: 48a, 48b, 48c Every Day Counts Feb., May, Jun.6.P.7Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant.Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant. Solve problems on speed as a ratio using formula S = D / T or D = R x T.Additional Resources Needed Every Day Counts None STRAND: GEOMETRYDOE Standard NumberSTATE STANDARDGrade 6 Progress IndicatorsResources6.G.1Identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides (e.g., squares, rectangles, rhombuses, parallelograms, trapezoids, and isosceles, equilateral and right triangles).Describe the distinction between similar and congruent figures. Recognize vertical angles and adjacent angles formed by intersecting lines. Describe the sum of angles of a quadrilateral. Use the correct terminology to describe parts of angles. Use the correct terminology to describe parts of triangles and quadrilaterals. Draw all types of triangles, including scalene, isosceles, and equilateral triangles. Shapes and Designs SE: 8-14, 15-21, 22-41, 42-50, 51-63, 76-78 TE: 14a, 14b, 21a, 21b, 21c, 21d, 21e, 21f, 21g, 41a, 41b, 41c, 41d, 41e, 41f, 41g, 41h, 41i, 50a, 50b, 50c, 50d, 50e, 50f, 50g, 63a, 63b, 63c, 63d, 78-79, 80-81, 82-85, 86-87, 88-89 TR: Transparencies: 106, 107, 108, 109, 117, 118, 119, 121 Additional Practice: 135, 136, 137, 138 Covering and Surrounding SE: 30, 46, 49-52, 59-61, 74, 76-78 TE: 34b, 34c, 45b, 45c, 55e, 55f, 68d, 68e, 68f, 81c, 81g, 90, 91-92, 93, 96-97, 98-99 TR: Transparencies; 130, 132, 133, 134, 135, 136, 138, 139, 140 Additional Practice: 153, 154, 156 Every Day Counts None6.G.2Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces.Describe and discuss three-dimensional figures. Identify the relationship among vertices, faces, and edges of three-dimensional figures.Ruins of Montarek SE: 7-25,26-39,40-51,52-61,62-71, 72-81,82-84 TE: 25a, 25b, 25c, 25d, 25e, 25f, 25g, 25h, 39a, 39b, 39c, 39d, 51a, 51b, 51c, 51d, 61a, 61b, 61c, 61d, 61e, 61f, 61g, 61h, 61i, 71a, 71b, 71c, 81a, 81b, 81c, 81d, 81e, 84-85, 87-89, 90-91, 92-96, 97-98 TR: Labsheets: 114-120 Transparencies: 121-136, 138-146; Additional Practice: 154-159; Every Day Counts Apr., May, June6.G.3Identify relationships among points, lines, and planes (e.g. intersecting, perpendicular).Identify and describe rays. Identify real-world examples that portray points, lines, segments, rays, and planes. Describe planes and identify points, lines, rays, and segments that lie in the plane and those that do not. Draw rays and planes. Describe intersecting lines. Describe parallel lines and perpendicular lines. Shapes and Designs SE: 18, 52-56 TE: 63a, 63b, 63c, 63d TR: Transparencies: 105-106 Ruins of Montarek SE: 10-12, 23-24 TE: 25b, 25c, 25d, 93 TR: Labsheets: 114,116 Transparencies: 123 Every Day Counts None6.G.4Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants)Graph points and identify coordinates of points on the Cartesian coordinate plane on all four quadrants.Bits and Pieces II SE: 47 Data About Us SE: 42-52 TE: 52c, 52d, 52e, 73, 77 TR: Labsheets: 94-95 Transparencies: 108-110 Additional Practice: 125 Every Day Counts None6.G.5Find the distance between two points on horizontal or vertical number lines.Find the distance between two points on horizontal or vertical number lines.Bits and Pieces I SE: 22-24, 27-28, 63-64, 82 TE: 30d, 92 TR: Transparencies: 141 Every Day Counts None 6.G.6Predict, describe, and perform transformations on two-dimensional shapes (e.g., translations, rotations, and reflections).Predict, describe, and perform transformations on two-dimensional shapes (e.g., translations, rotations, and reflections).Shapes and Designs SE: 52-56 TE: 63a, 63b, 63c, 63d TR: Transparencies: 105, 106 Ruins of Montarek SE: 10-12, 23-24 TE: 25b, 25c, 25d, 93 TR: Labsheets: 114, 116 Transparencies: 123 Every Day Counts None 6.G.7Identify types of symmetry, including line and rotational.Identify and describe various types of symmetry.Shapes and Designs SE: 52-56 TE: 63a, 63b, 63c, 63d TR: Transparencies: 105, 106 Ruins of Montarek SE: 10-12, 23-24 TE: 25b, 25c, 25d, 93 TR: Labsheets: 114, 116 Transparencies: 123 Every Day Counts Jan., Feb. 6.G.8Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions (e.g., translations, rotations, and reflections).Recognize reflections, slides, and rotations. Determine congruence through measurement and transformations.Shapes and Designs SE: 52-56 TE: 63a, 63b, 63c, 63d TR: Transparencies: 105, 106 Ruins of Montarek SE: 10-12, 23-24 TE: 25b, 25c, 25d, 93 TR: Labsheets: 114, 116 Transparencies: 123 Every Day Counts None 6.G.9Match three-dimensional objects and their two-dimensional representations (e.g., nets, projections, and perspective drawings).Identify and draw shapes and figures from different views/perspectives (e.g., nets, projections, orthogonal and isometric perspectives).Ruins of Montarek SE: 7-25,26-39,40-51,62-71, 72-81,82-84 TE: 25a, 25b, 25c, 25d, 25e, 25d, 25e, 25h, 39a, 39b, 39c, 39d, 51a, 51b, 51c, 51d, 61a, 61b, 61c, 61d, 61e, 61f, 61h, 61i, 71a, 71b, 71c, 81a, 81b, 81c, 81d, 81e, 84-85, 87-89, 90-91, 992-96, 97-98 TR: Labsheets: 114-120 Transparencies: 121-125,127-146 Additional Practice: 154-159 Every Day Counts May, Jun. STRAND: MEASUREMENTDOE Standard NumberSTATE STANDARDGRADE 6 Progress IndicatorsRESOURCES6.M.1Apply the concepts of perimeter and area to the solution of problems. Apply formulas where appropriate.Explain how changes in one or more dimensions of a figure result in a change in the area or perimeter of the figure. Define the size of a region as area. Apply correct formulas to find area and perimeter of basic shapes (e.g., 3 or 4 sided).Covering and Surrounding SE: 6-18, 19-28, 29-34, 35-45, 46-55, 56-68, 69-81; TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 28a, 28b, 34a, 34b, 34c, 34d, 34e, 45a, 45b, 45c, 45d, 45e, 55a, 55b, 55c, 55d, 55e, 55f, 68a, 68b, 68c, 68d, 68e, 68f, 81a, 81b, 81c, 81d, 81e, 81f, 81g, 81h, 86, 87-88, 89-90, 91-92, 93-97, 98-99 TR: Labsheets: 116-119 Transparencies: 120-136 Additional Practice: 150-156 Bits and Pieces II SE: 54-59 TE: 63a, 63b, 63c, 63d, 63e, 63f TR: Labsheets: 108 Transparencies: 117, 120-121; Additional Practice: 147- 149 Every Day Counts Sept., Oct., Nov. Dec., Jan., Feb., Mar., May, June 6.M.2Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals.Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals (e.g. acute, right, obtuse, straight, regular, trapezoid, parallelogram).Shapes and Designs SE: 8-14, 15-21, 22-41, 42-50, 51-63, 76-78 TE: 14a, 14b, 21a, 21b, 21c, 21d, 21e, 21f, 21g, 41a, 41b, 41c, 41d, 41e, 41f, 41g, 41h, 41i, 50a, 50b, 50c, 50d, 50e, 50f, 50g, 63a, 63b, 63c, 63d, 78-79, 80-81, 82-85, 86-87, 88-89; TR: Transparencies: 106-109, 117-119, 121 Covering and Surrounding SE: 6-18, 35-4 5, 46-55, 56-68 TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 45a, 45b, 45c, 45d, 45e, 55a, 55b, 55c, 55d, 55e, 55f, 68a, 68b, 68c, 68d, 68e, 68f, 86, 88, 89-90, 91- 92, 93-97, 98-99 TR: Labsheets: 116-118, Transparencies: 120-127, 129-137 Additional Practice: 150, 152- 155 Ruins of Montarek SE: 7-25, 26-39, 40-51, 52-61, 62-71, 72-81, 82-84 TE: 25a, 25b, 25c, 25d, 25e, 25f, 25g, 25h, 39a, 39b, 39c, 39d, 51a, 51b, 51c, 51d, 61a, 61b, 61c, 61d, 61e, 61f, 61g, 61h, 61i, 71a, 71b, 71c, 81a, 81b, 81c, 81d, 81e, 84-85, 87-89, 90-91, 92-96, 97-98 TR: Labsheets: 114-120 Transparencies: 121-146 Additional Practice: 154-159 Every Day Counts All months 6.M.3Solve problems involving proportional relationships and units of measurement (e.g., same system unit conversions, scale models, maps, and speed).Use a ratio to create a simple scale drawing or map. Recognize unit conversions as ratios and proportions.Bits and Pieces I SE: 61-62, 74 TE: 83b, 83c, 83d TR: Additional Practice: 178 Every Day Counts None6.M.4Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same areas. Develop strategies to find the area of more complex shapes.Develop strategies to find the area of more complex shapes. Recognize that complex regions can be divided into simpler shaped regions.Covering and Surrounding SE: 6-18, 19-28, 29-34, 35-45, 46-55, 56-68, 69-81 TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 28a, 28b, 34a, 34b, 34c, 34d, 34e, 45a, 45b, 45c, 45d, 45e, 55a, 55b, 55c, 55d, 55e, 55f, 68a, 68b, 68c, 68d, 68e, 68f, 81a, 81b, 81c, 81d, 81e, 81f, 81g, 81h, 86, 87-88, 89-90, 91-92, 93-97, 98-99 TR: Labsheets: 116- 119 Transparencies; 120-141 Additional Practice: 150-156 Every Day Counts Sept., Oct., Nov., Feb.6.M.5Identify, measure, and describe circles and relationships of the radius, diameter, circumference, and area (e.g., d = 2r, p = C/d), and use the concepts to solve problems.Recognize the ratio between the circumference of a circle and its diameter as a little more than 3. Use ( ( 3.14 in formulas to find area and circumference.Covering and Surrounding SE: 69-81 TE: 81a, 81b, 81c, 81d, 81e, 81f, 81g, 81h, 89-90, 91-92, 94, 96, 98-99 TR: Labsheets: 119 Transparencies; 137-141 Additional Practice: 156 Every Day Counts Sept., Oct., Nov., Dec., Jan., Feb., Mar. 6.M.6Find volumes and surface areas of rectangular prisms.Find volumes and surface areas of rectangular prisms.Additional Resources Needed Every Day Counts None6.M.7Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles.Using protractor, measure with accuracy to find sums of angles in simple polygons. Without a protractor find the sum of the angles in a polygon (3 to 8 sides).Shapes and Designs SE: 42-45, 47, 49-50, 59, 62-63, 77-78 TE: 50a, 50b, 50c, 50d, 50e, 80 TR: Transparencies: 117- 119 Every Day Counts None STRAND: DATA ANALYSIS, STATISTICS, AND PROBABILITYDOE Standard NumberSTATE STANDARDGRADE 6 Progress IndicatorsRESOURCES6.D.1Describe and compare data sets using the concepts of median, mean, mode, maximum and minimum, and range.Collect, organize, and record data using the concepts of median, mean, mode, maximum and minimum, and range.Data About Us SE: 9-18, 21, 24-27, 29, 38-39, 53-67, 69-70 TE: 21c, 21d, 21e, 21f, 21g, 21h, 21i, 29b, 29c, 41d, 67a, 67b, 67c, 67d, 67e, 67f, 67g, 67h, 67i, 67j, 67k, 67l, 71, 72-73, 74-75, 76, 78 TR: Transparencies: 100-101, 103-105, 112, 114-116 Additional Practice: 122-126 Every Day Counts Dec., Jan., Feb., Mar., May, June6.D.2Construct and interpret stem-and-leaf plots, line plots, and circle graphs.Construct circle graphs. Describe and interpret circle graphs. Construct and interpret stem-and-leaf plots.Data About Us SE: 6-11, 30-41, 56, 58, 60, 62 TE: 21c, 21d, 21e, 41a, 41b, 41c, 41d, 41e, 41f, 67c, 67d, 67e, 67g, 70, 74-75, 76, 78 TR: Transparencies: 97-99, 105-107, 114 Additional Practice: 122-126 Shapes and Designs TE: 41i Every Day Counts Sept., Oct., Nov., Jan., Feb.6.D.3Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials. Analyze the outcomes.Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials. Analyze the outcomes.How Likely Is It? SE: 12, 33, 43-48, 49, 59-64, 65 TE: 21c, 41b, 41c, 48a, 48b, 48c, 56a, 56b, 75 TR: Transparencies: 102, 104, 106 Additional Practice: 114-116 Every Day Counts All months 6.D.4Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event.Compare the theoretical probability of an event occurring with experimental results. Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions.How Likely Is It? SE: 5-13, 14-21, 22-28, 29-32, 35-38 TE: 13a, 13b, 13c, 13d, 21a, 21b, 21c, 28a, 28b, 41a, 41b, 48a, 67-68, 71-72, 76-77 TR: Labsheets: 92, 93 Transparencies: 95-97, 99-101 Additional Practice: 110-113 Every Day Counts May, June Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group  STRAND: NUMBER SENSE AND OPERATIONSDOE Standard NumberState StandardGrade 7 Progress IndicatorsResources7.N.1Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e. rational numbers), decimals, and percents.Compare, order, estimate, and translate among integers, fractions and mixed numbers, decimals and percents.Comparing and Scaling SE: 5-15, 16-25, 26-36, 37-51, 52-64, 65-81, 82-86 TE: 15a-d, 25a-c, 36a-f, 51a-f, 64a-h, 81a-c, 86-87, 88, 89-90, 91-95, 96-97, 98-99 TR: Labsheets: 118, 119, 120; Transparencies: 124-146 Additional Practice: 152-159 Data Around Us SE: 5-11, 12-22, 23-37, 38-50, 51-60, 61-69, 70-72 TE: 11a-d, 22a-e, 37a-g, 50a-f, 60a-f, 69a-d, 73, 74, 75-77, 78-79 TR: Transparencies: 106, 112, 116; Additional Practice: 130, 131, 133, 1347.N.2Use ratios and proportions in the solution of problems, involving unit rates, scale drawings, and reading of maps.Use ratios and proportions in the solution of problems involving unit rates and scale factors.Comparing and Scaling SE: 16-25, 26-33, 37-51, 52-64, 65-81, 82-86 TE: 25a-c, 36a-f, 51a-f, 64a-h, 81a-c, 86-87, 88, 89-90, 91-95, 96-97, 98-99 TR: Transparencies: 124-138 Additional Practice: 155-159 Data Around Us SE: 5-11, 12-22, 58-60, 61-69 TE: 11a-d, 22a-e, 60a-f, 69a-d, 76 TR: Transparencies: 108-113, 117, 120-123 Additional Practice: 128-134 7.N.3Represent numbers in scientific notation, (positive powers of ten only) and use in problem situations.Represent numbers in scientific notation with positive exponents.Data Around Us SE: 40-49 TE: 37j, 50e-f, 78 TR: Transparencies: 116 Additional Practice: 1317.N.4Demonstrate an understanding of absolute value (e.g., | -3 | = | 3 | = 3) This standard is intentionally the same as standard 8.N.6.Define and demonstrate an understanding of absolute value.Accentuate the Negative SE: 39 TE: 33g, 52h7.N.5Apply the rules of positive integer exponents to the solution of problems. Extend the Order of Operations to include positive integer exponents.Extend the Order of Operations to include positive integer exponents.Data Around Us SE: 40-49 TE: 37j, 50e-f, 78 TR: Transparencies: 116 Additional Practice: 1317.N.6Use the inverse relationships of addition and subtraction, multiplication and division, to simplify computations and solve problems (e.g. multiplying by or 0.5 is the same as dividing by 2).Use the inverse relationships of addition and subtraction, multiplication and division, to simplify computations and solve problems.Accentuate the Negative SE: 18-33, 34-52, 53-66 TE: 33a-g, 52a-l, 66a-I, 84-85, 86, 87-89, 90-92 TR: Labsheets: 102 Transparencies: 104-119 Additional Practice: 144-1497.N.7Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1). This standard is intentionally the same as standard 8.N.10.Estimate and compute with fractions (including simplification of fractions), decimals, and percents.Comparing and Scaling SE: 16-25, 28-33, 48, 52-64, 65-81 TE: 25a-b, 36c-f, 51d, 51f, 64a-h, 81a-c, 86-87, 88, 89-90, 91-95, 96-97 TR: Transparencies: 130-131, 140-142, 144-146 Additional Practice: 155-159 Accentuate the Negative SE: 18-33, 34-52, 54-55, 59, 61-62, 64 TE: 33a-g, 52a-l, 66a-e, 84-85, 86, 87-89, 90-92 TR: Labsheets: 102 Transparencies: 104-119 Additional Practice: 144-147, 149 Data Around Us SE: 38-47, 61-69, 70-72 TE: 50d-f, 73, 74, 75-77, 78-79 TR: Transparencies: 101-102, 118, 120-121 Additional Practice: 130-134 7.N.8Determine when an estimate rather than an exact answer is appropriate and apply in problem situations. This standard is intentionally the same as standard 8.N.11. Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.Comparing and Scaling SE: 16, 20-21, 52-64 TE: 25a, 64a-h TR: Transparencies: 124-125, 128, 137-138 Data Around Us SE: 16-21, 51-59, 63-68 TE: 11f, 22d-e, 60a-f, 69c-d, 73, 75-77, 78 TR: Transparencies: 100-102, 111, 118-119, 121 Additional Practice: 128-130 7.N.9Select and use appropriate operationsaddition, subtraction, multiplication, division, and positive integer exponentsto solve problems with rational numbers (including negatives). This standard is intentionally the same as standard 8.N.12.Select and use appropriate operations to solve problems with rational numbers (excluding negative integers).Comparing and Scaling SE: 16-25, 26-36, 48, 65-81 TE: 25a-b, 36c-f, 51d, 51f, 81a-c, 86-87, 88, 89-90, 91-95, 96-97 TR: Transparencies: 130-131, 140-142, 144-146 Additional Practice: 155-159 Accentuate the Negative SE: 18-33, 34-52, 53-66 TE: 33a-g, 52a-l, 66a-I, 84-85, 86, 87-89, 90-92 TR: Labsheets: 102 Transparencies: 104-119; Additional Practice: 144-147, 149 Data Around Us SE: 6-10,41-50,61-69, 71-72 TE: 50d-f, 60a-f, 69a-d, 73, 74, 75-77 TR: Transparencies: 101-102, 118, 120-121 Additional Practice: 130-134 Strand: Patterns, Relations, and AlgebraDOE Standard NumberState StandardGrade 7 Progress IndicatorsResources7.P.1Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions (e.g., compounding). This standard is intentionally the same as standard 8.P.1.Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and symbolic expressions. Include arithmetic and geometric progressions.Variables and Patterns SE: 6-7, 12-16, 19-21, 25, 33-34, 36-48, 49-60, 61-68, 69-70 TE: 35j-k, 48a-f, 60a-e, 68a-d, 74, 76-78, 79-82 TR: Transparencies: 102-126 Additional Practice: 134-136, 138-139 Comparing and Scaling SE: 26-36, 37-51, 68-69, 73 TE: 36a-f, 51a-f, 81b-c TR: Transparencies: 128, 134-136, 144 Additional Practice: 156 Moving Straight Ahead SE: 5-14, 15-34, 35-52, 53-63, 64-79, 80-91, 92-94 TE: 14a-c, 34a-l, 52a-k, 63a-g, 79a-j, 91a-g, 95-96, 97-99, 100-101, 102-104, 105-108 TR: Transparencies: 128-154 Additional Practice: 160-1697.P.2Evaluate simple algebraic expressions for given variable values (e.g., 3a2 - b for a = 3 and b = 7). This standard is intentionally the same as standard 8.P.2.Evaluate simple algebraic expressions for given variable values.Stretching and Shrinking SE: 11-13, 22-25, 28-40, 41-58, 59-74, 79-84, 85-87 TE: 27c-j, 40a-g, 58a-f, 74a-h, 84a-g, 90-92, 93-95, 96-98, 99-102, 103-105, 106, 107-108 TR: Transparencies: 150-156 Additional Practice: 178-179 Filling and Wrapping SE: 5-14, 15-23, 24-36, 37-45, 46-56, 57-67, 68-72, 73-76 TE: 14a-h, 23a-e, 36a-e, 45a-g, 56a-e, 67a-f, 72a, 77, 78-79, 80-82, 83-84, 85-86, 87 TR: Labsheets: 108- 110 Transparencies: 111-131 Additional Practice: 140-1497.P.3Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations.Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations.Variables and Patterns SE: 38-47, 49-60, 61-68, 69-70 TE: 48a-f, 60a-e, 68a-d, 74, 76-78, 79-82 TR: Transparencies: 101-126 Additional Practice: 134-139 Comparing and Scaling SE: 42-51, 68-69, 73 TE: 51d-f TR: Transparencies: 134-136, 144 Moving Straight Ahead SE: 5-14, 15-34, 35-52, 53-63, 64-79, 80-91, 92-94 TE: 14a-c, 34a-l, 52a-k, 63a-g, 79a-j, 91a-g, 95-96, 97-99, 100-101, 102-104, 105-108 TR: Transparencies: 128-154 Additional Practice: 160-1697.P.4Solve linear equations, using tables, graphs, models and algebraic methods.Set up and solve linear equations with one variable, using algebraic methods, models, and/or graphs.Variables and Patterns SE: 49-60, 62-65, 67 TE: 60a-e TR: Additional Practice: 138 Comparing and Scaling SE: 33-34 TR: Transparencies: 144 Additional Practice: 156 Moving Straight Ahead SE: 53-63, 85-86, 88, 93-94 TE: 63a-g, 98, 101, 104, 107-108 TR: Transparencies: 135, 137, 141-149, 152, 154 Additional Practice: 161, 163, 165, 167-169 7.P.5Identify, describe, and analyze linear relationships between two variables. Compare positive rate of change, e.g., y = 3x + 1, to negative rate of change, e.g., y = -3x + 1Explain and analyze how a change in one variable results in a change in another variable in functional relationships.Variables and Patterns SE: 49-60, 69-70 TE: 60a-e, 76, 81 TR: Transparencies: 101-126 Additional Practice: 134-139 Comparing and Scaling SE: 44 TE: 51d TR: Transparencies: 134-136 Additional Practice: 156 Moving Straight Ahead SE: 15-34, 42-43, 53-63, 80-83, 85-91, 92-94 TE: 34a-l, 52g-h, 63a-g, 91a-g, 98, 101, 104, 107-108 TR: Transparencies: 128-154 Additional Practice: 160-163, 165, 167-169 7.P.6Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. This standard is intentionally the same as standard 8.P.9.Variables and Patterns SE: 49-60, 62-65, 67 TE: 60a-e TR: Additional Practice: 138 Comparing and Scaling SE: 33-34 TR: Transparencies: 144 Additional Practice: 156 Moving Straight Ahead SE: 55-56, 68, 70-73, 76-77 Strand: GeometryDOE Standard NumberState StandardGrade 7 Progress IndicatorsResources7.G.1Analyze, apply, and explain the relationship between the number of sides and the sums of the interior angle measures of polygons.Analyze, apply, and explain the relationship between the number of sides and the sums of the interior angle measures of polygons.Additional Resources Needed7.G.2Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems. This standard is intentionally the same as standard 8.G.2.Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.Stretching and Shrinking SE: 5-13, 14-27, 28-40, 41-58, 59-74, 75-84, 85-87 TE: 13a-d, 27a-j, 40a-g, 58a-f, 74a-h, 84a-g, 90-92, 93-95, 96-98, 99-102, 103-105, 106, 107-108 TR: Labsheets: 124-134 Transparencies: 135-161 Additional Practice: 172-1807.G.3Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal. This standard is intentionally the same as standard 8.G.3.Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.Stretching and Shrinking SE: 59-74 TE: 74a-h, 100 TR: Transparencies: 154-156; Additional Practice: 174, 178-1797.G.4 Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants) * 7.G.5Use a ruler, protractor, and compass to draw polygons and circles.Use a ruler, protractor, and compass to draw polygons and circles.Stretching and Shrinking SE: 6-13, 28-40, 75-84 TE: 13a-d, 40a-g, 84a-g TR: Labsheets: 124-130, 134; Transparencies: 157- 161 Filling and Wrapping SE: 9-10, 13, 27-28, 39-40, 44, 48-49, 58-59 TE: 14a-h, 36d-e, 45b, 45d-f, 56a-e, 67a-b TR: Labsheets: 108-110 Transparencies: 111-117, 122-126, 128-1307.G.6Predict the results of translations and reflections of figures on unmarked or coordinate planes and draw the transformed figure.Predict the results of translations and reflections of figures on unmarked or coordinate planes and draw the transformed figure.Stretching and Shrinking SE: 5-13, 14-27, 28-40, 41-58, 59-74, 75-84, 85-87 TE: 13a-d, 27a-j, 40a-g, 58a-f, 74a-h, 84a-g, 90-92, 93-95, 96-98, 99-102, 103-105, 106, 107-108 TR: Labsheets: 124-134 Transparencies: 135- 161 Additional Practice: 172-180 7.G.7Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces. This standard is intentionally the same as standard 8.G.7.Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.Filling and Wrapping SE: 5-14, 15-23, 24-36, 37-45, 46-56, 57-67, 68-72,73-76 TE: 14a-h, 23a-e, 36a-e, 45a-g, 56a-e, 67a-f, 72a, 77, 78-79, 80-82, 83-84, 85-86, 87 TR: Transparencies: 114-131 Additional Practice: 140-149 Strand: MeasurementDOE Standard NumberState StandardGrade 7 Progress IndicatorsResources7.M.1Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. This standard is intentionally the same as standard 8.M.1.Select, convert, and use appropriate units of measurement or scale.Stretching and Shrinking SE: 10-13, 14-27, 28-40, 41-58, 59-74, 75-84, 85-87 TE: 13a-d, 27a-j, 40a-g, 58a-f, 74a-h, 84a-g, 90-92, 93-95, 96-98, 99-102, 103-105, 106, 107-108 TR: Labsheets: 130, 131 Transparencies: 135-142, 154-156 Additional Practice: 172-179 Filling and Wrapping SE: 5-14, 15-23, 24-36, 37-45, 46-56, 57-67, 68-72, 73-76 TE: 14a-h, 23a-e, 36a-e, 45a-g, 56a-e, 67a-f, 72a, 77, 78-79, 80-82, 83-84, 85-86, 87 TR: Labsheets: 108- 110 Transparencies: 111-131 Additional Practice: 140- 149 7.M.2Given the formulas, convert from one system of measurement to another. Use technology as appropriate. This standard is intentionally the same as standard 8.M.2.Given the formulas, convert from one system of measurement to another.Stretching and Shrinking SE:36, 49, 65 Filling and Wrapping SE: 54 TR: Additional Practice: 146 Data Around Us SE: 14-15 TE: 22a-d 7.M.3Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate. This standard is intentionally the same as standard 6.G.4., which is currently not being assessed at grade 6. This standard will be assessed at grade 7.Understand concepts and the application of formulas for area and perimeter of parallelograms, trapezoids, and circles.Stretching and Shrinking SE: 10-13, 19-20, 24, 36-37, 39 TE: 27e-g, 100 TR: Transparencies: 136, 142 Additional Practice: 172-177 Filling and Wrapping SE: 5-14, 15-23, 24-36, 37-45, 46-56, 57-67, 68-72, 73-76 TE: 14a-h, 23a-e, 36a-e, 45a-g, 56a-e, 67a-f, 72a, 77, 78-79, 80-82, 83-84, 85-86, 87 TR: Transparencies: 111-131 Additional Practice: 140-149 STRAND: DATA ANALYSIS, STATISTICS, AND PROBABILITYDOE Standard NumberState StandardGrade 7 Progress IndicatorsResources7.D.1Select, create, interpret, and utilize the following tabular and graphical representations of data: circle graphs, Venn diagrams, stem-and-leaf plots, tables, and charts). Select, create, interpret, and utilize the following tabular and graphical representations of data: circle graphs, Venn diagrams, stem-and-leaf plots, tables, and charts). What Do You Expect? SE: 8-9, 22-23, 30, 38-39, 42, 51-52 TE: 31a-b, 31e-f, 49a-b, 58a-b, 68b TR: Labsheets: 124-130 Transparencies: 134, 153 Additional Practice: 166 Comparing and Scaling SE: 48-49, 77-78 TE: 86, 91, 94-95 TR: Labsheets: 118-120 Transparencies: 124-130, 134, 138, 145-146 Additional Practice: 152- 154, 157 7.D.2Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. This standard is intentionally the same as standard 8.D.3.Find, describe, and interpret appropriate measures of central tendency and spread that represent a set of data.What Do You Expect? SE: 52-54 TE: 58a-58b7.D.3Use tree diagrams, tables, organized lists, and area models to compute probabilities for simple compound events (e.g., multiple coin tosses or rolls of dice).Use tree diagrams, tables, organized lists, and area models to compute probabilities for simple compound events (e.g., multiple coin tosses or rolls of dice).What Do You Expect? SE: 10-18, 24-25, 28-29, 42-44, 66, 69-78 TE: 21e-i, 31c-g, 49c-e, 49g, 68c-d, 68g, 78a-e, 83, 85-86, 91-92, 93-94, 95-96 TR: Labsheets: 126-127 Transparencies: 132, 135-137, 145, 152 Additional Practice: 165, 170 Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group  STRAND: NUMBER SENSE AND OPERATIONSDOE Standard NumberState StandardGrade 8 Progress IndicatorsResources8.N.1Compare, order, estimate, and translate among integers, fractions and mixed numbers (e.g., rational numbers), decimals, and percents.Compare, order, estimate, and translate among integers, rational numbers, decimals, and percents.Looking For Pythagoras SE: 19-26, 27-40 TE: 26a-h, 40a-j, 74, 80, 84,85-86 TR: Transparencies: 119, 121-123, 128-129; Additional Practice: 139, 141, 143, 145-146 Clever Counting SE: 20-26, 30-31, 41-46, 50-56 TE: 26d-g, 46d-f, 56a, 61, 65-66 TR: Transparencies: 86-89, 97; Additional Practice: 102-1098.N.2Define, compare, order, and apply frequently used irrational numbers, such as "2 and .Compare, order, and apply frequently used irrational numbers such as "2 and .Looking For Pythagoras SE: 53-63,64-72 TE: 63a-f, 72a-f, 82, 85-86 TR: Labsheets: 108, 109; Transparencies: 127, 131, 132; Additional Practice: 140-143,146,1478.N.3Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.Use ratios and proportions in the solution of problems involving rate of change.Growing. Growing. Growing SE: 33-37, 49-52 TE: 30h, 44a-g, 60c-i TR: Transparencies: 103-107 Additional Practice: 1248.N.4Represent numbers in scientific notation, and use them in calculations and problem situations.Represent numbers in scientific notation, and use them in calculations and problem solving (including negative exponents). Growing, Growing, Growing SE: 268.N.5Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.Looking For Pythagoras SE: 19-26, 28-40, 53-63 TE: 26a-h, 40a-j, 63a-f, 80, 82, 86 TR: Labsheets: 108; Transparencies: 119, 122, 123, 127-129 Additional Practice: 140, 146-1478.N.6Demonstrate an understanding of absolute value (e.g., | -3 | = | 3 | = 3).Define and demonstrate an understanding of absolute value.Additional Resources Needed8.N.7Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots.Use the rules of powers and roots to the solution of problems, including positive integer exponents, and square roots in the Order of Operations.Looking For Pythagoras SE: 19-26, 28-40, 53-63 TE: 26a-h, 40a-j, 63a-f, 78-79, 80-82, 86 TR: Transparencies: 118, 119, 127-129 Additional Practice: 140, 143, 147 Growing, Growing, Growing SE: 17-30 TE: 30a-f, 65-66, 70-73 TR: Transparencies: 99- 101, 113; Additional Practice: 122-126 8.N.8Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., -7 + 7 = 0; 3/4 x 4/3 =1); and the notion of closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition). Use the properties of the identity and inverse elements and the notion of closure of a subset of the rational numbers under an operation.Looking For Pythagoras SE: 19-26, 27-40 TE: 26a-h, 40a-j, 74, 80, 84-86 TR: Transparencies: 119, 121-123,128,129 Additional Practice: 139, 141, 143, 145, 146 Say It With Symbols SE: 34-52, 53-64, 65-70, 71-75 TE: 52a-m, 64a-m, 70a-f, 76-77, 78, 79-81, 82-85 TR: Transparencies: 103-104, 107-116, 121, 124- 127 Additional Practice: 134-135, 138, 140,141-1438.N.9Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems (e.g. multiplying by or 0.5 is the same as dividing by 2).Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. Looking For Pythagoras SE: 19-26, 28-40, 53-63 TE: 26a-h, 40a-j, 63a-f, 78-79, 80-82, 86 TR: Transparencies: 118-119, 127-129; Additional Practice: 140, 143, 1478.N.10Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).Looking For Pythagoras SE: 19-26, 27-40, 41-52, 53-63 TE: 26a-h, 40a-j, 52a-h, 63a-f, 77, 78-79, 80-84, 85-86 TR: Labsheets: 108 Transparencies: 119, 121-124, 126, 128-129 Additional Practice: 139-146 Clever Counting SE: 8-13,15-26, 28-36, 41-46, 50-56, 59-61 TE: 14c-e, 26d-g, 36a-f, 46a-f, 56a, 61, 65-66 TR: Transparencies: 86-89, 97 Additional Practice: 102-1098.N.11Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.Looking For Pythagoras SE: 56-60 TE: 63b TR: Transparencies: 1278.N.12Select and use appropriate operationsaddition, subtraction, multiplication, division, and positive integer exponentsto solve problems with rational numbers (including negatives).Select and use appropriate operations to solve problems with rational numbers (including negative integers).Looking For Pythagoras SE: 19-26, 27-40 TE: 26a-h, 40a-j, 74, 80, 84, 85-86 TR: Transparencies: 119, 121-123,128-129 Additional Practice: 139, 141, 143, 145-146 Say It With Symbols SE: 34-52, 53-64, 65-70, 71-75 TE: 52a-m, 64a-m, 70a-f, 76-77, 78, 79-81, 82-85 TR: Transparencies: 103, 104, 107-116, 118- 121, 124-127 Additional Practice:134-135, 138, 140-143 STRAND: PATTERNS, RELATIONS, AND ALGEBRADOE Standard NumberState StandardGrade 8 Progress IndicatorsResources8.P.1Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions (e.g., compounding).Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and symbolic expressions. Include arithmetic and geometric progressions.Thinking With Mathematical Models SE: 5-25, 26-36, 37-46, 47-59, 60-62 TE: 25a-j, 36a-g, 46a-e, 59a-f, 63-64, 65-66, 67-68, 69-71 Labsheets: 92, 93 Transparencies: 94-109 Additional Practice: 116-125 Looking For Pythagoras SE: 44-52 TE: 52a-b, 52f-h TR: Labsheets: 108 Transparencies: 119, 122-123 Growing. Growing. Growing SE: 5-16, 17-30, 31-44, 45-60, 61-64 TE: 16a-g, 30a-f, 44a-g, 60a-i, 65-66, 67-68, 69-73, 74-77 Labsheets: 96 Transparencies: 97-113 Additional Practice: 120-127 Frogs. Fleas, and Painted Cubes SE: 5-18, 19-40, 41-51, 52-70, 71-84, 85-87 TE: 18a-k, 40a-r, 51a-i, 70a-i, 84a-g, 87-88, 89, 90-92, 93-95, 96-98 TR: Labsheets: 112-114 Transparencies: 115-122, 127-140 Additional Practice: 146-154 Say It With Symbols SE: 22-23, 25-27, 48-49,53-64, 65-70, 71-75 TE: 33d-g, 52e-h, 64a-m, 70a-f, 76-77, 78, 79-81, 82-85 TR: Transparencies: 103-104, 107-121 124-127 Additional Practice: 134-135, 138, 140-1438.P.2Evaluate simple algebraic expressions for given variable values (e.g., 3a2 - b for a = 3 and b = 7).Evaluate simple algebraic expressions for given variable values.Looking For Pythagoras SE: 17-26, 27-40, 41-52, 53-57, 60-63, 64-72 TE: 26a-h, 40a-j, 52a-h, 63a-f, 72a-f, 76-77, 78-79, 80-84, 85-86 TR: Labsheets: 99-102, 107-108 Transparencies: 116-120, 126 Additional Practice: 138-141, 143-146 Say It With Symbols SE: 5-19, 51, 53-64, 65-70, 71-75 TE: 19a-h, 52g, 76-77, 81, 83-84 TR: Transparencies: 104, 106-108, 116 118-119; Additional Practice: 134- 1378.P.3Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions (e.g., -2[-x+2] = 2x 4).Demonstrate an understanding of the identity (-x)(-y) = xy and use this identity to simplify algebraic expressions. Say It With Symbols SE: 38-398.P.4Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.Thinking With Mathematical Models SE: 5-25, 26-36, 37-46, 47-59, 60-62 TE: 25a-j, 36a-g, 46a-e, 59a-f, 63-64, 65-66, 67-68, 69-71 TR: Labsheets: 92, 93; Transparencies: 94-101, 103-109 Additional Practice: 116-125 Looking For Pythagoras SE: 44-52 TE: 52a-b, 52f-h TR: Transparencies: 119, 122-123 Growing, Growing. Growing SE: 5-16,17-30, 31-44, 45-60, 61-64 TE: 16a-g, 30a-f, 44a-g, 60a-i, 65-66, 67-68, 69-73, 74-77 TR: Labsheets: 96 Transparencies: 97-113 Additional Practice: 120-127. Frogs. Fleas, and Painted Cubes SE: 5-18, 19-40, 41-51, 52-70, 71-84, 85-87 TE: 18a-k, 40a-r, 51a-i, 70a-i, 84a-g, 87-88, 89, 90-92, 93-95, 96-98 TR: Labsheets: 112-114; Transparencies: 115, 117-122, 127-140 Additional Practice: 146-154 Say It With Symbols SE: 34-52, 53-64, 65-70, 71-75 TE: 52a-m, 64a-m, 70a-f, 76-77, 78, 79-81, 82-85 TR: Transparencies: 103-104, 107-116, 118-121, 124-127 Additional Practice:134-135, 138, 140-1438.P.5Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.Thinking With Mathematical Models SE: 8-25, 60-61 TE: 25a-j, 63-64, 65-66, 68 TR: Transparencies: 97-100; Additional Practice: 116-119, 121,123,125 Looking For Pythagoras SE: 64-72 TE: 83-84,85 TR: Labsheets: 109 Transparencies: 131, 132; Additional Practice: 1488.P.6Identify the roles of variables within an equation (e.g., y = mx + b, expressing y as a function of x with parameters m and b).Identify the roles of variables within an equation. Identify coefficientsThinking With Mathematical Models SE: 5-25, 26-36, 37-46, 47-59, 60-62 TE: 25a-j, 36a-g, 46a-e, 59a-f, 63-64, 65-66, 67- 68, 69 TR: Transparencies: 106, 107, 108, 109; Additional Practice 125 Growing, Growing. Growing SE: 17-30, 31-44, 45-60, 61-64 TE: 30a-f, 44a-g, 60a-i, 65-66, 67-68, 69-73, 74-77 TR: Transparencies: 97-113 Additional Practice: 120-127 Frogs. Fleas, and Painted Cubes SE: 6-18,19-40, 52-53, 56-70, 71-84, 85-87 TE: 18b-k, 40a-r, 70a-i, 84a-g, 87-88, 89, 90-92, 93-95, 96-98 TR: Labsheets: 113-114 Transparencies: 115-122, 131-134, 136- 140 Additional Practice:146-147, 150-152 Say It With Symbols SE: 38-41, 57-58, 60-63, 71-75 TE: 64a-c, 76-77, 78, 79-81, 82-83, 85 TR: Transparencies: 103-104, 106-107, 113, 115, 118-120, 124, 127; Additional Practice: 135, 140-1438.P.7Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs. Add like termsThinking With Mathematical Models SE: 9, 12-14, 16, 18-25, 29-36, 37-38, 44-45, 56, 60-62 TE: 36b-g, 46a-b, 63-64, 65-66, 67-68, 69-71 TR: Additional Practice: 124 Looking For Pythagoras SE: 44-52 TE: 52a-b, 52f-h Say It With Symbols SE: 53-64, 65-70, 71-75 TE: 64a-m, 70a-f, 76-77, 78, 79-81, 82-85 TR: Transparencies: 121-123,125-12 Additional Practice: 141, 1428.P.8Explain and analyzeboth quantitatively and qualitatively, using pictures, graphs, charts, or equationshow a change in one variable results in a change in another variable in functional relationships (e.g., C = d, A = r2 [A as a function of r], Arectangle = lw [Arectangle as a function of l and w]).Explain and analyze how a change in one variable results in a change in another variable in functional relationships.Thinking With Mathematical Models SE: 5-25, 26-36, 37-46, 47-59, 60-62 TE: 25a-j, 36a-g, 46a-e, 59a-f, 63-64, 65-66, 67-68,69 TR: Transparencies: 106-109 Additional Practice:125 Growing. Growing. Growing SE: 17-30, 31-44, 45-60, 61-64 TE: 30a-f, 44a-g, 60a-i, 65-66, 67-68, 69-73, 74-77 TR: Transparencies: 97- 113 Additional Practice: 120-127 Frogs. Fleas, and Painted Cubes SE: 6-18,19-40, 52-53, 56-70, 71-84, 85-87 TE: 18b-k, 40a-r, 70a-i, 84a-g, 87-88, 89, 90-92, 93-95, 96-98 TR: Labsheets: 113-114 Transparencies: 115-122, 131-134, 136-140; Additional Practice: 146-147, 150-152 Say It With Symbols SE: 38-41, 57-58, 60-63, 71-75 TE: 64a-c, 76-77, 78, 79-81, 82-83, 85 TR: Transparencies: 103-104, 106-107, 113, 115, 118-120, 124, 127 Additional Practice: 135, 140-1438.P.9Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. (i.e. computer programs, graphing calculators, etc.) Thinking With Mathematical Models SE: 5-13, 15-15,18-25, 26-36, 37-46, 47-59, 60-62 25a-e, 25g-j, 36a-g, 46a-e, 59a-f, 64, 65-66, 67-68, 69-71 TE: Transparencies: 94-108 Additional Practice: 119, 122, 124, 125 Looking For Pythagoras SE: 46-52 TE: 52a-b Growing. Growing. Growing SE: 5-16,17-30, 31-44, 45-60, 61-64 TE: 16a-g, 30a-f, 44a-g, 60a-i, 65-66, 67-68, 69-73, 74, 76-77 TR: Labsheets: 96 Transparencies: 97-109, 111-113 Additional Practice: 120, 122, 124, 126, 127 Frogs. Fleas, and Fainted Cubes SE: 5-7,19-21, 36-37, 41-42, 45-46, 49, 52-57, 60-63, 65, 67-69, 85-86 TE: 18a-c, 51a-d, 70a-g, 92, 95, 96, 98 TR: Transparencies: 116, 120, 129, 130, 132-135 Additional Practice: 149, 152 Say It With Symbols SE: 36-39, 41-42, 48-49, 53-64, 65-70, 71-75 TE: 52e-h, 64a-m, 70a-f, 76-77, 79-81, 82, 84 TR: Transparencies: 103-106, 108-116, 118-120 Additional Practice: 134-135, 140-1428.P.10Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.Use tables and graphs to represent and compare linear growth patterns. Compare rates of change and x- and y-intercepts of different linear patterns.Thinking With Mathematical Models SE: 5-13,14-15, 18-25, 26-36, 37-46, 47-59, 60-62 TE: 25a-e, 25g-j, 36a-g, 46a-e, 59a-f, 64, 65-66, 67-68, 69-71 TR: Transparencies: 94-108 Additional Practice: 119, 122, 124, 125 STRAND: GEOMETRYDOE Standard NumberState StandardGrade 8 Progress IndicatorsResources8.G.1Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons. Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons.Additional Resources Needed8.G.2Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.Kaleidoscopes. Hubcaps, and Mirrors SE: 5-23, 24-41, 42-58, 59-70, 71-77 TE: 23a-k, 41a-o, 58a-j, 70a-k, 79, 80-83, 84-85, 86-89, 90-93 TR: Labsheets: 116-146 Transparencies 147-173 Additional Practice: 184-1958.G.3Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.Kaleidoscopes. Hubcaps, and Mirrors SE: 27 TE: 23h, 41d, 41i8.G.4 Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problemsDemonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems. Looking For Pythagoras SE: 27-40, 41-52, 53-63 TE: 40a-j, 52a-h, 63a-f, 77, 78-79, 80-84, 85-86 TR: Labsheets: 108; Transparencies: 119, 121-124, 126, 128-129; Additional Practice: 139-1468.G.5Use a straightedge, compass, or other tools to formulate and test conjectures, and to draw geometric figures.Use a straightedge, compass, or other tools to formulate and test conjectures, and to draw geometric figures.Looking For Pythagoras SE: 17-26 TE: 26a-h, 83-84, 85-86 TR: Labsheets: 100, 101, 106, 111; Transparencies: 117-118; Additional Practice: 1468.G.6Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure (e.g., predict how tessellations transform under translations, reflections, and rotations).Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure.Kaleidoscopes. Hubcaps, and Mirrors SE: 5-23, 24-41, 42-58, 59-70, 71-77 TE: 23a-k, 41a-o, 58a-j, 70a-k, 79, 80-83, 84-85, 86-89, 90-93 TR: Labsheets: 116-146; Transparencies: 147-173; Additional Practice: 184-195;8.G.7Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.Identify three-dimensional figures by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.Say It With Symbols SE: 16-17, 67-69 TE: 70c-e TR: Transparencies: 127; Additional Practice: 1368.G.8Recognize and draw two-dimensional representations of three-dimensional objects (e.g., nets, projections, and perspective drawings).Recognize and draw two-dimensional representations of three-dimensional objects.Say It With Symbols SE: 16-17, 67-69 TE: 70c-e TR: Transparencies: 127; Additional Practice: 136 STRAND: MEASUREMENTDOE Standard NumberState StandardGrade 8 Progress IndicatorsResources8.M.1Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.Select, convert, and use appropriate units of measurement or scale.Looking For Pythagoras SE: 17-26, 27-40, 41-52, 53-57, 60-63, 64-72 TE: 26a-h, 40a-j, 52a-h, 63a-f, 72a-f, 76-77, 78-79, 80-84, 85-86 TR: Labsheets: 99-102, 107-108; Transparencies: 116-120,126 Additional Practice: 138-141, 143-1468.M.2Given the formulas, convert from one system of measurement to another. Use technology as appropriate.Given the formulas, convert from one system of measurement to another.Additional Resources Needed8.M.3Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/ circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate. Determine formulas and understand surface area and volume of rectangular prisms, cylinders, and spheres.Looking For Pythagoras SE: 17-26,45 TE: 26a-e, 52f-h, 76-77, 78-79, 85-86 Labsheets: 99-102, 107-108; Transparencies: 116-120, 126 Additional Practice: 138-141, 143-146:8.M.4Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement.Looking For Pythagoras SE: 64-72 TE: 72a-f, 83-84, 85 TR: Transparencies: 122 Kaleidoscopes. Hubcaps, and Mirrors SE: 5-23, 24-41, 42-58, 59-70, 71-77 TE: 23a-k, 41a-o, 58a-j, 70a-k, 79, 80-83, 84-85, 86-89, 90-93 TR: Labsheets: 116-146 Transparencies: 147-173 Additional Practice: 184-95 8.M.5Use models, graphs, and formulas to solve simple problems involving rates (e.g., velocity and density).Use models, graphs, and formulas to solve simple problems involving velocity and density rate of change.Looking For Pythagoras SE: 64-72 TE: 72a-f, 83-84, 85 TR: Labsheets: 109 Transparencies: 131, 132  STRAND: DATA ANALYSIS, STATISTICS, AND PROBABILITYDOE Standard NumberState StandardGrade 8 Progress IndicatorsResources8.D.1Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling).Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample.Samples and Populations SE: 24-28, 32, 34-35, 37-47,148 TE: 36b-d, 48a-h, 75, 76-78 TR: Transparencies: 112-15, 117-21 Additional Practice: 134-388.D.2Select, create, interpret, and utilize various tabular and graphical representations of data (e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box-and-whisker plots, histograms, tables, and charts). Differentiate between continuous and discrete data and ways to represent them.Differentiate between continuous and discrete data and ways to represent them.Samples and Populations SE: 5-23, 24-36, 37-48, 49-62, 63-69 TE: 23a-o, 36a-e, 48a-h, 62a-f, 69-70, 71, 72-75, 76-78 TR: Labsheets: 96-102 Transparencies: 103-122 Additional Practice: 130-1408.D.3Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. Use measures of central tendency and spread to compare different sets of data.Samples and Populations SE: 7-11, 21, 23, 33, 41-44, 63-69 23e-n, 48d-h, 70, 72, 74-75, 76 Labsheets: 100 Transparencies: 104, 105, 106, 107, 108, 118, 119, 120; Additional Practice: 131, 132,137,138,139,1408.D.4Use tree diagrams, tables, organized lists, basic combinatorics (fundamental counting principle), and area models to compute probabilities for simple compound events (e.g., multiple coin tosses or rolls of dice).Use tree diagrams, tables, organized lists, basic combinatorics and area models to compute probabilities for simple compound events.Clever Counting SE: 5-14,15-26, 27-36, 7-46, 47-56, 57-61 TE: 14a-e, 26a-g, 36a-f, 46a-f, 56a, 60-67-69 Transparencies: 85-98; Additional Practice: 102-109 Additional ResourcesThe following are Pre K 8 Resources to be used to supplement the core programs where needed Question of the Day, Lakeshore Publishing K only Every Day Counts Pattern Games K-3 only Great Source Games for Number Sense Great Source K Only Playing Math Games Teacher Resource Center K Only Developing Number Concepts: Counting, Comparing and Patterns Dale Seymour Publications K Only Super Source K-8 All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes Tangrams Hundred Chart ETA Cuisenaire Analog Clocks ETA Cuisenaire Equa Beam ETA Cuisenaire Hands-On Equations ETA Cuisenaire Fraction Strips ETA Cuisenaire Math to Learn Grades 1&2 Great Source Educational Group Math to Know Grades 3&4 Great Source Educational Group Math at Hand Grades 5&6 Great Source Educational Group Math on Call Grades 6-8 Great Source Educational Group Algebra to Go Grade 8 Great Source Educational Group 5/16/06  PAGE 1 PAGE 4 1/12/05 rev. PAGE  PAGE 5 5/16/06 Brockton Public Schools NUMBER SENSE: PRE-KINDERGARTEN Brockton Public Schools PATTERNS AND RELATIONS: PRE-KINDERGARTEN Brockton Public School SHAPES & SPATIAL SENSE: PRE-KINDERGARTEN PAGE  Brockton Public Schools MEASUREMENT: PRE-KINDERGARTEN PAGE  PAGE  Brockton Public Schools DATA ANALYSIS, STATISTICS, AND PROBABILITY: PRE-KINDERGARTEN Brockton Public Schools Pre-Kindergarten: Additional Resources Brockton Public Schools Number Sense and Operations: Kindergarten Brockton Public Schools Patterns, Relations, & Algebra: Kindergarten Brockton Public Schools Geometry: Kindergarten Brockton Public Schools Measurement: Kindergarten Brockton Public Schools Data Analysis, Statistics, and Probability: Kindergarten Brockton Public Schools Additional Resources: Kindergarten Brockton Public Schools Number Sense and Operations: Grade 1 & 2 Brockton Public Schools Patterns, Relations, and Algebra: Grade 1 & 2 Brockton Public Schools Geometry: Grade 1 & 2 Brockton Public Schools MEASUREMENT: GRADES 1 AND 2 Brockton Public Schools DATA ANALYSIS, STATISTICS AND PROBABILITY: Grade 1 & 2 PAGE  Brockton Public Schools additional resources: grade 1 and 2 Brockton Public Schools NUMBER SENSE AND OPERATIONS: GRADE 3 Brockton Public Schools Patterns, Relations, and Algebra: Grade 3 Brockton Public Schools Geometry: Grade 3 Brockton Public Schools measurement: Grade 3 Brockton Public Schools data analysis, statistics and probability: Grade 3 Brockton Public Schools ADDITIONAL RESOURCES: Grade 3 Brockton Public Schools number sense and operations: Grade 4 Brockton Public Schools Patterns, Relations, and ALGEBRA: Grade 4 Brockton Public Schools GEOMETRY: Grade 4 Brockton Public Schools MEASUREMENT: GRADE 4 Brockton Public Schools Data Analysis, Statistics, and Probability: GRADE 4 Brockton Public Schools Additional Resources: Grade 4 PAGE  Brockton Public Schools Number Sense and Operations: Grade 5 Brockton Public Schools Patterns, Relations, and Algebra: Grade 5 Brockton Public Schools Geometry: Grade 5 Brockton Public Schools Measurement: Grade 5 Brockton Public Schools Data Analysis, Statistics, and Probability: Grade 5 Brockton Public Schools Additional Resources: Grade 5 PAGE  Brockton Public Schools Number Sense and Operations: Grade 6 Brockton Public Schools Patterns, Relations, and Algebra: Grade 6 Brockton Public Schools Geometry: Grade 6 Brockton Public Schools Measurement: Grade 6 Brockton Public Schools Data Analysis, Statistics, and Probability: Grade 6 Brockton Public Schools Additional Resources: Grade 6 PAGE  Brockton Public Schools Number Sense and Operations: Grade 7 Brockton Public Schools Patterns, Relations, and Algebra: Grade 7 Brockton Public Schools Geometry: Grade 7 Brockton Public Schools Measurement: Grade 7 Brockton Public Schools Data Analysis, Statistics, and Probability: Grade 7 ?FPUVn  ? e f  i v zpgh>B5\aJhth>B5aJh>B5:CJ \aJ(h>B5:CJ \aJehrh h>B5:CJ \aJhB5:CJ \aJh>B h>BCJ\ h>BCJh>BCJ aJh>B5CJ$\aJh>BCJaJh>BCJ8aJh>BCJ<aJ h>BaJh>BCJHaJ%+?@ABCDEFPQRSTUVn222222222a2a22222222I=222222 $`^`a$gd>B`^`gd>B$a$gd>Bf  P  2 3 D c 222222222  i $&`#$/IfgdB`^`gd>B $`^`a$gd>Bc d v j|X X XiX X$&`#$/IfgdBkd$$IfTlhr xY(7X A { 6`@864 laT  j|X X XiX X$&`#$/IfgdBkd$$IfTlhr xY(7X A { 6`@864 laT  $ > ? 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" # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~  Root Entry FEy Data <V1Table; WordDocumentGv SummaryInformation( DocumentSummaryInformation8 CompObjj  FMicrosoft Word Document MSWordDocWord.Document.89q