ࡱ> 7 hbjbjUU J7|7|dcAltttCCC8CLDR{ EZFpFpFpFHHHzzzzzzz$r} dztHsH@HHHzsQpFpF {sQsQsQHRpFtpFzsQHzsQ sQ}VZ k R"t]wpFE lIz=CJiu]wt"{0R{cvsQ]wsQGrade K Kindergarten Number, Number Sense and Operations Standard Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods.BenchmarksGrade level IndicatorsStrategies/ResourcesUse place value concepts to represent whole numbers using numerals, words and physical models. (A) Recognize, classify, compare and order whole numbers. (B) Number and Number Systems Relate, read and write numerals for single-digit numbers (0-9). (5) Number and Number Systems Compare and order whole numbers up to 10. (1) Compare the number of objects in two or more sets when one set has one or two more, or one or two fewer objects. (7) Computation and Estimation Recognize the number or quantity of sets up to 5 without counting such as, recognize without counting the dot arrangement on a domino as 5. (13) 5. zero, one, two, three, four, five, six, seven, eight, nine Resource: sand trays to write numbers in, number posters as visual cues And sandpaper numbers, dry erase boards, markers, Website:  HYPERLINK "http://www.bbc.co.uk/schools/numbertime/index.shtml" www.bbc.co.uk/schools/numbertime/index.shtml Play Number Bingo 1. Given a set of numbers 1-10, the student will be able to place the numbers in correct order. Use flashcards, magnetic numbers or large numbers. Have students use large numbers and line themselves up in correct order. 7. Students should be able to use and explain strategies when comparing objects in two or more sets. Resources: manipulatives (cubes, counters, dot stickers), paper, dry erase board, markers. Divide manipulatives into 2 sets and have students tell which has more or less. Make sure student has concept of more or less. 13. Display dot arrangements on overhead for two to three seconds. Resources: Dice, dominoes, overhead, overhead counters Related Literature: Ten Black Dots D. Crews Every Buddy Counts- Stuart J. Murphy Ten, Nine, Eight M. Bang Counting Kisses-Karen Katz The M & Ms Brand Counting Book B. B. McGrath The Cheerios Counting Book-B.B. McGrath 1,2,3 to the Zoo: A Counting Book-Eric Carle The Icky Bug Counting Book & The Butterfly Counting Book-Jerry Pallotta Determine the value of a collection of coins and dollar bills. (D) Count, using numerals and ordinal numbers. (F) Model, represent and explain addition as combining sets and counting on. (G)Number and Number Systems Identify and state the value of a penny, nickel and dime. (9) Number and Number Systems Explain rules of counting such as, each object should be counted once and that order does not change the number. (2) Count to twenty such as, in play situations or while reading number books. (3) Determine how many in sets (groups) of 10 or fewer objects. (4) Number and Number Systems Represent and use whole numbers in flexible ways, including relating, composing and decomposing numbers such as, 5 marbles can be 2 red and 3 green or 1 red and 4 green. (8) Meaning of Operations Model and represent addition as combining sets and counting on, and subtraction as take-away and comparison. For example: a. combine and separate small sets of objects in contextual situation such as, add or subtract one, two or another small amount. b. count on (forward) and count back (backward) on a number line between 0 and 10. (10) 9. Students should describe attributes of a penny, nickel and dime. When identifying a coin, ask How do you know? Complete Coin Poems Lesson Resources: Coins, Pictures of Coins, visual Posters of Coins. Once students are aware of coins a daily review and possibly counting dimes and pennies or pennies and nickels daily would be a good reinforcement of the coins and their value. 4. Show a number card. Student counts and places the number of cubes on his/her desk. Resources: Counters, Flashcards, Students can practice counting in groups or individually. Count during Calendar time: number of sunny/rainy, etc days in the week Count number of students need milk/lunch that day Count number of absent students in a day Count number of students wearing a certain color that day Playful ways to count: count and nod your head or tap your foot or rub your stomach, count and raise your arm, count and clap, count in whispers, count and do a physical movement such as jumping jacks, knee bends or toe touching. Count starting at a different number. 10. Introduce one more and one less. Present a real-life situation involving the addition or subtraction of numbers. Students represent the problem situation using cubes. Use 5 Little Monkey Books- E. Chirstelow Counters, wipe off boards, crafts sticks, number cards, dominoes, interlocking cubes and walking number line Read it, Draw it, and Solve it Activities, (k-2)- Elizabeth H. Miller Related Literature: Feast for 10 C. Falwell Ten Sly Piranha William Wise Bennys Pennies P. Brisson Monster Musical Chairs- Stuart J. Murphy How Many Snails P. Giganti Jr. Mrs. Satos Hens L. Min Henry the Fourth- Stuart J. Murphy The Button Box M. Reid 10 for Dinner J. Bogart Ten Black Dots D. Crews Websites:  HYPERLINK "http://www.illuminations.nctm.org/lessonplans/prek-2/links/index.html" www.illuminations.nctm.org/lessonplans/prek-2/links/index.html Model, represent and explain subtraction as comparison, take-away and part-to-whole. (H) Model, represent and explain multiplication as repeated addition, rectangular arrays and skip counting. (I)Number and Number Systems Represent and use whole numbers in flexible ways, including relating, composing and decomposing numbers such as, 5 marbles can be 2 red and 3 green or 1 red and 4 green. (8) Meaning of Operations Model and represent addition as combining sets and counting on, and subtraction as take-away and comparison. For example: a. Combine and separate small sets of objects in a contextual situation such as, add or subtract one, two or another small amount. b. Count on (forward) and count back (backward) on a number line between 0 and 10. (10) Number and Number Systems Construct multiple sets of objects each containing the same number of objects. (6) Meaning of Operations Demonstrate joining multiple groups of objects, each containing the same number of objects such as, combining 3 bags of candy, each containing 2 pieces. (11)8. Ask students to show different ways to represent a number, such as 7, using two sets of objects. -Use a hula hoop to create the 2 groups and students can be the objects -Paper can be divided into 2 and stickers can be the objects -Dry erase board can be divided half and manipulatives can be the objects 10a. Use manipulatives to act out the solution to a problem. Complete Read it, Draw it, solve it Activities from Elizabeth H. Millers K-2 book. 10b. Students should be provided many opportunities to count on or count back using a number line. A large number line can be made with masking tape on the floor. Students can physically count on or count back by hopping to represent an addition or subtraction situation. -Store bought number lines or ones made of construction paper/bulletin board paper can also be used -Students can then use a ruler or number line at their desk once they grasp the concept of counting forward and back Read it, Draw it, Solve it Activities (k-2)- Elizabeth H. Miller Related Literature: Mouse Count E. S. Walsh Fish Eyes: A Book You Can Count On L. Ehlert There Were Ten in the Bed P. Adams Ten, Nine, Eight M. Bang One Less Fish K.M. Toft Seaweed Soup- Stuart J. Murphy Website:  HYPERLINK "http://www.arcytech.org/java/integers/index.html" www.arcytech.org/java/integers/index.html  Model, represent and explain division as sharing equally, repeated subtraction and rectangular arrays. (J) Demonstrate fluency in addition facts with addends through 9 and corresponding subtractions. (K) Meaning of Operations Partition or share a small set of objects into groups of equal size such as, sharing 6 stickers equally among 3 children. (12) Number and Number Systems Represent and use whole numbers in flexible ways, including relating, composing and decomposing numbers such as, 5 marbles can be 2 red and 3 green or 1 red and 4 green. (8)12. Ask students how they would share 6 M&Ms with 2 people. Students should model this situation. Ask students how they would share if 3 people were sharing the M&Ms. Read it, Draw it and solve it( K-2)-Elizabeth H. Miller Use pictures with manipulatives and/or stickers to solve problems 8. During opening activities for the day, have students come up with as many combinations of numbers to make a certain number between 0 and 10. Begin this activity mid-year-do one number a day and come up with as many combinations as possible using manipulatives and visual cues. Related Literature: The Doorbell Rang P. Hutchins Mission Addition L. Leedy Add the Animals M. Burton etc. (Benchmark Education) Ten Friends B. Goldstone Two Ways to Count to 10- Ruby Dee 12 Ways to get to 11- Eve Merriam Kindergarten Measurement Standard Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies.BenchmarksGrade level IndicatorsStrategies/ResourcesSelect appropriate units for length, weight, volume (capacity) and time, using: Objects; must include, non-standard units; U.S. customary units: inch, foot, yard, once, pound, cup, quart, gallon, minute, hour, day, week and year; metric units: centimeter, meter, gram and liter. (B) Develop common referents for units of measure for length, weight, volume (capacity) and time to make comparisons and estimates. (C) Measurement Units Identify units of time (day, week, month, year) and compare calendar elements such as, weeks are longer than days. (1) Use Measurement Techniques and Tools Compare and order objects of different lengths, areas, weights and capacities and use relative terms such as, longer, shorter, bigger, smaller, heavier, lighter, more and less. (2) Measurement Units Identify units of time (day, week, month, year) and compare calendar elements such as, weeks are longer than days. (1) Use Measurement Techniques and Tools Compare and order objects of different lengths, areas, weights and capacities; and use relative terms such as, longer, shorter, bigger, smaller, heavier, lighter, more and less. (2) Order events based on time. For example: a. Activities that take a long or short time; b. Review what we do first, next, last; c. Recalls what we did or plan to do yesterday, today, tomorrow. (4) Daily Calendar 2. Students can snap together 10 cubes. Several collections of objects can be compared to the cube train. Students state which of these is longer/shorter. Ask student to share, How do you know? Use a variety of non-standard units with students. Resources: in addition to the variety of non -standard units such as paper clips, toothpicks, Popsicle sticks, cubes, etc, you need a Balance and a inch ruler. Large Calendar Area Sequence games and Activities Calendar Activities Related Literature: The Line Up Book M. Russo Corduroy D. Freeman Big Pig and Little Pig D. McPhail Too Big, Too Small, Just Right F. Minters Rabbits Pajama party-Stuart J. Murphy The Best Bug Parade-Stuart J. Murphy Just Enough Carrots-Stuart J. Murphy How big is a foot?- Rolf Myller Hersheys Milk Chocolate Weights and Measures-Jerry Pallotta & Rob Bolster Apply measurement techniques to measure length, weight and volume (capacity). (D)Use Measurement Techniques and Tools Measure length and volume (capacity) using uniform objects in the environment. For example, find: a. How many paper clips long is a pencil; b. How many small containers it takes to fill one big container using sand, rice, beans. (3)3. Provide a number of experiences measuring capacity. Use as a station or learning center after students have a grasp of the concept. Until students have a grasp of the concept, allow them to explore with guidance in this area. Students love to measure and experiment. Use non-standard units such as paper clips, containers of various sizes and shapes, beans, Popsicle sticks, etc, to measure length and volume. Centimeter cubes would also be useful. Related Literature: Long, Short, High, Low, Thin, Wide J.T. Fey Fannie in the Kitchen: Whole Story from Soup to Nuts of How Fannie Farmer Invented Recipes With Precise Measurements D. Hopkinson Me and the Measure of Things J. Sweeney Measure Up: A Bug Contest- Frank Wilson Carrie Measures Up- Linda Aber and Joy Allen Kindergarten Geometry and Spatial Sense Standard Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects, and transformations to analyze mathematical situations and solve problems.BenchmarksGrade level IndicatorsStrategies/ResourcesSort and compare two-dimensional figures and three-dimensional objects according to their characteristics and properties. (C) Describe location, using comparative (before, after), directional (above, below), and positional (first, last) words. (F)Characteristics and Properties Identify and sort two-dimensional shapes and three-dimensional objects. For example: a. Identify and describe two-dimensional figures and three- dimensional objects from the environment using the childs own vocabulary; b. Sort shapes and objects into groups based on student-defined categories; c. Select all shapes or objects of one type from a group; d. Build two-dimensional figures using paper shapes or tangrams; build simple three-dimensional objects using blocks. (1) Spatial Relationships Name and demonstrate the relative position of objects as follows: a. place objects over, under, inside, outside, on, beside, between, above, below, on top of, upside-down, behind, in back of, in front of; b. describe placement of objects with terms such as, on, inside, outside, above, below, over, under, beside, between, in front of , behind. (2)1. Two-dimensional shapes Circle Square Triangle Rectangle Three-dimensional objects Sphere Cylinder Cone Cube Have both visual cues(posters) and manipulative shapes available. Other resources: pattern blocks, straws, crafts sticks, pipe cleaners, and anything else that may allow the children to form the shapes. 1d. Provide a variety of tangram puzzles to students. Students cover puzzle using tangram pieces and trace around each tangram piece on the puzzle. Website: illuminations.nctm.org//lessonplans/prek-2/tangram/index.html 2b. Teacher places an object on, besides, below another object. Students verbalize placement of object using appropriate placement terms. Positional Posters are useful in giving students visual cues in remembering positional terms. Related Literature: Shapes, Shapes, Shapes T. Hoban Grandfather Tangs Story- Ann Tompert Tatums Favorite Shape D. Thole The Shapes Game P. Rogers The Berenstain Bears Inside, Outside, Upside Down S. Berenstain I See Shapes- Marcia Fries The Greatest Grymnast of All- Stuart J. Murphy Twizzlers Shapes and Patterns- Jerry Pallotta Circus Shapes & Bug Dance Stuart J. Murphy Websites:  HYPERLINK "http://www.pbs.org.teachersource/mathline/lessonplans/esmp/perfectfit/perfectfit_procedure.shtm" www.pbs.org.teachersource/mathline/lessonplans/esmp/perfectfit/perfectfit_procedure.shtm  Kindergarten Patterns, Functions and Algebra Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as, tables, graphs and equations.BenchmarksGrade level IndicatorsStrategies/ResourcesSort, classify, and order objects by size, number, and other properties, and describe the attributes used. (A) Extend sequences of sounds and shapes or simple number patterns, and create and record similar patterns. (B) Create and extend patterns and describe the rule in words. (C) Model problem situations using objects, pictures, tables, numbers, letters, and other symbols. (D)Use Patterns, Relations and Functions Sort, classify and order objects by size, number and other properties. For example: a. identify how objects are alike and different; b. order three events or objects according to a given attribute, such as time or size; c. recognize and explain how objects can be classified in more that one way; d. identify what attribute was used to sort groups of objects that have already been sorted. (1) Use Patterns, Relations and Functions Identify, create, extend and copy sequences of sounds (such as, musical notes), shapes (such as, buttons, leaves or blocks), motions (such as, hops or skips), and numbers from 1 to 10. (2) Use Patterns, Relations and Functions Describe orally the pattern of a given sequence. (3) Use Algebraic Representation Model a problem situation using physical materials. (4) See the Ladybug and Leaf Activity in the addendum or use a variation of that as a suggestion. 1b. Order three events or objects. Use sequential games, activities, cut/paste or listening projects. 1d. Introduce use of Venn diagram to sort groups of objects. Use 2 or more hula hoops for the Venn diagrams. 2. Student pairs analyze, describe, copy and extend patterns made by each other. Start a rhythmic pattern and invite children to join in when they feel ready. clap, clap, palms out (AAB) snap, snap, clap, clap (AABB) Resources: beads/pasta of varying colors, string, pattern papers, magazines, craft sticks of varying sizes, crayons, pattern blocks, colored paper clips, different shaped pasta, etc. Assessment Suggestion Using The Very Busy Spider, ask students to verbally describe the pattern. Challenge students to translate this pattern in another way (use shapes, colors, etc.). Prior to assessing, give students many opportunities to orally describe patterns. Related Literature: The Button Box M. Reid Brown Bear, Brown Bear, What Do You See? B. Martin, Jr. Pattern H. Pluckrose The Very Busy Spider E. Carle Sorting- Henry Pluckrose Beep, Beep, Vroom, Vroom- Stuart J. Murphy Grandmas Button Box- Linda Aber The M & Ms Brand Pattern Book- B.B. McGrath Websites:  HYPERLINK "http://www.pbs.org/teachersource/mathline/lessonplans/esmp/magicbox/magicbox_procedure.shtm" www.pbs.org/teachersource/mathline/lessonplans/esmp/magicbox/magicbox_procedure.shtm  HYPERLINK "http://www.pbs.org/teachersource/mathline/lessonplans/esmp/herethere/herethereprocedure.shtm" www.pbs.org/teachersource/mathline/lessonplans/esmp/herethere/herethere_procedure.shtm  Kindergarten Data Analysis & Probability Standard Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data.BenchmarksGrade level IndicatorsStrategies/ResourcesPose questions and gather data about everyday situations and familiar objects. (A) Sort and classify objects by attributes, and organize data into categories in a simple table or chart. (B) Data Collection Gather and sort data in response to questions posed by teacher and students such as, how many sisters and brothers, what color shoes. (1) Data Collection Arrange objects in a floor or table graph according to attributes such as, use, size, color, or shape. (2) Statistical Methods Select the category or categories that have the most or fewest objects in a floor or table graph. (3) 2. Some graphing suggestions: pets favorite food favorite ice cream flavor number of letters in first name After constructing graph, ask students what they notice about the graph. Introduce term attributes (size, color, shape, thickness) 3. After selecting categories with the most and fewest, ask How do you know? Websites:  HYPERLINK "http://www.illuminations.nctm.org/lessonplans/prek-2/button/index.html" www.illuminations.nctm.org/lessonplans/prek-2/button/index.html  HYPERLINK "http://www.illuminations..nctm.org/lessonplans/prek-2/button-old/index.html" www.illuminations..nctm.org/lessonplans/prek-2/button-old/index.html  HYPERLINK "http://www.illuminations.nctm.org/lessonplans/prek-2/eye/index.html" www.illuminations.nctm.org/lessonplans/prek-2/eye/index.html  Kindergarten Mathematical Processes Standard Students use mathematical process and knowledge to solve problems. Students apply problem-solving and decision-making techniques, and communicate mathematical ideas. The benchmarks for mathematical processes articulate what students should demonstrate in problem-solving, representation, communication, reasoning and connections at key points in their mathematics program.BenchmarksGrade level IndicatorsStrategies/ResourcesUse a variety of strategies to understand problem situations; such as, discussing with peers, stating problems in own words, modeling problems with diagrams or physical materials, identifying a pattern. (A) Identify and restate in own words the question or problem and the information needed to solve the problem. (B) Generate alternative strategies to solve problems. (C) Evaluate the reasonableness of predictions, estimations and solutions. (D) Explain to others how a problem was solved. (E)  Specific grade-level indicators have not been included for the mathematical processes standard because content and processes should be interconnected at the indicator level. Therefore, mathematical processes have been embedded within the grade-level indicators for the five content standards.compare: to determine how two things are alike and/or different; the common/critical attributes must be identified. Compare is involved in nearly ALL of the following: demonstrate: to make clear by using examples or experiments; to show your reasoning describe: to analyze into its parts but less detailed than explain identify: to show or prove the sameness of recognize: to examine closely and identify the common and critical attributes sort: to put things together that have the same feature(s) (classify, categorize, group) Students must distinguish common and critical attributes. Other Stated Verbs in the Indicators: discuss model copy select gather build arrange create restate use order determine name extend draw relate construct represent state Draw pictures and use physical models to represent problem situations and solutions. (F) Use invented and conventional symbols and common language to describe a problem situation and solution. (G) Recognize the mathematical meaning of common words and phrases, and relate everyday language to mathematical language and symbols. (H) Communicate mathematical thinking by using everyday language and appropriate mathematical language. (I)  Specific grade-level indicators have not been included for the mathematical processes standard because content and processes should be interconnected at the indicator level. Therefore, mathematical processes have been embedded within the grade-level indicators for the five content standards.Common attribute: the special characteristic that is shared by all of the objects in the set. Critical attribute: the special characteristic that makes this object different from all other objects in the set. The critical thinking skill of attributing is needed in order to: sequence compare - contrast, and classify a set of ideas or objects. (categorize, group, sort) Explain means to: make plain or clear; understandable give reasons for. Their responses must include sufficient quality information and proof. This frequently involves providing evidence about relationships. Explain requires more details than describe. Kindergarten Technique: Use the term tell, but require students to begin giving quality evidence and reasons for their responses. (Think Alouds) Explain is one of the most frequently stated verbs in the Indicators K-12.  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