ࡱ>  " qbjbjFF $$$g((43$E/WWWWW222.......24n.-22226.@WW.@@@:WW.@2.@@@ w%^@@\t/0E/@/5@/5@@@222( :    Math Curriculum Grades K-2 Submitted by: Samuel Greco Fran Muhlenbruch Math Curriculum Grades K-2 Introduction The New Jersey DOE has adopted the Common Core State Standards (CCSS). Therefore, the following document reflects the revision of the Allamuchy Township School Districts math curriculum for grades Kindergarten through 2nd grade. This revision is in compliance with the CCSS. Within this document will be found Cumulative Progress Indicators (CPI) for each math standard. Along with these are listed suggested activities and resources to help students achieve mastery of each CPI. This is a living document. It is will be updated as new materials and strategies become available. Teachers should not limit themselves to the listed activities and resources but should feel encouraged to share different activities and resources with one another. Please share with the curriculum committee as well for inclusion in updated versions of this document. Standard Grade KStrandBehavioral Objective/ CPIActivityK.CCCounting and Cardinality Know number names and count sequences.T.G. lessons #16,17; 21,22; 24; 38,39; 40 p.65b Macaroni number cards; L.C. Count by Denise Fleming M. Win Them All game p.101b Funny Number game L.A. connection p.153 Monthly calendar activity1Count to 100 by ones and tensUse # chart to highlight 10, 20, 30, etc Practice sheets; T.G. lessons # 38,392Count forward beginning from a given number within the known sequence (instead of having to begin at 10)Duck Pond Game p.244/45 Pattern Game p.247/483Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).T.G. lessons #17; 22; 39; Number writing practice sheets Wiki sticks, sandwriting, etc... Count to tell the number of objects.4Understand the relationship between numbers and quantities; connect counting to cardinality. T.G. lessons # 6; 8,9; 13a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. T.G. lessons # 4,5, 6b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. T.G. lessons # 4,5; 13c. Understand that each successive number name refers to a quantity that is one larger.T.G. lesson #14; 18,205Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects.Compare numbers.6Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1T.G. lessons #7; 14, 15; 43; 49-54  7 Compare two numbers between 1 and 10 presented as written numerals. T.G lessons # 16,17; 21,22; 24; 38,39; 40 K.OAOperations and Algebraic Thinking Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.1Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.T.G. lessons # 18, 20; 49-54 Listen &count game (see attached) Use number lines, unifix cubes 2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.T.G. lesson # 55 Duck Pond Game p. 244/45 Juggling Game p.2463Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).T.G. lesson #564For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.T.G. lesson #56 L.C. 12 Ways to Count to 11 by Eve Merriam5Fluently add and subtract within 5.T.G. lesson # 51,52 Use a number line Duck Pond Game p.244/45 Juggling Game p.246K.NBTNumber and Operations in Base Ten Work with numbers 1119 to gain foundations for place value.1Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.T.G. lessons # 38,39 L.A. connection p. 153 # line game, start at ten add ones p.157a Bunches of 10K.MDMeasurement and Data Describe and compare measurable attributes.1Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.p.115 review measuring with non-standard units p.117a estimating weight p.117 manipulatives L.C. Inch by Inch by Leo Lionni2Directly compare two objects with a measurable attribute in common, to see which object has more of/less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.p.119b Activity units of children T.S. p119b p.123a Warm-up p.123b Whats My Rule? gameClassify objects and count the number of objects in each category.3Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.T.G. lessons # 1-5 p.119 math connectionK.GGeometry Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).1Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as: above, below, beside, in front of, behind, and next to.T.G: warm up p. 143a (make shape books) p.143 (yarn graph) p.150 (enrichment page)2Correctly name shapes regardless of their orientations or overall size.T.G. lessons # 32-34 M. activity- geoboards Shape bingo 3 Identify shapes as two-dimensional (lying in a plane, flat) or threedimensional (solid).T.G. lessons# 32-34 M. p.141 review boxAnalyze, compare, create, and compose shapes.4Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/corners) and other attributes (e.g., having sides of equal length).T.S. p.139B guessing game: p. 139B A.L. Boxes by Rose Griffiths5Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.Geoboards/clay shapes6Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle?Use attribute blocks to create new shapes Standard Grade 1StrandBehavioral Objective/ CPIResources G = Game L = Lesson in TE NLVM = Natl Library of Virtual Manipulatives SBR = Smart Board Resources 1.OAOperations and Algebraic Thinking Represent and solve problems involving addition and subtraction1Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.NLVM: Number Line Arithmetic G: What Number Comes Next? p 30 G: What Number Comes Before? p 32 L: 25, 1252Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.NLVM: Number Line Bars L: 47, 72Understand and apply properties of operations and the relationship between addition and subtraction.3Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)L: 28 G: Four Keys p 2844Understand subtraction as an unknown-addend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8.G: Dont Take Them all Away p 64 L: 26-38, 41-43, 53, 65Add and subtract within 20.5Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). L: 26-38, 41-43, 48-49, 51, 76-77, 80 NLVM: Hundreds Chart G: Guess How Many p. 14 G: Count to 20 by Ones and Twos p 1676Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).G: Add the Counters, p 58 G: Take Away the Counter p 68 G: Add or Take Away the Counters p 72 G: Flea Market Game Mat G: Roll a Double p 128 G: Roll and Add p 142 G: Roll a Ten p 242 G: Addition Table Game Mat G: Duck Pond Game Mat G: Frog Pond Game Mat L: 26-38, 41-43, 47, 51, 53, 58, 61-64, 106, 110, 129-131, 133-135 NLVM: Diffy Work with addition and subtraction equations.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.NLVM: Number Line Bounce L: 34-37, 42, 51, 538Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 =  3, 6 + 6 = .L: 34-35, 52, 60, 66, 102, 128 G:  Guess the Rule p 184 G:  Hidden Counters Puzzle p 217 G:  Space Game Mat G:  Stolen treasure p 284 1.NBTNumber and Operations in Base Ten Extend the counting sequence. 1Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.L: 54-57, 74-75, 84, 91-92, 117 G: Get to 100 by Tens or Ones p 266Understand place value.2Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:NLVM: Base Blocks L: 55-57, 75-77, 80, 87-89, 111-113a. 10 can be thought of as a bundle of ten ones called a ten.L: 47, 56-57 G: Flea Market Game Matb. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.L: 56-57, 74-77, 80c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).G: Macaroni Tens Game p 246 G: School Bookstore Game Mat G: Yard Sale Game Mat L: 87, 111-113, 1183Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.G: Hungry Alligator Game p 148 G: Make the Alligator Tell the Truth Game p 280 L: 67-68, 97-99, 126-127, 144Use place value understanding and properties of operations to add and subtract.NLVM: Base Blocks Addition4Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.L: 92-93, 95, 97, 137-138 G: Get to 100 By Tens or Ones Game p 266 G: Yard Sale Game Mat 5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.NLVM: Place Value Number Line6Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.Describe several measurable attributes of a single object.1.MDMeasurement and Data Measure lengths indirectly and by iterating length units.1Order three objects by length; compare the lengths of two objects indirectly by using a third object.G: Number Strip Game, p 50 TE G: How Long Is It? p 52 TE L: 22, 242Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.L: 25, 78-79, 94, 96, 104, 107 G: Measurement Game Mat G: Add to the Number Strip p 308Tell and write time.3Tell and write time in hours and half-hours using analog and digital clocks.NLVM: Time Analog and Digital Clocks NLVM: Time Matching Clocks L: 145-6 G: Clock Game Mat Represent and interpret data.4Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.NLVM: Bar Charts L: 17-21, 1231.GGeometry Reason with shapes and their attributes.1Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.NLVM: Color Patterns NLVM: Attribute Blocks NLVM: Attribute Trains L: 93, 121, 1322Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.NLVM: Pattern Blocks 3Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.L: 89-90, 100-101, 103, 105, 148Lessons 1 17 Review of Grade K standards, use only as needed. Standard Grade 2StrandBehavioral Objective/ CPIActivity2.OAOperations and Algebraic Thinking Represent and solve problems involving addition and subtraction1Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.T.G. lessons # 2; 6-8 Space game p. 425/26Add and subtract within 20T.G. lesson # 8-19; 23-28; Addition Table game p. 408/9 Frog Pond Game p.416/17 Space game p. 425/262Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.T.G. lesson # 8-19; 23-28; Space game p. 425/26Work with equal groups of objects to gain foundations for multiplicationT.G. lessons # 117-123 ; 134 Multiplication Table Game p.421/223Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s. Write an equation to express an even number as a sum of two equal addends.T.G. lessons # 9; 102-1054Use addition to find the total number objects arranged in rectangular arrays with up to 5 rows and up to 5 columns Write an equation to express the total as a sum of equal addends.T.G. lessons # 117-122; T.G. lessons #123-1242.NBTNumber and Operation in Base Ten Understand place value1Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:T.G. lessons # 36-38; 48; 92a. 100 can be thought of as a bundle of ten tens- called a hundred.Get 100 by Tens or Ones game p.76 b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Get to 100 by Tens or Ones game p. 762Count within 1000; skip-count by 5s, 10s, and 100s.T.G. lesson # 38; 48; 58; 138-139; 152 Get to 100 by Tens or Ones game p. 763Read and write numbers to 1000 using base-ten numerals, number names, and expanded formT.G. lesson# 48-52; 138-1394Compare two three-digit numbers based on meaning of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisonsT.G. lesson #91Use place value understanding and properties of operations to add and subtract.T.G. lesson# 48-52; 138-139 Checkbook Game p.411/4125Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.T.G. lesson # 150 Checkbook Game p.411/4126Add up to four two-digit numbers using strategies based on place value and properties of operations.T.G. lesson# 153-154,156-57; Four Digit Addition game p.156 Make 1000 game p.3387Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction: relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. T.G. lesson# 153-154,156-57; 155-157 Four Cubes from 10,000 to 0 p.354 Make 1000 game p.3388Mentally add 10 or 100 to given number 100-900; and mentally subtract 10 or 100 from a given number 100-900.T.G. lessons # 36-38 Get to 100 by Tens or Ones Game p. 76 9 Explain why addition and subtraction strategies work, using place value and the properties of operations. T.G. lessons # 6-17; 2.MDMeasurement and Data Measure and estimate lengths in standard units.1Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapesMeasurement game p. 419/20 2 Measure the length of an object twice using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.3Estimate lengths using units of inches, feet, centimeters, and meters.Find the Distance game p.413/4144Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.T.G. lessons # 39-44 Measurement Game p.244Relate addition and subtraction to lengthT.G. lessons # 39-44 Measurement Game p.2445Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.T.G. lessons # 39-44 Measurement Game p.2446 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, , and represent whole-number sums and differences within 100 on a number line diagram.T.G. lessons # 39-44 Measurement Game p.244Work with time and money7Tell and write the time from analog and digital clocks to nearest five minutes, using a.m. and p.m.T.G. lessons # 70-72; 93-95 Time Game p.427/288Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and cent symbols appropriately. Ex., if you have 2 dimes and 3 pennies, how many cents do you have?Rummage Sale game p. 423/24 Yard Sale game p.429/30 Represent and interpret data 9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. Find the Distance game p.413/414 Map Game p. 418 10 Draw a picture graph and bar graph (with single-unit scale) to represent a data set with up to four catergories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph.2.GGeometry Reason with shapes and their attributes1Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.Fraction Game p. 4152Partition a rectangle into rows and columns of same-size squares and count to find total number of them. Fraction Game p. 4153Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.T.G. lessons # 73-78Fraction Game p. 415 Thinking Stories Thinking Story Problems are word problems that provide valuable problem solving practice. Some lessons include only Thinking Story problems, and some include both a story and a set of problems. Some of the problems relate to the accompanying stories, but others extend to new and different situations. Thinking Story Problems-choose one or two problems to do each day before the lesson begins. Kindergarten: K.CC: (Counting and Cardinality) pp. 17d; 33b; 39b; 51b; 69b; 75b; 79b; 119b; 123b; 127b; 129b; 143b; 151b; 153b; 161b; 171b; 195b; 205b; 207b; 217b; K.OA: (Operations and Algebraic Thinking) pp. 17d; 33b; 39b; 47b; 51b; 55b; 61b; 69b; 75b; 85d; 95bl 113bl 119b; 123b; 127b; 129b; 139b; 143b; 151b; 153b; 157b; 171b; 185b; 195b; 199b; 205b; 207b; 215b; 217b; 219b K.MD: (Measurement and Data) pp. 43b; 47b; 65b; 75b; 101b; 147b; 149b; 163b; 179b; 207b211b; 215b K.G (Geometry) pp. 145b; 161b; 167b; 173b; 175b; 199b; 213b First Grade: 1.OA (Operations and Algebraic Thinking) pp. 10a-d; 26a-d; 52a-d; 64a-d; 76a-d; 96a-d; 116a-d; 144a-d; 164a-d; 196a-d; 210a-d; 228a-d; 248a-d; 274c-f; 330a-d 1.NBT (Number and Operations in Base Ten) pp. 64a-d; 116a-d; 154a-d; 164a-d; 196a-d; 330a-d; 1.MD (Measurement and Data) pp. 130a-d; 154a-d; 196a-d; 228a-d; 248a-d:296a-d; 314a-d Second Grade: 2.OA (Operations and Algebraic Thinking) pp. 24a-d;58a-d; 76a-d; 88a-d; 128a-d; 144a-d; 158a-d; 170a-d; 218a-d; 268a-d; 284a-d; 300a-d; 2.NBT (Numbers and Operations in Base Ten) 24a-d; 46a-d; 188a-d; 204a-d; 218a-d; 2.MD (Measurement and Data) pp. 8a-d; 88a-d;110a-d; 144a-d; 188a-d; 204a-d; 218a-d; 236a-d; 248a-d; 268a-d; 284a-d; 300a-d; 2.G (Geometry) pp. 88a-d; 236a-d; 320a-d; Assessments Minimally teachers should use assessments included in the district approved text book/teachers guides. These include pre-knowledge, mastery checkpoints, mid-unit assessments, and end-of-unit assessments. Additionally, periodic benchmarks will be administered throughout the school year. Additional Resources 1.) Teachers should utilize SMARTboard tools. There are a wealth of visual aids and manipulative tools, too numerous to list, available using SMART technology. Open a SMARTnotebook file. Click on the 2nd icon down on the left. It looks like a picture frame. Then choose Gallery Essentials. Expand and select Mathematics. This is where you can find a great number of useful tools, separated by content type. 2.) Additional lesson ideas can be found at http://exchange.smarttech.com. This is a web based collection of lessons that other teachers have created using SMARTtechnology. There is a wealth of lessons here to choose from in all disciplines. As with any lesson, teachers are advised to preview the content for accuracy and grade level appropriateness before using. Go to http://exchange.smarttech.com Search by lesson content or browse by grade level or even by Common Core Standard 3.) Mailbox Magazine. There are many ideas for math centers, small and whole group instruction, as well as supplemental activities in Mailbox Magazine. Subscriptions for all grade levels are available through the ATS libraries. See library clerk for assistance. 4.) Additional instruction strategies can be found in the following cited mathematics teaching methodologies textbooks: Cathcart, W. George, Pothier, Yvonne M., Vance, James H., Bezuk, Nadine S. (2006). Learning Mathematics in Elementary and Middle Schools. Upper Saddle River, NJ: Pearson Merrill Prentice Hall. Van De Walle, John A. (2004). Elementary and Middle School Mathematics: Teaching Developmentally. Boston, MA: Pearson Education, Inc. Van De Walle, John A. (1990). Elementary School Mathematics: Teaching Developmentally. White Plains, NY: Longman. 5) There is also a wealth of materials, manipulative and written, available in the Math Lab, room 147 at ATS. l n @ g ? 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