Math Curriculum - Allamuchy Township School District



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 District’s 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 |Strand |Behavioral Objective/ |Activity |

|Grade K | |CPI | |

| | |Counting and Cardinality |T.G. lessons #16,17; 21,22; 24; 38,39; 40 |

| | |Know number names and count sequences. |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 activity |

| |1 |Count to 100 by ones and tens |Use # chart to highlight 10, 20, 30, etc… |

| | | |Practice sheets; |

| | | |T.G. lessons # 38,39 |

| |2 |Count forward beginning from a given number within the known |Duck Pond Game p.244/45 |

| | |sequence (instead of having to begin at 10) |Pattern Game p.247/48 |

| |3 |Write numbers from 0 to 20. Represent a number of objects with |T.G. lessons #17; 22; 39; |

| | |a |Number writing practice sheets |

| | |written numeral 0-20 (with 0 representing a count of no |Wiki sticks, sandwriting, etc... |

| | |objects). | |

| | |Count to tell the number of objects. | |

| |4 |Understand the relationship between numbers and quantities; |T.G. lessons # 6; 8,9; 13 |

| | |connect counting to cardinality. | |

| | |a. When counting objects, say the number names in the standard |T.G. lessons # 4,5, 6 |

| | |order, pairing each object with one and only one number name | |

| | |and each number name with one and only one object. | |

| | |b. Understand that the last number name said tells the number |T.G. lessons # 4,5; 13 |

| | |of objects counted. The number of objects is the same | |

| | |regardless of their arrangement or the order in which they were| |

| | |counted. | |

| | |c. Understand that each successive number name refers to a |T.G. lesson #14; 18,20 |

| | |quantity that is one larger. | |

| |5 |Count 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 1–20, count out that many objects. | |

| | |Compare numbers. | |

| |6 |Identify whether the number of objects in one group is greater |T.G. lessons #7; 14, 15; 43; 49-54 |

| | |than, less than, or equal to the number of objects in another | |

| | |group, e.g., by using matching and counting strategies.1 | |

| | | | |

| | | | |

| |7 | | |

| | | |T.G lessons # 16,17; 21,22; 24; 38,39; 40 |

| | |Compare two numbers between 1 and 10 presented as written | |

| | |numerals. | |

|K.OA | |Operations and Algebraic Thinking | |

| | |Understand addition as putting together and adding to, and | |

| | |understand subtraction as taking apart and taking from. | |

| |1 |Represent addition and subtraction with objects, fingers, |T.G. lessons # 18, 20; 49-54 |

| | |mental images, drawings2, |Listen &count game (see attached) |

| | |sounds (e.g., claps), acting out situations, verbal |Use number lines, unifix cubes |

| | |explanations, expressions, or equations. | |

| | | |T.G. lesson # 55 |

| |2 | |Duck Pond Game p. 244/45 |

| | |Solve addition and subtraction word problems, and add and |Juggling Game p.246 |

| | |subtract within 10, e.g., by using objects or drawings to | |

| | |represent the problem. | |

| |3 |Decompose numbers less than or equal to 10 into pairs in more |T.G. lesson #56 |

| | |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). | |

| |4 |For any number from 1 to 9, find the number that makes 10 when |T.G. lesson #56 |

| | |added to the given number, e.g., by using objects or drawings, |L.C. “12 Ways to Count to 11” by Eve Merriam |

| | |and record the answer with a drawing or equation. | |

| |5 |Fluently add and subtract within 5. |T.G. lesson # 51,52 |

| | | |Use a number line |

| | | |Duck Pond Game p.244/45 |

| | | |Juggling Game p.246 |

| | | | |

|K.NBT | |Number and Operations in Base Ten | |

| | |Work with numbers 11–19 to gain foundations for place value. | |

| |1 |Compose and decompose numbers from 11 to 19 into ten ones and |T.G. lessons # 38,39 |

| | |some further ones, e.g., by using objects or drawings, and |L.A. connection p. 153 |

| | |record each composition or decomposition by a drawing or |# line game, start at ten add ones |

| | |equation (e.g., 18 = 10 + 8); understand that these numbers are|p.157a Bunches of 10 |

| | |composed of ten ones and one, two, three, four, five, six, | |

| | |seven, eight, or nine ones. | |

| | | | |

|K.MD | |Measurement and Data | |

| | |Describe and compare measurable attributes. | |

| |1 |Describe measurable attributes of objects, such as length or |p.115 review measuring with non-standard units|

| | |weight. |p.117a estimating weight |

| | |Describe several measurable attributes of a single object. |p.117 manipulatives |

| | | |L.C. “Inch by Inch” by Leo Lionni |

| |2 |Directly compare two objects with a measurable attribute in |p.119b Activity |

| | |common, |units of children |

| | |to see which object has “more of”/“less of” the attribute, and |T.S. p119b |

| | |describe |p.123a Warm-up |

| | |the difference. For example, directly compare the heights of |p.123b “What’s My Rule?” game |

| | |two | |

| | |children and describe one child as taller/shorter. | |

| | |Classify objects and count the number of objects in each | |

| | |category. | |

| |3 |Classify objects into given categories; count the numbers of |T.G. lessons # 1-5 |

| | |objects in each category and sort the categories by count. |p.119 math connection |

| | | | |

| | | | |

|K.G | |Geometry | |

| | |Identify and describe shapes (squares, circles, triangles, | |

| | |rectangles, hexagons, cubes, cones, cylinders, and spheres). | |

| |1 |Describe objects in the environment using names of shapes, and |T.G: warm up p. 143a (make shape books) |

| | |describe the relative positions of these objects using terms |p.143 (yarn graph) |

| | |such as: above, below, beside, in front of, behind, and next |p.150 (enrichment page) |

| | |to. | |

| |2 |Correctly name shapes regardless of their orientations or |T.G. lessons # 32-34 |

| | |overall size. |M. activity- geoboards |

| | | |Shape bingo |

| | | |T.G. lessons# 32-34 |

| | | | |

| |3 |Identify shapes as two-dimensional (lying in a plane, “flat”) | |

| | |or threedimensional |M. p.141 review box |

| | |(“solid”). | |

| | |Analyze, compare, create, and compose shapes. | |

| |4 |Analyze and compare two- and three-dimensional shapes, in |T.S. p.139B “guessing game: |

| | |different sizes and orientations, using informal language to |p. 139B A.L. “Boxes” by Rose Griffiths |

| | |describe their similarities, differences, parts (e.g., number | |

| | |of sides and vertices/“corners”) and other attributes (e.g., | |

| | |having sides of equal length). | |

| |5 |Model shapes in the world by building shapes from components |Geoboards/clay shapes |

| | |(e.g., sticks and clay balls) and drawing shapes. | |

| |6 |Compose simple shapes to form larger shapes. For example, “Can |Use attribute blocks to create new shapes |

| | |you | |

| | |join these two triangles with full sides touching to make a | |

| | |rectangle?” | |

| | | | |

|Standard |Strand |Behavioral Objective/ |Resources G = Game |

|Grade 1 | |CPI |L = Lesson in TE |

| | | |NLVM = Nat’l Library of |

| | | |Virtual Manipulatives |

| | | |SBR = Smart Board Resources |

|1.OA | |Operations and Algebraic Thinking | |

| | |Represent and solve problems involving addition and subtraction| |

| |1 |Use addition and subtraction within 20 to solve word problems |NLVM: Number Line Arithmetic |

| | |involving situations of adding to, taking from, putting |G: “What Number Comes Next?” p 30 |

| | |together, taking apart, and comparing, with unknowns in all |G: “What Number Comes Before?” p 32 |

| | |positions, e.g., by using objects, drawings, and equations with|L: 25, 125 |

| | |a symbol for the unknown number to represent the problem. | |

| |2 |Solve word problems that call for addition of three whole |NLVM: Number Line Bars |

| | |numbers whose sum is less than or equal to 20, e.g., by using |L: 47, 72 |

| | |objects, drawings, and equations with a symbol for the unknown | |

| | |number to represent the problem. | |

| | |Understand and apply properties of operations and the | |

| | |relationship between addition and subtraction. | |

| |3 |Apply properties of operations as strategies to add and |L: 28 |

| | |subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is|G: “Four Keys” p 284 |

| | |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.) | |

| |4 |Understand subtraction as an unknown-addend problem. For |G: “Don’t Take Them all Away” p 64 |

| | |example, subtract 10 – 8 by finding the number that makes 10 |L: 26-38, 41-43, 53, 65 |

| | |when added to 8. | |

| | |Add and subtract within 20. | |

| |5 |Relate counting to addition and subtraction (e.g., by counting |L: 26-38, 41-43, 48-49, 51, 76-77, 80 |

| | |on 2 to add 2). |NLVM: Hundreds Chart |

| | | |G: Guess How Many p. 14 |

| | | |G: Count to 20 by Ones and Twos p 167 |

| |6 |Add and subtract within 20, demonstrating fluency for addition |G: “Add the Counters”, p 58 |

| | |and subtraction within 10. Use strategies such as counting on; |G: “Take Away the Counter” p 68 G: “Add or Take Away |

| | |making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing|the Counters” p 72 |

| | |a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 =|G: “Flea Market” Game Mat |

| | |9); using the relationship between addition and subtraction |G: “Roll a Double” p 128 |

| | |(e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and |G: “Roll and Add” p 142 |

| | |creating equivalent but easier or known sums (e.g., adding 6 + |G: “Roll a Ten” p 242 |

| | |7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). |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. | |

| |7 |Understand the meaning of the equal sign, and determine if |NLVM: Number Line Bounce |

| | |equations involving addition and subtraction are true or false.|L: 34-37, 42, 51, 53 |

| | |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. | |

| |8 |Determine the unknown whole number in an addition or |L: 34-35, 52, 60, 66, 102, 128 |

| | |subtraction equation relating three whole numbers. For example,|G: “Guess the Rule” p 184 |

| | |determine the unknown number that makes the equation true in |G: “Hidden Counters Puzzle” p 217 |

| | |each of the equations 8 + |G: “Space” Game Mat |

| | |? = 11, 5 = ������ – 3, 6 + 6 = ������. |G: “Stolen treasure” p 284 |

| | | | |

| | | | |

|1.NBT | |Number and Operations in Base Ten | |

| | |Extend the counting sequence. | |

| |1 |Count to 120, starting at any number less than 120. In this |L: 54-57, 74-75, 84, 91-92, 117 |

| | |range, read and write numerals and represent a number of |G: Get to 100 by Tens or Ones p 266 |

| | |objects with a written numeral. | |

| | |Understand place value. | |

| |2 |Understand that the two digits of a two-digit number represent |NLVM: Base Blocks |

| | |amounts of tens and ones. Understand the following as special |L: 55-57, 75-77, 80, 87-89, 111-113 |

| | |cases: | |

| | |a. 10 can be thought of as a bundle of ten ones — called a |L: 47, 56-57 |

| | |“ten.” |G: “Flea Market” Game Mat |

| | |b. The numbers from 11 to 19 are composed of a ten and one, |L: 56-57, 74-77, 80 |

| | |two, three, four, five, six, seven, eight, or nine ones. | |

| | |c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one,|G: “Macaroni Tens” Game p 246 |

| | |two, three, four, five, six, seven, eight, or nine tens (and 0 |G: School Bookstore Game Mat |

| | |ones). |G: Yard Sale Game Mat |

| | | |L: 87, 111-113, 118 |

| |3 |Compare two two-digit numbers based on meanings of the tens and|G: “Hungry Alligator” Game p 148 |

| | |ones digits, recording the results of comparisons with the |G: “Make the Alligator Tell the Truth” Game p 280 |

| | |symbols >, =, and , =, and < symbols to | |

| | |record the results of comparisons | |

| | |Use place value understanding and properties of operations to |T.G. lesson# 48-52; 138-139 |

| | |add and subtract. |Checkbook Game p.411/412 |

| |5 |Fluently add and subtract within 100 using strategies based on |T.G. lesson # 150 |

| | |place value, properties of operations, and/or the relationship |Checkbook Game p.411/412 |

| | |between addition and subtraction. | |

| |6 |Add up to four two-digit numbers using strategies based on |T.G. lesson# 153-154,156-57; |

| | |place value and properties of operations. |Four Digit Addition game p.156 |

| | | |Make 1000 game p.338 |

| |7 |Add and subtract within 1000, using concrete models or drawings|T.G. lesson# 153-154,156-57; 155-157 |

| | |and strategies based on place value, properties of operations, |Four Cubes from 10,000 to 0 p.354 |

| | |and/or the relationship between addition and subtraction: |Make 1000 game p.338 |

| | |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. | |

| |8 |Mentally add 10 or 100 to given number 100-900; and mentally |T.G. lessons # 36-38 |

| | |subtract 10 or 100 from a given number 100-900. |Get to 100 by Tens or Ones Game p. 76 |

| | | | |

| | | | |

| | | |T.G. lessons # 6-17; |

| |9 |Explain why addition and subtraction strategies work, using | |

| | |place value and the properties of operations. | |

|2.MD | |Measurement and Data | |

| | |Measure and estimate lengths in standard units. | |

| |1 |Measure the length of an object by selecting and using |Measurement game p. 419/20 |

| | |appropriate tools such as rulers, yardsticks, meter sticks, and| |

| | |measuring tapes | |

| | | | |

| | |Measure the length of an object twice using length units of | |

| | |different lengths for the two measurements; describe how the | |

| |2 |two measurements relate to the size of the unit chosen. | |

| |3 |Estimate lengths using units of inches, feet, centimeters, and |Find the Distance game p.413/414 |

| | |meters. | |

| |4 |Measure to determine how much longer one object is than |T.G. lessons # 39-44 |

| | |another, expressing the length difference in terms of a |Measurement Game p.244 |

| | |standard length unit. | |

| | |Relate addition and subtraction to length |T.G. lessons # 39-44 |

| | | |Measurement Game p.244 |

| |5 |Use addition and subtraction within 100 to solve word problems |T.G. lessons # 39-44 |

| | |involving lengths that are given in the same units, e.g., by |Measurement Game p.244 |

| | |using drawings (such as drawings of rulers) and equations with | |

| | |a symbol for the unknown number to represent the problem. | |

| |6 |Represent whole numbers as lengths from 0 on a number line |T.G. lessons # 39-44 |

| | |diagram with equally spaced points corresponding to the numbers|Measurement Game p.244 |

| | |0, 1, 2, …, and represent whole-number sums and differences | |

| | |within 100 on a number line diagram. | |

| | |Work with time and money | |

| |7 |Tell and write the time from analog and digital clocks to |T.G. lessons # 70-72; 93-95 |

| | |nearest five minutes, using a.m. and p.m. |Time Game p.427/28 |

| |8 |Solve word problems involving dollar bills, quarters, dimes, |Rummage Sale game p. 423/24 |

| | |nickels, and pennies, using $ and cent symbols appropriately. |Yard Sale game p.429/30 |

| | |Ex., if you have 2 dimes and 3 pennies, how many cents do you | |

| | |have? | |

| | | | |

| | |Represent and interpret data | |

| | | | |

| | |Generate measurement data by measuring lengths of several | |

| |9 |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.G | |Geometry | |

| | |Reason with shapes and their attributes | |

| |1 |Recognize and draw shapes having specified attributes, such as |Fraction Game p. 415 |

| | |a given number of angles or a given number of equal faces. | |

| | |Identify triangles, quadrilaterals, pentagons, hexagons, and | |

| | |cubes. | |

| |2 |Partition a rectangle into rows and columns of same-size |Fraction Game p. 415 |

| | |squares and count to find total number of them. | |

| |3 |Partition circles and rectangles into two, three, or four equal|T.G. lessons # 73-78Fraction Game p. 415 |

| | |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. | |

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:

: (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/teacher’s 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 . 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

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.

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