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Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Addition and NNSO 2-6(H). Model, represent and Addend Grade 2 Content: SF Chapter 1, Subtraction Concepts explain subtraction as comparison, take- Sum Lessons 1,2,4,5,6,8,9,10,11 away and part-to-whole; e.g., solve Altogether Quarter 1 missing addend problems by counting Difference Problem Solving and Applications: SF (September) up or subtracting, such as “I had six Related fact Chapter 1, Lessons 3,7,12 baseball cards, my sister gave me more, Fact family 13 days and I now have ten. How many did she Addition Investigations Blending Units: Coins, give me?” can be represented as 6 + ? = Subtraction Coupons, and Combinations; Putting 10 or 10 - 6 = ?. Commutative (order) Together and Taking Apart property NNSO 2-9(M). Model and use the Short or related lessons can be commutative property for addition. combined to allow for blending of Investigations activities. NNSO 2-10(K). Demonstrate fluency in addition facts with addends through 9 See page 29 of the Joint Usage Plan to and corresponding subtractions; e.g., 9 identify activities that can be blended + 9 = 18, 18 – 9 = 9. from Investigations. Consider which SF lessons can be replaced by the PFA 2-4(D). Use objects, pictures, respective Investigations activities. numbers and other symbols to represent a problem situation. PFA 2-5(E). Understand equivalence and extend the concept to situations involving symbols; e.g., 4 + 5 = 9 and 9 = 4 + 5, and 4 + 5 = 3 + 6 = ∆ + □… NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 1 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Addition and NNSO 2-6(H). Model, represent and Add Grade 2 Content: SF Chapter 2, Subtraction Facts explain subtraction as comparison, take- Count on Lessons 1,2,3,4,5,6,8,9,10 away and part-to-whole; e.g., solve Sum Quarter 1 missing addend problems by counting Doubles fact Problem Solving and Applications: SF (September/October) up or subtracting, such as “I had six Addition fact Chapter 2, Lessons 7,11,12 baseball cards, my sister gave me more, Addend 13 days and I now have ten. How many did she Doubles plus 1 Investigations Blending Units: Coins, give me?” can be represented as 6 + ? = Number sentence Coupons, and Combinations; Putting 10 or 10 - 6 = ?. Count back Together and Taking Apart Subtract NNSO 2-9(M). Model and use the Commutative Short or related lessons can be commutative property for addition. property combined to allow for blending of Data table Investigations activities. NNSO 2-10(K). Demonstrate fluency in Data chart addition facts with addends through 9 See page 30 of the Joint Usage Plan to and corresponding subtractions; e.g., 9 identify activities that can be blended + 9 = 18, 18 – 9 = 9. from Investigations. Consider which SF lessons can be replaced by the PFA 2-4(D). Use objects, pictures, respective Investigations activities. numbers and other symbols to represent a problem situation. PFA 2-5(E). Understand equivalence and extend the concept to situations involving symbols; e.g., 4 + 5 = 9 and 9 = 4 + 5, and 4 + 5 = 3 + 6 = ∆ + □… PFA 2-6(F). Use symbols to represent unknown quantities and identify values for symbols in an expression or equation using addition and subtraction; e.g., □ + О = 10, ∆ - 2 = 4. DAP 2-2(C). Read, interpret and make comparisons and predictions from data represented in charts, line plots, picture graphs and bar graphs. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 2 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Place Value (to 100) NNSO 2-1.(A,B)Use place value Tens Grade 2 Content: SF Chapter 3, Money concepts to represent, compare and Ones Lessons 1,2,3,6,7,8,9,12,13,14,17,18 order whole numbers using physical Digit Quarter 1 models, numerals and words, with ones, Place value Problem Solving and Applications: SF (October) tens and hundreds. For example: Number word Chapter 3, Lessons 3,11,19 a. Recognize 10 can mean “10 ones” Organized list 20 days or a single entity (1 ten) through Greater than (>) Investigations Blending Units: Coins, physical models and trading Less than (<) Coupons, and Combinations; Putting games. Equal to (+) Together and Taking Apart b. b. Read and write 3-digit numerals About (e.g., 243 as two hundred forty Closest Short or related lessons can be three, 24 tens and 3 ones, or 2 Before combined to allow for blending of hundreds and 43 ones, etc.) and After Investigations activities. construct models to represent Between each. Skip counting See page 31-32 of the Joint Usage Plan Pattern to identify activities that can be blended NNSO 2-2(B) Recognize and classify Even from Investigations. Consider which SF numbers as even or odd. Odd lessons can be replaced by the Ordinal number respective Investigations activities. NNSO 2-3(E) Count money and make Coin change using coins and a dollar bill. Cent (¢) Dime NNSO 2-4(D) Represent and write the Nickel value of money using the ¢ sign and in Penny decimal form when using the $ sign. Quarter Half-dollar NNSO 2-10(K) Demonstrate fluency in Greatest value addition facts with addends through 9 Least value and corresponding subtractions; e.g., 9 Table + 9 = 18, 18 – 9 = 9. Tally mark Record PFA 2-1(B) Extend simple number Change patterns (both repeating and growing Price patterns), and create similar patterns Dollar bill using different objects, such as using Dollar coin physical materials or shapes to Dollar sign ($) represent numerical patterns. Decimal point (.) NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 3 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Addition and NNSO 2-1(A,B) Use place value concepts to represent, Mental math Grade 2 Content: SF Chapter 4, Subtraction compare and order whole numbers using physical Tens digit Lessons 1,2,3,4,5,6,7,9,10 (Mental Math) models, numerals and words, with ones, tens and Ones digit hundreds. For example: Estimate Problem Solving and Applications: SF a. Recognize 10 can mean “10 ones” or a single entity Quarter 2 (1 ten) through physical models and trading games. More Chapter 4, Lessons 8,11,12 (November) b. b. Read and write 3-digit numerals (e.g., 243 as two Less hundred forty three, 24 tens and 3 ones, or 2 Revise Investigations Blending Units: Putting 13 days hundreds and 43 ones, etc.) and construct models to Pattern Together and Taking Apart represent each. Short or related lessons can be NNSO 2-6(H) Model, represent and explain subtraction combined to allow for blending of as comparison, take-away and part-to-whole; e.g., solve Investigations activities. missing addend problems by counting up or subtracting, such as “I had six baseball cards, my sister gave me more, and I now have ten. How many did she give me?” See page 32 of the Joint Usage Plan to can be represented as 6 + ? = 10 or 10 - 6 = ?. identify activities that can be blended from Investigations. Consider which SF NNSO 2-10(K) Demonstrate fluency in addition facts with lessons can be replaced by the addends through 9 and corresponding subtractions; e.g., respective Investigations activities. 9 + 9 = 18, 18 – 9 = 9. NNSO 2-11(L) Add and subtract multiples of 10. NNSO 2-12 Demonstrate multiple strategies for adding and subtracting 2- or 3-digit whole numbers, such as: a. compatible numbers; b. compensatory numbers; c. informal use of commutative and associative properties of addition. NNSO 2-13(3/4B) Estimate the results of whole number addition and subtraction problems using front-end estimation, and judge the reasonableness of the answers. PFA 2-1(B) Extend simple number patterns (both repeating and growing patterns), and create similar patterns using different objects, such as using physical materials or shapes to represent numerical patterns. PFA 2-3(C) Create new patterns with consistent rules or plans, and describe the rule or general plan of existing patterns. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 4 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Two Digit Addition NNSO 2-4(D) Represent and write the Add Grade 2 Content: SF Chapter 5, value of money using the ¢ sign and in Regroup Lessons 1,2,3,4,5,6,8,9 Quarter 2 decimal form when using the $ sign. Sum (November/ Two digit number Problem Solving and Applications: SF December) NNSO 2-9(M) Model and use the Table Chapter 5, Lessons 7,10,11 commutative property for addition. Data 13 days Estimate Investigations Blending Units: Putting NNSO 2-12 Demonstrate multiple Together and Taking Apart strategies for adding and subtracting 2- or 3-digit whole numbers, such as: Short or related lessons can be a. compatible numbers; combined to allow for blending of b. compensatory numbers; Investigations activities. c. informal use of commutative and associative properties of addition. See page 33 of the Joint Usage Plan to identify activities that can be blended NNSO 2-13(3/4B) Estimate the results from Investigations. Consider which SF of whole number addition and lessons can be replaced by the subtraction problems using front-end respective Investigations activities. estimation, and judge the reasonableness of the answers. PFA 2-4(D) Use objects, pictures, numbers and other symbols to represent a problem situation. DAP 2-2(C) Read, interpret and make comparisons and predictions from data represented in charts, line plots, picture graphs and bar graphs. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 5 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Two Digit Subtraction NNSO 2-4(D) Represent and write the Subtract Grade 2 Content: SF Chapter 6, value of money using the ¢ sign and in Regroup Lessons 1,2,3,4,6,7,8 Quarter 2 decimal form when using the $ sign. Difference (December/January) Number sentence Problem Solving and Applications: SF NNSO 2-6(H) Model, represent and Price Chapter 6, Lessons 5,10,11 13 days explain subtraction as comparison, take- Change away and part-to-whole; e.g., solve Estimate Investigations Blending Units: Putting missing addend problems by counting Information Together and Taking Apart up or subtracting, such as “I had six baseball cards, my sister gave me more, Short or related lessons can be and I now have ten. How many did she combined to allow for blending of give me?” can be represented as 6 + ? = Investigations activities. 10 or 10 - 6 = ?. See page 33-34 of the Joint Usage Plan NNSO 2-11(L) Add and subtract to identify activities that can be blended multiples of 10. from Investigations. Consider which SF lessons can be replaced by the NNSO 2-12(M) Demonstrate multiple respective Investigations activities. strategies for adding and subtracting 2- or 3-digit whole numbers, such as: a. compatible numbers; b. compensatory numbers; c. informal use of commutative and associative properties of addition. NNSO 2-13(3/4B) Estimate the results of whole number addition and subtraction problems using front-end estimation, and judge the reasonableness of the answers. PFA 2-4(D) Use objects, pictures, numbers and other symbols to represent a problem situation. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 6 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Geometry and GSS 2-1(A,B,C) Identify, describe, compare and sort Solid figure Grade 2 Content: SF Chapter 7, Fractions three-dimensional objects (i.e., cubes, spheres, Cube Lessons 1,4,5,7,10,11,12,13 prisms, cones, cylinders and pyramids) according to Rectangular prism the shape of the faces or the number of faces, edges Quarter 3 Sphere Problem Solving and Applications: SF or vertices. (January/February) Pyramid Chapter 7, Lessons 3,8,14 GSS 2-2(A) Predict what new shapes will be formed Cylinder 16 days by combining or cutting apart existing shapes. Cone Investigations Blending Units: Shapes, Flat surface Halves and Symmetry GSS 2-3(E) Recognize two-dimensional shapes and Vertex three-dimensional objects from different positions. Vertices Short or related lessons can be Edge combined to allow for blending of GSS 2-(D) Identify and determine whether two- Plane shape Investigations activities. dimensional shapes are congruent (same shape and size) or similar (same shape different size) by copying Circle or using superposition (lay one thing on top of Square See page 34-35 of the Joint Usage Plan another). Triangle to identify activities that can be blended Rectangle from Investigations. Consider which SF GSS 2-5(G) Create and identify two-dimensional Trapezoid lessons can be replaced by the figures with line symmetry; e.g., what letter shapes, Parallelogram respective Investigations activities. logos, polygons are symmetrical? Hexagon Side NNSO 2-5(C) Represent fractions (halves, thirds, fourths, sixths and eighths), using words, numerals Angle and physical models. For example: Congruent a. Recognize that a fractional part can mean Line of symmetry different amounts depending on the original Equal quantity. Halves b. Recognize that a fractional part of a rectangle Thirds does not have to be shaded with contiguous Fourths parts. Unequal c. Identify and illustrate parts of a whole and parts of sets of objects. Fraction d. Compare and order physical models of halves, Estimate thirds and fourths in relation to 0 and 1. NNSO 2-7(I) Model, represent and explain multiplication as repeated addition, rectangular arrays and skip counting. PFA 2-4(D) Use objects, pictures, numbers and other symbols to represent a problem situation. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 7 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Time, Data and M 2-1(B) Identify and select appropriate Hour hand Grade 2 Content: SF Chapter 8, Graphs units of measure for: Minute hand Lessons 1,2,3,6,10,12,13, a. length – centimeters, meters, Hour Quarter 3 inches, feet or yards; Half hour Problem Solving and Applications: SF (February) b. volume (capacity) – liters, cups, Quarter past Chapter 8, Lessons 9,16,17 pints or quarts; Half past 18 days c. weight – grams, ounces or pounds; After Investigations Blending Units: Timelines d. time – hours, half-hours, quarter- Before and Rhythm Patterns, How Many hours or minutes and time Quarter to Pockets? How Many Teeth?, Does It designations, a.m. or p.m. Midnight Walk, Swim or Crawl? a.m. M 2-4(C) Tell time to the nearest minute noon Short or related lessons can be interval on digital and to the nearest 5 p.m. combined to allow for blending of minute interval on analog (dial) Survey Investigations activities. timepieces. Data Pictograph See page 35-36 of the Joint Usage Plan DAP 2-1(A,B) Pose questions, use Bar graph to identify activities that can be blended observations, interviews and surveys to from Investigations. Consider which SF collect data, and organize data in charts, lessons can be replaced by the picture graphs and bar graphs. respective Investigations activities. DAP 2-2(C) Read, interpret and make Note that much of this chapter is review comparisons and predictions from data of content from previous grades and a rd represented in charts, line plots, picture preview of 3 grade content. graphs and bar graphs. Instruction and use of the textbook should be adjusted to allow the chapter DAP 2-4(B) Write a few sentences to to be “streamlined”. describe and compare categories of data represented in a chart or graph, and make statements about the data as a whole. DAP 2-6(A) Recognize that data may vary from one population to another; e.g., favorite TV shows of students and of parents. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 8 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Measurement and M 2-1(B) Identify and select appropriate units Inch Grade 2 Content: SF Chapter 9, Probability of measure for: Ruler Lessons 2,3,4,6,7,11,12,14 a. length – centimeters, meters, inches, feet Foot Quarter 3 or yards; Width Problem Solving and Applications: SF (March) b. volume (capacity) – liters, cups, pints or Yard Chapter 9, Lessons 5,16,17 quarts; Yardstick c. weight – grams, ounces or pounds; Centimeter Investigations Blending Units: How 20 days d. time – hours, half-hours, quarter-hours or Centimeter ruler Long? How Far?, How Many Pockets? minutes and time designations, a.m. or Meter How Many Teeth?, Things That Come p.m. Meter stick In Groups, Exploring Boxes and Solids Capacity M 2-2(C) Establish personal or common Cup Short or related lessons can be referents for units of measure to make Pint combined to allow for blending of estimates and comparisons; e.g., the width of Quart Investigations activities. a finger is a centimeter, a large bottle of soda Pound pop is 2 liters, a small paper clip weighs about Ounce See page 36-37 of the Joint Usage Plan one gram. Kilogram to identify activities that can be blended Gram from Investigations. Consider which SF M 2-3(E) Describe and compare the Predict lessons can be replaced by the relationships among units of measure, such More likely respective Investigations activities. as centimeters and meters; inches, feet and Less likely yards; cups, pints and quarts; ounces and Equally likely Note that much of this chapter is review pounds; and hours, half-hours, and quarter- of content from previous grades and a rd hours; e.g., how many inches in a foot? preview of 3 grade content. Instruction and use of the textbook M 2-5(D) Estimate and measure the length should be adjusted to allow the chapter and weight of common objects, using metric to be “streamlined”. and U.S. customary units, accurate to the nearest unit. M 2-6(D) Select and use appropriate measurement tools; e.g., a ruler to draw a segment 3 inches long, a measuring cup to place 2 cups of rice in a bowl, a scale to weigh 50 grams of candy. PFA 2-4(D) Use objects, pictures, numbers and other symbols to represent a problem situation. DAP 2-7(D) List some of the possible outcomes of a simple experiment, and predict whether given outcomes are more, less or equally likely to occur. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 9 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Numbers to 1000 NNSO 2-1(A,B) Use place value concepts to Hundreds Grade 2 Content: SF Chapter 10, represent, compare and order whole numbers Thousands Lessons 1,2,3,4,6,8,9 Quarter 4 using physical models, numerals and words, Three digit number (April) with ones, tens and hundreds. For example: Digit Problem Solving and Applications: SF a. Recognize 10 can mean “10 ones” or a Expanded form Chapter 10, Lessons 7,10,11 12 days single entity (1 ten) through physical Standard form models and trading games. Number form Investigations Blending Units: Coins, b. Read and write 3-digit numerals (e.g., 243 Mental math Coupons and Combinations, Putting as two hundred forty three, 24 tens and 3 Chart together and Taking Apart ones, or 2 hundreds and 43 ones, etc.) and Data construct models to represent each. Before Short or related lessons can be After combined to allow for blending of NNSO 2-11(L) Add and subtract multiples of 10. Between Investigations activities. Order NNSO 2-12(M) Demonstrate multiple strategies Least See page 37-38 of the Joint Usage Plan for adding and subtracting 2- or 3-digit whole Greatest to identify activities that can be blended numbers, such as: Pattern from Investigations. Consider which SF a. compatible numbers; Increase lessons can be replaced by the b. compensatory numbers; Decrease respective Investigations activities. c. informal use of commutative and associative properties of addition. PFA 2-1(B) Extend simple number patterns (both repeating and growing patterns), and create similar patterns using different objects, such as using physical materials or shapes to represent numerical patterns. PFA 2-2(C) Use patterns to make generalizations and predictions; e.g., determine a missing element in a pattern. PFA 2-3(C) Create new patterns with consistent rules or plans, and describe the rule or general plan of existing patterns. DAP 2-2(C) Read, interpret and make comparisons and predictions from data represented in charts, line plots, picture graphs and bar graphs. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 10 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources 3 Digit Addition and NNSO 2-11(L) Add and subtract Three digit number Grade 2 Content: SF Chapter 11, Subtraction multiples of 10. Estimate Lessons 1,2,3,4,5,7,8,910,11 Regroup Quarter 4 NNSO 2-12(M) Demonstrate multiple Problem Solving and Applications: SF (April/May) strategies for adding and subtracting 2- Chapter 11, Lessons 6,12,13 or 3-digit whole numbers, such as: 15 days a. compatible numbers; Investigations Blending Units: Putting b. compensatory numbers; Together and Taking Apart c. informal use of commutative and associative properties of addition. Short or related lessons can be combined to allow for blending of NNSO 2-13(3/4B) Estimate the results Investigations activities. of whole number addition and subtraction problems using front-end See page 38-39 of the Joint Usage Plan estimation, and judge the to identify activities that can be blended reasonableness of the answers. from Investigations. Consider which SF lessons can be replaced by the PFA 2-5(E) Understand equivalence and respective Investigations activities. extend the concept to situations involving symbols; e.g., 4 + 5 = 9 and 9 = 4 + 5, and 4 + 5 = 3 + 6 = ∆ + □… DAP 2-2(C) Read, interpret and make comparisons and predictions from data represented in charts, line plots, picture graphs and bar graphs. DAP 2-4(B) Write a few sentences to describe and compare categories of data represented in a chart or graph, and make statements about the data as a whole. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 11 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006 Grade 2 Math Curriculum Map Hamilton City School District Content and Pacing Grade Level Indicator (Benchmark) Assessment Vocabulary Resources Introduction to NNSO 2-7(I) Model, represent and Equal groups Grade 2 Content: SF Chapter 12, Multiplication and explain multiplication as repeated Multiply Lessons 1,2,3,4,7,8, Division addition, rectangular arrays and skip Multiplication counting. sentence Problem Solving and Applications: SF Quarter 3 Times Chapter 12, Lessons 6,9,10 (May) NNSO 2-8(J) Model, represent and Product explain division as sharing equally and Array Investigations Blending Units: 12 days repeated subtraction. Factor Landmarks in the Hundreds, Things that Equal share Come in Groups PFA 2-4(D) Use objects, pictures, Divide numbers and other symbols to represent Division sentence Short or related lessons can be a problem situation. Divided by combined to allow for blending of Investigations activities. See page 39 of the Joint Usage Plan to identify activities that can be blended from Investigations. Consider which SF lessons can be replaced by the respective Investigations activities. NNSO: Number, Number Sense and Operations M: Measurement GSS: Geometry and Spatial Sense 12 PFA: Patterns, Functions and Algebra DAP: Data Analysis and Probability August 2006