Gewertz, C. (August 25, 2010). “Curriculum Producers Work to Reflect Common Standards.” Education Week, 30(1), 1, 20-21. National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: The Council. National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: The Council. National Council of Teachers of Mathematics (2009). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: The Council. National Council of Teachers of Mathematics (2011). Focus in High School Mathematics: Fostering Reasoning and Sense Making for All Students. Reston, VA: The Council. User’s Guide CCSS Mathematics Curriculum Materials Analysis Project
CCSS Grade 3 CCSS Grade 4 CCSS Grade 5 3.NBT Number and Operations in Base Ten Chap. Pages Cont N-L-M- A-H Bal N-L-M- A-H 4.NBT Number and Operations in Base Ten Chap. Pages Cont N-L-M- A-H Bal N-L-M- A-H 5.NBT Number and Operations in Base Ten Chap. Cont N-L-M- A-H Bal N-L-M- A-H Generalize place value understanding for multi-digit whole numbers. Understand the place value system 2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 3. Read, write, and compare decimals to 1000ths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4. Use place value understanding to round decimals to any place. Use place value understanding and properties of operations perform multi-digit arithmetic Use value understanding and properties of operations to perform multi-digit arithmetic. Perform operations with multi-digit whole numbers and with decimals to hundredths. 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 4. Fluently add and subtract whole numbers using the standard algorithm. 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. 5, Multiply a whole number of up to four digits by a one-digit whole Number and multiply two numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 5. Fluently multiply multi-digit whole numbers using the standard algorithm.
Curriculum Analysis Tool 1—Number and Operations for in Base 10 for Grades 3-5 Use place value understanding and properties of operations perform multi-digit arithmetic. Chap. Pages Cont N-L-M- A-H Bal N-L-M- A-H Use place value understanding and properties of operations to perform multi-digit arithmetic. Chap. Pages Cont N-L-M- A-H Bal N-L-M- A-H Perform operations with whole numbers and with decimals to hundredths. Chap. Pages Cont N-L-M- A-H Bal N-L-M- A-H 6. Find whole-number quotients and remainders with up to dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 7. Add, subtract, multiply, and divide decimals to hundredths, 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. and Examples Overall Impressions: What are your overall impressions of the curriculum materials examined? Balance between Mathematical Understanding and Procedural Skills:
CCSSM Grade K CCSSM Grade 1 CCSSM Grade 2 Cont N-L-M- A-H Bal N-L-M- A-H Represent and solve problems involving addition and subtraction Cont N-L-M- A-H Bal N-L-M- A-H Represent and solve problems involving addition and subtraction Cont N-L-M- A-H Bal N-L-M- A-H 2. Solve addition and subtraction word problems, and add and subtract within 10. 1. Use 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. 2. word problems that call for addition of three whole numbers whose sum is less than or equal to 20. 1. Use 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. Work with addition and subtraction equations 7. Understand 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. 8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
CCSSM Grade 3 CCSSM Grade 4 Grade 5 3.OA Operations and Algebraic Thinking Cont N-L-M- A-H Bal N-L-M- A-H 4.OA Operations and Algebraic Thinking Cont N-L-M- A-H Bal N-L-M- A-H 5.OA Operations and Algebraic Thinking Chap Pages Cont N-L-M- A-H Bal N-L-M- A-H 4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of these equations: 8 x ? = 48, 5 = 3, 6 x 6 = ?. Understand properties of multiplication and the relationship between multiplication and division Gain familiarity with factors and multiples. 5. Apply properties of operations as strategies to multiply and divide. Examples: Commutative Property of Multiplication; Associative Property of Multiplication; Distributive Property). 4. Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. 6. Understand division as an unknown-factor problem. Multiply and Divide 7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8). Know from memory all products of 2 numbers) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit number. Chap
Curriculum Analysis Tool 1—Geometry for Grades K-2 CCSSM Grade K CCSSM Grade 1 CCSSM Grade 2 Analyze, compare, create, and compose shapes Cont N-L-M- A-H Bal N-L-M- A-H Reason with shapes and their attributes Cont N-L-M- A-H Bal N-L-M- A-H Reason with shapes and their attributes Cont N-L-M- A-H Bal N-L-M- A-H 4. Analyze and compare 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). 5. Model shapes in the world by building shapes from components (sticks and clay balls) and drawing shapes. 6. Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” 2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or 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. 2. Partition a rectangle into rows and columns of the same-size squares and count to find the total number of them. 3. Partition 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 that for these examples that decomposing into more equal shares creates smaller shares. 3. Partition 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. Notes/Examples CCSSM Curriculum Analysis Tool 1—Geometry for Grades K-2 Pages Pages
Overall Impressions: What are your overall impressions of the curriculum materials examined? What are the strengths and weaknesses of the materials you examined? Standards Alignment: Have you identified gaps within this domain? What are they? If so, can these gaps be realistically addressed through supplementation? 4. Within grade levels, do the curriculum materials provide sufficient experiences to support student learning within this standard? 5. Within this domain, is the treatment of the content across grade levels consistent with the progression within the Standards? Balance between Mathematical Understanding and Procedural Skills: 6. Do the curriculum materials support the development of students’ mathematical understanding? Do the curriculum materials support the development of students’ proficiency with procedural skills? Do the curriculum materials assist students in building connections between mathematical understanding and procedural skills? To what extent do the curriculum materials provide a balanced on mathematical understanding and procedural skills? Do student activities build on each other within and across grades in a logical way that supports mathematical understanding and procedural skills? CCSS Curriculum Analysis Tool 1—Geometry for Grades 3-5
6.EE Expressions and Equations Cont N-L-M- A-H Bal N-L-M- A-H 7.EE Expressions and Equations Cont N-L-M- A-H Bal N-L-M- A-H 8.EE Expressions and Equations Cont Bal Apply and extend previous understandings of arithmetic to algebraic expressions Use properties of operations to generate equivalent expressions Work with radicals and integer exponents 2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. b. Identify parts of an expression using mathematical terms (sum, term, product, quotient, coefficient); view one or more parts of an expression as a single entity. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations that include exponents, in the order when there are no parentheses to specify order. 1. properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property or properties of operations. 2. Understand that rewriting an expression in different in a problem context can shed light on the problem and how the quantities are related. 4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). 6. Use variables to represent numbers and expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or any number in a specified set. CCSSM Curriculum Analysis Tool 1—Expressions and Equations for Grades 6-8 Grade 6 CCSSM Grade 7 CCSSM Grade 8
6.SP Statistics and Probability Pages Cont N-L-M- A-H Bal N-L-M- A-H 7.SP Statistics and Probability Chap Pages Content N-L-M- A-H Bal N-L-M- A-H 8.SP Statistics and Probability Chap Page Cont N-L-M- A-H Bal N-L-M- A-H Summarize and describe distributions. 4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 5. Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations; b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement; c. giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered; and d. relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Investigate chance processes and develop, use, and evaluate probability models 5. Understand that the probability of a chance event is a between 0 and 1 and expresses the likelihood of the event. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is not unlikely or likely, and a probability near 1 indicates a likely event. CCSSM Curriculum Analysis Tool 1—Statistics and Probability for Grades 6-8 CCSSM Grade 6 CCSSM Grade 7 Grade 8
domain on which it is always increasing or always decreasing allows its inverse to be constructed. CCSS Curriculum Analysis Tool 1—Similarity, Right Triangles, and Trigonometry & Trigonometric Functions in Grades 9-12 CCSSM Standards Grades 9-12 Chapter pages Cont N-L-M- A-H Bal N-L-M- A-H Notes/Explanation (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. ★ Prove and apply trigonometric identities Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. Overall Impressions: What are your overall impressions of the curriculum materials examined? What are the strengths and weaknesses of the materials you examined? Standards Alignment: Have you identified gaps within this domain? What are they? If so, can these gaps be realistically addressed through supplementation? Within grade levels, do the curriculum materials provide sufficient experiences to support student learning within this standard? Within this domain, is the treatment of the content across grade levels consistent with the progression within the Standards? Balance between Mathematical Understanding and Procedural Skills Do the curriculum materials support the development of students’ mathematical understanding? Do the curriculum materials support the development of students’ proficiency with procedural skills? Do the curriculum materials assist students in building connections between mathematical understanding and procedural skills? To what extent do the curriculum materials provide a balanced focus on mathematical understanding and procedural skills? Do student activities build on each other within and across grades in a logical way that supports mathematical understanding and procedural skills?