Table of Contents Overview of the CCSS Mathematics Curriculum Materials Analysis Project….... 3 Purpose of the Project ……………………………………………………... 4 Development of the Tools……………………………………..…………… 5 User’s Guide ……………………………………………………………………… 9 Too1 1—Mathematics Content Alignment—Grades K-5 …..……………..…..... 16 Number and Operations in Base Ten for Grades K-2 Number and Operations for in Base 10 for Grades 3-5 Operations and Algebraic Thinking for Grades K-2 Operations and Algebraic Thinking for Grades 3-5 Geometry for Grades K-2 Geometry for Grades 3-5 Number and Operations―Fractions for Grades 3 - 5 Tool 1—Mathematics Content Alignment—Grades 6-8………………………… 43 Ratios and Proportional Relationships for Grades 6-8 Geometry for Grades 6-8 Expressions and Equations for Grades 6-8 Statistics and Probability for Grades 6-8 Tool 1—Mathematics Content Alignment—Grades 9-12 ………………………. 60 Interpreting Functions in Grades 9-12 Reasoning with Equations and Inequalities in Grades 9-12 Geometric Measurement and Dimension; Modeling with Geometry in Grades 9-12 Interpreting Categorical and Quantitative Data in Grades 9-12 Similarity, Right Triangles, and Trigonometry & Trigonometric Functions in Grades 9-12 Tool 2—Mathematical Practices Alignment …………………………………..... 73 Tool 3—Overarching Considerations …………………………………………… 80 Professional Development Facilitator Guide ……………………………………. 83 Facilitator Guide PowerPoint Slides …………………………………………...... 90 Overview of the Common Core State Standards Mathematics Curriculum Analysis Project In June 2010, the Council of Chief State School Officers and National Governor’s Association released the Common Core State Standards for
K-2 3-5 6-8 9-12 Number/Operations in Base 10 Operations and Algebraic Thinking Geometry Number/Operations in Base 10 Operations and Algebraic Thinking Geometry Number and Operations-Fractions Ratios and Proportional Relationships Expressions and Equations Geometry Statistics and Probability Interpreting Functions Reasoning with Equations & Inequalities Similarity, Right Triangles and Trigonometry Geometric Measurement and Dimension Interpreting Categorical and Quantitative Data Tool 2 focuses on the extent to which the Standards for Mathematical Practice are embedded and integrated in the curriculum materials. Since the Mathematical Practices describe the essence of “doing mathematics,” mathematics curriculum materials that align with the CCSSM must also provide teachers support in incorporating these Mathematical Practices into their lessons, thereby providing students ample opportunities to engage in the Practices. Tool 3 focuses on the extent to which mathematics curriculum materials address overarching considerations related to equity, assessment, and technology. This tool guides reviewers to find evidence of teacher support with regard to establishing equitable teaching practices, integrating formative assessment into teaching, and using technology to support the learning and teaching of mathematics. The three tools developed by the team provide school administrators, teachers, and others involved in selecting mathematics curriculum materials with information to carefully analyze the materials based on important criteria and provide evidence on which to base curriculum materials adoption decisions. The sections that follow include: a User’s Guide to assist reviewers in using the tools; grade-level versions of Tool 1, along with Tool 2 and Tool 3; and a Professional Development Guide with PowerPoint slides that can be used to prepare reviewers for using the tools reliably. References Common Core State Standards for Mathematics (2010). Washington, D.C.: Council of Chief State School Officers and National Governors Association.
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
Grade K CCSSM Grade 1 CCSSM Grade 2 Use place value understanding and properties of operations to add and subtract Use place value understanding and properties of operations to add and subtract 5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. 6. Subtract multiples of 10 in the range 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. 9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Notes/Examples CCSSM Curriculum Analysis Tool 1—Number and Operations in Base Ten for Grades K-2 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 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 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?
CCSS 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. Pages Cont N-L-M- A-H Bal N-L-M- A-H Generalize place value understanding for multi-digit whole numbers. Understand the 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 value understanding to round decimals to any place. Use place value understanding and properties of operations perform multi-digit arithmetic Use place 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 two-digit 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—Operations and Algebraic Thinking for Grades 3-5 CCSSM Grade 3 Grade 4 Grade 5 problems involving the four operations, and identify and explain patterns in arithmetic. Chap Pages Cont N-L-M- A-H Bal N-L-M- A-H Use the four operations with numbers to solve problems Chap Pages Cont A-H Bal N-L-M- A-H Cont N-L-M- A-H Bal N-L-M- A-H 8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 3. Solve multistep word problems posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Asses the reasonableness of answers using mental computation and estimation strategies including rounding Solve problems involving the four operations, and identify and explain patterns in arithmetic. Generate and analyze patterns Analyze patterns and relationships 9. Identify arithmetic patterns (including patterns in the addition or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends 5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. 3. Generate two numerical patterns two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on the coordinate plane. For example, given the rule “Add 3” and starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Chap.
CCSSM 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 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 Curriculum Analysis Tool 1—Geometry for Grades K-2 Pages Pages Pages
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? 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?