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 ……………………………………………………………………… 9 Too1 1—Mathematics Content Alignment—Grades K-5 …..……………..…..... 16 Tool 1—Mathematics Content Alignment—Grades 6-8………………………… 42 Tool 1—Mathematics Content Alignment—Grades 9-12 ………………………. 59 Tool 2—Mathematical Practices Alignment …………………………………..... 72 Tool 3—Overarching Considerations …………………………………………… 79 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 State School Officers and National Governor’s Association released the Common Core State Standards for mathematics and literacy (CCSSO/NGA, 2010). By June 1, 2011, these standards had been adopted by 44 states, the District of Columbia and the US Virgin Islands. This work represents the first significant attempt in our nation’s history to systematically align common K-12 mathematics standards across the states in our nation’s history, building on previous efforts to create a national vision for mathematics education, including the National Council of Teachers of Mathematics’ standards documents
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). 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
CCSSM Curriculum Analysis Tool 1—Number and Operations in Base Ten for Grades K-2 Grade K CCSSM Grade 1 Grade 2 K.NBT/CC Counting and Cardinality/ Number and Operations in Base Ten Chap. Pages Cont N-L-M- A-H Bal N-L-M- A-H 1.NBT Number and Operations in Base Ten Chap. Pages Cont A-H Bal N-L-M- A-H 2.NBT Number and Operations in Base Ten Chap. Pages Contt A-H Bal A-H Work with numbers 11-19 to gain foundations for place value Understand place value Understand place value. 4. Identify whether a number of objects is one is greater than, less than, or equal to the number of objects in another group. 5. Compare two numbers between 1 and 10 presented as written numerals. 3. Compare two numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Notes/Examples
CCSS Grade 3 CCSS Grade 4 CCSS 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 place value system 2. Read and 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 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.
CCSSM Grade 3 CCSSM Grade 4 CCSSM 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 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
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 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. CCSSM Curriculum Analysis Tool 1—Geometry for Grades K-2 Pages 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?
CCSSM Grade 6 CCSSM Grade 7 CCSSM Grade 8 6.SP Statistics and Probability Chap 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 Pages Cont N-L-M- A-H Bal N-L-M- A-H Develop understanding of statistical variability Draw informal comparative inferences about two populations 2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable 3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a science book. 4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables Notes/Examples CCSSM Curriculum Analysis Tool 1—Statistics and Probability for Grades 6-8 CCSSM Grade 6 CCSSM Grade 7 Grade 8
Notes/Examples 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?