Grade 4 Math Standards Map - Instructional Materials (CA Dept of Education)

Common Core State Standards with California Additions Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) Grade 4 – Mathematics

© California Department of Education Common Core State Standards Map January 16, 2013 Page 2 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) Common Core State Standards with California Additions1 Standards Map for a Basic Grade-Level Program

Grade Four – Mathematics

For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations OPERATIONS AND ALGEBRAIC THINKING Use the four operations with whole numbers to solve problems. 4.OA 1. Interpret a multiplication equation as a SE/TE: 18-19, SE/TE: 30-31 comparison, e.g., interpret 35 = 5 × 7 as a 24-25 statement that 35 is 5 times as many as 7 TE: 30A-31B and 7 times as many as 5. Represent TE: 18A-19B, verbal statements of multiplicative 24A-25B comparisons as multiplication equations.

4.OA 2. Multiply or divide to solve word problems SE/TE: 20-23, SE/TE: involving multiplicative comparison, e.g., 24-25, 30-31, 148-151 by using drawings and equations with a 154-157 symbol for the unknown number to TE: represent the problem, distinguishing TE: 20A-23B, 148A-151B multiplicative comparison from additive 24A-25B, comparison. 30A-31B, 154A-157B

1 These standards were originally produced by the Common Core State Standards Initiative, a state-led effort coordinated by the National Governors Association Center for Best Practices and the Council of Chief State School Officers. California additions were made by the State Board of Education when it adopted the Common Core on August 2, 2010 and modified pursuant to Senate Bill 1200 located at http://tinyurl.com/CASB1200 on January 16, 2013. Additions are marked in bold and underlined.

© California Department of Education Common Core State Standards Map January 16, 2013 Page 3 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations 4.OA 3. Solve multistep word problems posed with SE/TE: 54-57, SE/TE: whole numbers and having whole-number 126-129, 104-107, answers using the four operations, 176-177, 122-123, including problems in which remainders 196-197, 142-143, must be interpreted. Represent these 244-245 152-153 problems using equations with a letter standing for the unknown quantity. Assess TE: 54A-57B, TE: the reasonableness of answers using 126A-129B, 104A-107B, mental computation and estimation 176A-177B, 122A-123B, strategies including rounding. 196A-197B, 142A-143B, 244A-245B 152A-153B

Gain familiarity with factors and multiples. 4.OA 4. Find all factor pairs for a whole number in SE/TE: the range 1–100. Recognize that a whole 256-257, number is a multiple of each of its factors. 258-259, Determine whether a given whole number 260-261 in the range 1–100 is a multiple of a given one-digit number. Determine whether a TE: given whole number in the range 1–100 is 256A-257B, prime or composite. 258A-259B, 260A-261B

© California Department of Education Common Core State Standards Map January 16, 2013 Page 4 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations Generate and analyze patterns. 4.OA 5. Generate a number or shape pattern that SE/TE: 10-11, SE/TE: 44-45, follows a given rule. Identify apparent 40-41, 42-43, 46-49, features of the pattern that were not 50-53 442-443 explicit in the rule itself. For example, given the rule “Add 3” and the starting TE: 10A-11B, TE: 44A-45B, number 1, generate terms in the resulting 40A-41B, 46A-49B, sequence and observe that the terms 42A-43B, 442A-443B appear to alternate between odd and even 50A-53B numbers. Explain informally why the numbers will continue to alternate in this way.

NUMBER AND OPERATIONS IN BASE TEN2 Generalize place value understanding for multi-digit whole numbers. 4.NBT 1. Recognize that in a multi-digit whole SE/TE: 68-69, number, a digit in one place represents 80-81 ten times what it represents in the place to its right. For example, recognize that 700 TE: 68A-69B, ÷ 70 = 10 by applying concepts of place 80A-81B value and division.

2 Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

© California Department of Education Common Core State Standards Map January 16, 2013 Page 5 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations 4.NBT 2. Read and write multi-digit whole numbers SE/TE: 66-67, SE/TE: 68-69, using base-ten numerals, number names, 70-73, 74-77 80-81 and expanded form. Compare two multi-digit numbers based on meanings of TE: 66A-67B, TE: 68A-69B, the digits in each place, using >, =, and 70A-73B, 80A-81B

TE: 126A-129B, 152A-153B, 174A-175B

Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT 4. Fluently add and subtract multi-digit whole SE/TE: 96-99, SE/TE: numbers using the standard algorithm. 100-101, 104-107 102-103 TE: TE: 96A-99B, 104A-107B 100A-101B, 102A-103B

© California Department of Education Common Core State Standards Map January 16, 2013 Page 6 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations 4.NBT 5. Multiply a whole number of up to four SE/TE: SE/TE: digits by a one-digit whole number, and 116-117, 126-129, multiply two two-digit numbers, using 120-121, 154-157, strategies based on place value and the 148-151, 192-193, properties of operations. Illustrate and 152-153, 194-195 explain the calculation by using equations, 166-169, rectangular arrays, and/or area models. 186-189, TE: 196-197 126A-129B, 154A-157B, TE: 192A-193B, 116A-117B, 194A-195B 120A-121B, 148A-151B, 152A-153B, 166A-169B, 186A-189B, 196A-197B

4.NBT 6. Find whole-number quotients and SE/TE: SE/TE: 212- remainders with up to four-digit dividends 206-207, 213, 218-219, and one-digit divisors, using strategies 214-217, 234-237 based on place value, the properties of 238-239, operations, and/or the relationship 240-241, TE: 212A- between multiplication and division. 242-243 213B, 218A- Illustrate and explain the calculation by 219B, 234A- using equations, rectangular arrays, TE: 237B and/or area models. 206A-207B, 214A-217B, 238A-239B, 240A-241B, 242A-243B

© California Department of Education Common Core State Standards Map January 16, 2013 Page 7 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations NUMBER AND OPERATIONS—FRACTIONS3 Extend understanding of fraction equivalence and ordering. 4.NF 1. Explain why a fraction a/b is equivalent to SE/TE: a fraction (n × a)/(n × b) by using visual 262-265, fraction models, with attention to how the 266-267, number and size of the parts differ even 274-277 though the two fractions themselves are the same size. Use this principle to TE: recognize and generate equivalent 262A-265B, fractions. 266A-267B, 274A-277B

4.NF 2 Compare two fractions with different SE/TE: numerators and different denominators, 266-267, e.g., by creating common denominators or 268-271, numerators, or by comparing to a 272-273, benchmark fraction such as 1/2. 274-277 Recognize that comparisons are valid only when the two fractions refer to the same TE: whole. Record the results of comparisons 266A-267B, with symbols >, =, or <, and justify the 268A-271B, conclusions, e.g., by using a visual fraction 272A-273B, model. 274A-277B

Build fractions from unit fractions by

3 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

© California Department of Education Common Core State Standards Map January 16, 2013 Page 8 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations applying and extending previous understandings of operations on whole numbers. 4.NF 3a. Understand a fraction a/b with a > 1 as a SE/TE: SE/TE: sum of fractions 1/b. Understand addition 288-289, 296-299 and subtraction of fractions as joining and 290-291, separating parts referring to the same 292-293, TE: whole. 294-295, 296A-299B 314-317

TE: 288A-289B, 290A-291B, 292A-293B, 294A-295B, 314A-317B

4.NF 3b. Understand a fraction a/b with a > 1 as a SE/TE: sum of fractions 1/b. Decompose a 300-303, fraction into a sum of fractions with the 304-307, same denominator in more than one way, 312-313 recording each decomposition by an equation. Justify decompositions, e.g., by TE: using a visual fraction model. Examples: 300A-303B, 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 304A-307B, 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 312A-313B

4.NF 3c. Understand a fraction a/b with a > 1 as a SE/TE: SE/TE:

© California Department of Education Common Core State Standards Map January 16, 2013 Page 9 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations sum of fractions 1/b. Add and subtract 304-307, 300-303 mixed numbers with like denominators, 308-309, e.g., by replacing each mixed number with 310-311 TE: an equivalent fraction, and/or by using 300A-303B properties of operations and the TE: relationship between addition and 304A-307B, subtraction. 308A-309B, 310A-311B

4.NF 3d. Understand a fraction a/b with a > 1 as a SE/TE: SE/TE: sum of fractions 1/b. Solve word problems 290-291, 312-313 involving addition and subtraction of 292-293, fractions referring to the same whole and 294-295, TE: having like denominators, e.g., by using 296-299, 312A-313B visual fraction models and equations to 314-317 represent the problem. TE: 290A-291B, 292A-293B, 294A-295B, 296A-299B, 314A-317B

4.NF 4a. Apply and extend previous understandings SE/TE: SE/TE: of multiplication to multiply a fraction by a 328-329 330-331 whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a TE: 328A-329B TE: visual fraction model to represent 5/4 as 330A-331B the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

4.NF4b. Apply and extend previous understandings SE/TE:

© California Department of Education Common Core State Standards Map January 16, 2013 Page 10 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations of multiplication to multiply a fraction by a 330-331, whole number. Understand a multiple of 332-333 a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a TE: whole number. For example, use a visual 330A-331B, fraction model to express 3 × (2/5) as 6 × 332A-333B (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) 4.NF4c. Apply and extend previous understandings SE/TE: of multiplication to multiply a fraction by a 330-331, whole number. Solve word problems 332-333 involving multiplication of a fraction by a whole number, e.g., by using visual TE: fraction models and equations to represent 330A-331B, the problem. For example, if each person 332A-333B at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? Understand decimal notation for fractions, and compare decimal fractions. 4.NF 5. Express a fraction with denominator 10 as SE/TE: SE/TE: an equivalent fraction with denominator 336-339 340-343 100, and use this technique to add two fractions with respective denominators 10 TE: 336A-339B TE: and 100.4 For example, express 3/10 as 340A-343B 30/100, and add 3/10 + 4/100 = 34/100. 4.NF 6. Use decimal notation for fractions with SE/TE: SE/TE:

4 Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.

© California Department of Education Common Core State Standards Map January 16, 2013 Page 11 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations denominators 10 or 100. For example, 334-335, 344-345 rewrite 0.62 as 62/100; describe a length 336-339, as 0.62 meters; locate 0.62 on a number 340-343 TE: line diagram. 344A-345B TE: 334A-335B, 336A-339B, 340A-343B

4.NF 7. Compare two decimals to hundredths by SE/TE: SE/TE: reasoning about their size. Recognize that 346-349 356-357 Set comparisons are valid only when the two G decimals refer to the same whole. Record TE: 346A-349B the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model.

MEASUREMENT AND DATA

© California Department of Education Common Core State Standards Map January 16, 2013 Page 12 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 4.MD 1. Know relative sizes of measurement units SE/TE: SE/TE: within one system of units including km, m, 368-369, 364-365, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within 370-373, 366-367, a single system of measurement, express 376-377, 374-375 measurements in a larger unit in terms of 378-379, a smaller unit. Record measurement 380-381, TE: equivalents in a two-column table. For 382-385, 364A-365B, example, know that 1 ft is 12 times as long 386-387 366A-367B, as 1 in. Express the length of a 4 ft snake 374A-375B as 48 in. Generate a conversion table for TE: feet and inches listing the number pairs (1, 368A-369B, 12), (2, 24), (3, 36), ... 370A-373B, 376A-377B, 378A-379B, 380A-381B, 382A-385B, 386A-387B

4.MD 2. Use the four operations to solve word SE/TE: SE/TE:

© California Department of Education Common Core State Standards Map January 16, 2013 Page 13 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations problems involving distances, intervals of 352-353, 350-351, time, liquid volumes, masses of objects, 374-375, 370-373, and money, including problems involving 388-389, 382-385 simple fractions or decimals, and 406-407, problems that require expressing 408-409 TE: measurements given in a larger unit in 350A-351B, terms of a smaller unit. Represent TE: 370A-373B, measurement quantities using diagrams 352A-353B, 382A-385B such as number line diagrams that feature 374A-375B, a measurement scale. 388A-389B, 406A-407B, 408A-409B

4.MD 3. Apply the area and perimeter formulas for SE/TE: rectangles in real world and mathematical 404-406 problems. For example, find the width of a rectangular room given the area of the TE: 404A-406B flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Represent and interpret data. 4.MD 4. Make a line plot to display a data set of SE/TE: measurements in fractions of a unit (1/2, 400-401, 1/4, 1/8). Solve problems involving 402-403 addition and subtraction of fractions by using information presented in line plots. TE: For example, from a line plot find and 400A-401B, interpret the difference in length between 402A-403B the longest and shortest specimens in an insect collection.

Geometric measurement: understand

© California Department of Education Common Core State Standards Map January 16, 2013 Page 14 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations concepts of angle and measure angles. 4.MD 5a. Recognize angles as geometric shapes SE/TE: SE/TE: that are formed wherever two rays share a 426-427 428-429, common endpoint, and understand 430-431, concepts of angle measurement: An angle TE: 426A-427B 432-433, is measured with reference to a circle with 444-445 Set C its center at the common endpoint of the rays, by considering the fraction of the TE: circular arc between the points where the 428A-429B, two rays intersect the circle. An angle that 430A-431B, turns through 1/360 of a circle is called a 432A-433B “one-degree angle,” and can be used to measure angles.

4.MD 5b. Recognize angles as geometric shapes SE/TE: SE/TE: that are formed wherever two rays share a 428-429 430-431, common endpoint, and understand 432-433, concepts of angle measurement: An angle TE: 428A-429B 444-445 Set D that turns through n one-degree angles is said to have an angle measure of n TE: degrees. 430A-431B, 432A-433B

4.MD 6. Measure angles in whole-number degrees SE/TE: SE/TE: using a protractor. Sketch angles of 430-431 432-433, specified measure. 444-445 Set E TE: 430A-431B TE: 432A-433B

© California Department of Education Common Core State Standards Map January 16, 2013 Page 15 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations 4.MD 7. Recognize angle measure as additive. SE: 432-433 SE/TE: When an angle is decomposed into 446-447 non-overlapping parts, the angle measure TE: 432A-433B Set F of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

GEOMETRY Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G 1. Draw points, lines, line segments, rays, SE/TE: SE/TE: angles (right, acute, obtuse), and 422-423, 428-429, perpendicular and parallel lines. Identify 424-425, 430-431 these in two-dimensional figures. 436-437, 438-439 TE: 428A-429B, TE: 430A-431B 422A-423B, 424A-425B, 436A-437B, 438A-439B

© California Department of Education Common Core State Standards Map January 16, 2013 Page 16 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations 4.G 2. Classify two-dimensional figures based on SE/TE: the presence or absence of parallel or 436-437, perpendicular lines, or the presence or 438-439, absence of angles of a specified size. 442-443 Recognize right triangles as a category, and identify right triangles. (Two TE: dimensional shapes should include 436A-437B, special triangles, e.g., equilateral, 438A-439B, isosceles, scalene, and special 442A-443B quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.)

4.G 3. Recognize a line of symmetry for a SE: 440-441 SE/TE: two-dimensional figure as a line across the 446-447 Set figure such that the figure can be folded TE: 440A-441B I along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. MATHEMATICAL PRACTICES MP 1. Make sense of problems and persevere in SE: xviii, xix, solving them. xxvii

TE: 2A, 2B, 2F

MP 2. Reason abstractly and quantitatively. SE: xviii, xx, xxvii

TE: 2A, 2B, 2F MP 3. Construct viable arguments and critique SE: xviii, xxi, the reasoning of others. xxvii

TE: 2A, 2C, 2F

© California Department of Education Common Core State Standards Map January 16, 2013 Page 17 Publisher: Pearson Scott Foresman & Prentice Hall Program Title: enVisionMATH California Common Core Edition, Grade 4 Components: Student Edition (SE); Teacher’s Edition (TE) For Reviewer Use Only Meets Publisher Citations Standard Standard Standard Language Primary Supporting Y N Reviewer Notes No. Citations Citations MP 4. Model with mathematics. SE: xviii, xxii, xxvii

TE: 2A, 2C, 2F MP 5. Use appropriate tools strategically. SE: xviii, xxiii, xxvii

TE: 2A, 2D, 2F

MP 6. Attend to precision. SE: xviii, xxiv, xxvii

TE: 2A, 2D, 2F

MP 7. Look for and make use of structure. SE: xviii, xxv, xxvii

TE: 2A, 2E, 2F

MP 8. Look for and express regularity in SE: xviii, xxvi, repeated reasoning. xxvii

TE: 2A, 2E, 2F

Appendix

California Department of Education Posted February 2013