Iowa Core K-12 Mathematics (PDF) - Green Hills AEA

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6. Find whole-number quotients and remainders with up to four-digit dividends and onedigit 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. (4.NBT.6.) Number and Operations—Fractions 3 4.NF Extend understanding of fraction equivalence and ordering. 1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (4.NF.1.) 2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. (4.NF.3.) 4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person 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? (4.NF.4.) 3 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Disclaimer: This document is up-to-date as of 11/17/2010. The language provided may not be Page 32 of 98 modified in any way. The most current Iowa Core can be found at http://iowacore.educateiowa.gov.
Understand decimal notation for fractions, and compare decimal fractions. 5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. 4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (4.NF.5.) 6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (4.NF.6.) 7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or
Page 1 and 2: Mathematics November 17, 2010
Page 3 and 4: Introduction Iowa Core Mathematics
Page 5 and 6: These Standards endeavor to follow
Page 7 and 8: How to read the grade level standar
Page 9 and 10: 4. Model with mathematics. Mathemat
Page 11 and 12: Mathematics | Kindergarten In Kinde
Page 13 and 14: Counting and Cardinality K.CC Know
Page 15 and 16: Mathematics | Grade 1 In Grade 1, i
Page 17 and 18: Operations and Algebraic Thinking 1
Page 27 and 28: 2. Measure and estimate liquid volu
Page 31: Operations and Algebraic Thinking 4
Page 39 and 40: 7. Apply and extend previous unders
Page 43 and 44: Ratios and Proportional Relationshi
Page 45 and 46: Expressions and Equations 6.EE Appl
Page 49 and 50: Ratios and Proportional Relationshi
Page 51 and 52: Geometry 7.G Draw, construct, and d
Page 55 and 56: The Number System 8.NS Know that th
Page 57 and 58: 3. Describe the effect of dilations
Page 59 and 60: Mathematics | High School—Number
Page 61 and 62: The Real Number System N-RN Extend
Page 63 and 64: Mathematics | High School—Algebra
Page 65 and 66: Seeing Structure in Expressions A-S
Page 67 and 68: 6. Solve systems of linear equation
Page 69 and 70: Functions Overview Interpreting Fun
Page 71 and 72: 9. Compare properties of two functi
Page 73 and 74: Mathematics | High School—Modelin
Page 75 and 76: Mathematics | High School—Geometr
Page 77 and 78: Geometry Overview Congruence • Ex
Page 79 and 80: Similarity, Right Triangles, and Tr
Page 81 and 82: (IA) Use diagrams consisting of ver
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Statistics and Probability Overview
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4. Use data from a sample survey to
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Note on courses and transitions The
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First quartile. For a data set with
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Tape diagram. A drawing that looks
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Table 2. Common multiplication and
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Sample of Works Consulted Existing
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Schmidt, W., Houang, R., and Cogan,
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Iowa Core K-12 Mathematics (PDF) - Green Hills AEA

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