LAC 28:CXLII.1103. Numeracy and Operational Fluency

A. Extend understanding of fraction equivalence and ordering. 1. Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models or number line diagrams, 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. Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100. 2. Compare two fractions with different numerators and different denominators. Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100. B. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 1. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction, including mixed numbers and fractions greater than 1, into a sum of fractions, including unit fractions and non-unit fractions, with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions. c. Evaluate the reasonableness of sums and differences of fractions using benchmark fractions, 0, 14, 12, 34, 1, referring to the same whole. 2. Add and subtract fractions with like denominators. a. Add and subtract mixed numbers with like denominators. b. Solve real-world mathematical tasks involving addition and subtraction of fractions, including mixed numbers and fractions greater than 1, referring to the same whole and having like denominators 3. Multiply a fraction by a whole number. Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100. a. Understand a fraction a/b as a multiple of 1/b. 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. c. Solve real-world mathematical tasks involving multiplication of a fraction by a whole number. C. Understand decimal notation for fractions, and compare decimal fractions. 1. 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. 2. Use decimal notation and precise language for fractions with denominators 10 or 100. 3. 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 <, and justify the conclusions. D. Gain familiarity with factors and multiples. 1. Use whole numbers in the range 1–100. a. Find all factor pairs for a given whole number. b. Recognize that a given whole number is a multiple of each of its factors. c. Determine whether a given whole number is a multiple of a given one-digit number. d. Determine whether a given whole number is prime or composite. E. Generalize place value understanding for multi-digit whole numbers. 1. Recognize that in a multi-digit whole number less than or equal to 1,000,000, a digit in one place represents ten times what it represents in the place to its right. 2. Read and write multi-digit whole numbers up to 1,000,000 using base-ten numerals/standard form, written form (number names), unit form, and expanded form. 3. Use place value understanding. a. Round multi-digit whole numbers up to 1,000,000, to any place. b. Use compatible numbers to estimate solutions to real-world mathematical tasks. F. Add and subtract multi-digit numbers. 1. Fluently add and subtract multi-digit whole numbers with sums or differences less than or equal to 1,000,000, using a standard algorithm.