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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.) 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.
Recognize that comparisons are valid only when the two decimals refer to the same whole.
Record the results of comparisons with the symbols Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.
Record the results of comparisons with symbols 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.
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.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.Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.Explain informally why the numbers will continue to alternate in this way.Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.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.Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.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.