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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.
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.
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.
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.
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.
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.