Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations:
• add and subtract decimals to hundredths;
• multiply and divide decimals to hundredths.
Relate the strategy to a written method and explain the reasoning used.
Interpret the product a/b Ă— q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a Ă— q/b.
Recognize that a cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
Use place value understanding to round decimals to any place.
Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
Recognize volume as additive. Find volumes of solid figures composed of two non- overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit 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.
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
Find the area of a rectangle with fractional side lengths by tiling it with rectangles of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Classify two-dimensional figures in a hierarchy based on properties.
Convert among different-sized standard measurement units within a given measurement system when the conversion factor is given. Use these conversions in solving multi-step, real world problems.
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