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.
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.
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Classify two-dimensional figures in a hierarchy based on properties.
Interpret multiplication as scaling (resizing).
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
Read, write, and compare decimals to thousandths.
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem
Solve real world problems involving multiplication of fractions and mixed numbers
Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
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