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.
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
Apply the formulas V=lĂ—wĂ—h and V=BĂ—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.
Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
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.
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.
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 that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
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.
Solve real world problems involving multiplication of fractions and mixed numbers.
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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