Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
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.
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 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.
Classify two-dimensional figures in a hierarchy based on properties.
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.
Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case). Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence a/b = a/b x n/n to the effect of multiplying a/b by 1.
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.
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.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Interpret division of a whole number by a unit fraction, and compute such quotients.
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.
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.
Solve real world problems involving multiplication of fractions and mixed numbers.
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
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.
Use place value understanding to round decimals to any place.
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.
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.
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.
Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.
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