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STANDARDS

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US-VA

Math

Virginia Math

Grade 5: Computation and Estimation

5.CE.1

The student will estimate, represent, solve, and justify solutions to single-step and multistep contextual problems using addition, subtraction, multiplication, and division with whole numbers.

5.CE.1.a

Estimate the sum, difference, product, and quotient of whole numbers in contextual problems.
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5.CE.1.b

Represent, solve, and justify solutions to single-step and multistep contextual problems by applying strategies (e.g., estimation, properties of addition and multiplication) and algorithms, including the standard algorithm, involving addition, subtraction, multiplication, and division of whole numbers, with and without remainders, in which:

5.CE.1.b.i

sums, differences, and products do not exceed five digits;

5.CE.1.b.ii

factors do not exceed two digits by three digits;

5.CE.1.b.iii

divisors do not exceed two digits; or
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5.CE.1.b.iv

dividends do not exceed four digits.
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5.CE.1.c

Interpret the quotient and remainder when solving a contextual problem.
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5.CE.2

The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including those in context, using addition and subtraction of fractions with like and unlike denominators (with and without models), and solve single-step contextual problems involving multiplication of a whole number and a proper fraction, with models.

5.CE.2.a

Determine the least common multiple of two numbers to find the least common denominator for two fractions.
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5.CE.2.b

Estimate and determine the sum or difference of two fractions (proper or improper) and/or mixed numbers, having like and unlike denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12 (e.g., 5/8 + 1/4, 4/5 – 2/3, 3 3/4 + 2 5/12), and simplify the resulting fraction.

5.CE.2.c

Estimate and solve single-step and multistep contextual problems involving addition and subtraction with fractions (proper or improper) and/or mixed numbers having like and unlike denominators, with and without models. Denominators should be limited to 2, 3, 4, 5, 6, 8, 10, and 12. Answers should be expressed in simplest form.

5.CE.2.d

Solve single-step contextual problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction (e.g., 9 × 2/3, 8 × 3/4), with models. The denominator will be a factor of the whole number and answers should be expressed in simplest form.
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5.CE.3

The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including those in context, using addition, subtraction, multiplication, and division with decimal numbers.

5.CE.3.a

Apply estimation strategies (e.g., rounding to the nearest whole number, tenth or hundredth; compatible numbers, place value) to determine a reasonable solution for single-step and multistep contextual problems involving addition, subtraction, and multiplication of decimals, and single-step contextual problems involving division of decimals.
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5.CE.3.b

Estimate and determine the product of two numbers using strategies and algorithms, including the standard algorithm, when given:

5.CE.3.b.i

a two-digit factor and a one-digit factor (e.g., 2.3 × 4; 0.08 × 0.9; .16 × 5);

5.CE.3.b.ii

a three-digit factor and a one-digit factor (e.g., 0.156 × 4, 3.28 × 7, 8.09 × 0.2); and

5.CE.3.b.iii

a two-digit factor and a two-digit factor (e.g., 0.85 × 3.7, 14 × 1.6, 9.2 × 3.5).

5.CE.3.c

Estimate and determine the quotient of two numbers using strategies and algorithms, including the standard algorithm, in which:

5.CE.3.c.i

quotients do not exceed four digits with or without a decimal point;

5.CE.3.c.ii

quotients may include whole numbers, tenths, hundredths, or thousandths;

5.CE.3.c.iii

divisors are limited to a single digit whole number or a decimal expressed as tenths; and
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5.CE.3.c.iv

no more than one additional zero will need to be annexed.
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5.CE.3.d

Solve single-step and multistep contextual problems involving addition, subtraction, and multiplication of decimals by applying strategies (e.g., estimation, modeling) and algorithms, including the standard algorithm.

5.CE.3.e

Solve single-step contextual problems involving division with decimals by applying strategies (e.g., estimation, modeling) and algorithms, including the standard algorithm.
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5.CE.4

The student will simplify numerical expressions with whole numbers using the order of operations.

5.CE.4.a

Use order of operations to simplify numerical expressions with whole numbers, limited to addition, subtraction, multiplication, and division in which:

5.CE.4.a.i

expressions may contain no more than one set of parentheses;

5.CE.4.a.ii

simplification will be limited to five whole numbers and four operations in any combination of addition, subtraction, multiplication, or division;

5.CE.4.a.iii

whole numbers will be limited to two digits or less; and

5.CE.4.a.iv

expressions should not include braces, brackets, or fraction bars.

5.CE.4.b

Given a whole number numerical expression involving more than one operation, describe which operation is completed first, which is second, and which is third.