Grade 5

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Read and write decimals to thousandths using base-ten numerals, number names, and expanded form (e.g. 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × ( ) + 9 × ( ) + 2 × ( )). 5.NOS.A.3.a

Estimate decimal quantities by reasoning about their location on a number line, their relationship to benchmark numbers (e.g. 0, 0.25, 0.5, 0.75, 1) and rounding to any place.5.NOS.A.3.b

Compare two decimals to thousandths by reasoning about the values of the digits and the location on the number line. Record the results of comparisons with the symbols , =, . 5.NOS.A.3.c

Apply estimation strategies to estimate products. 5.NOS.B.4.a

Use computational strategies (e.g., partial products, doubling and halving) efficiently to multiply. 5.NOS.B.4.b

Use a standard algorithm to multiply. 5.NOS.B.4.c

Determine and explain when a strategy or algorithm is most efficient.5.NOS.B.4.d

Apply estimation strategies to estimate quotients.  5.NOS.B.5.a

Use partial quotients efficiently to divide. 5.NOS.B.5.b

Use properties of operations and/or the inverse relationship between multiplication and division to divide.  5.NOS.B.5.c

Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of division.5.NOS.B.5.d

Apply estimation strategies to estimate sums and differences of decimals. 5.NOS.B.6.a

Use concrete models, drawings, strategies based on place value (e.g., partial sums), properties of operations and/or the inverse relationship between addition and subtraction to add and subtract decimals.  5.NOS.B.6.b

Use an algorithm to add and subtract decimals. 5.NOS.B.6.c

Determine and explain when a strategy or algorithm is most efficient.5.NOS.B.6.d

Apply estimation strategies to estimate products and quotients.5.NOS.B.7.a

Use concrete models, drawings, and arrays to multiply and divide.  5.NOS.B.7.b

Use strategies based on place value (e.g., partial products, partial quotients) to multiply and divide.5.NOS.B.7.c

Use properties of operations and/or the inverse relationship between multiplication and division to multiply and divide.5.NOS.B.7.d

Represent and explain the computation by connecting concrete models, drawings, and/or equations to the meaning of multiplication and division.5.NOS.B.7.e

Estimate sums and differences by reasoning about benchmark numbers and assess reasonableness of answers (e.g., will be more than 1 because both fractions are greater than ).5.NOS.C.8.a

Apply and extend whole number addition and subtraction strategies (e.g. counting on, making a whole, partial sums, compensation, properties of operations, the inverse relationship between addition and subtraction) to add and subtract fractions.5.NOS.C.8.b

Use equivalent fractions to produce an equivalent sum or difference of fractions with like denominators (e.g. . In general, ). 5.NOS.C.8.c

Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., will be less than 2 because I am creating a fractional part of 2). 5.NOS.D.11.a

Multiply a whole number by a fraction (e.g., interpret as of b when is greater than or less than 1). 5.NOS.D.11.b

Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., will be less than because I will have one half of ). 5.NOS.D.12.a

Apply and extend whole number multiplication strategies (e.g. area models).5.NOS.D.12.b

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths.5.NOS.D.12.c

Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.5.NOS.D.13.a

Apply and extend whole number multiplication strategies (e.g. area model, partial products).5.NOS.D.13.b

Compare the size of a product to the size of one factor based on the size of the other factor, without performing the indicated multiplication.  5.NOS.D.14.a

Explain why multiplying a given number by a fraction greater than a 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; and relate the principle of fraction equivalence to the Identity Property of Multiplication.5.NOS.D.14.b

Apply estimation strategies to estimate quotients and assess reasonableness of answers. 5.NOS.D.16.a

Use visual fraction models and equations to interpret division of a unit fraction by a non-zero whole number and compute quotients.5.NOS.D.16.b

Use visual fraction models and equations to interpret division of a whole number by a unit fraction and compute quotients.5.NOS.D.16.c

Represent and explain the computation by connecting visual fraction models and/or equations to the meaning of division with unit fractions. 5.NOS.D.16.d