13.a 5.NF.B.5a Math.5.NF.5a 5.NF.5.a 5.NF.5.a 5.NF.5a 5.NF.a 5.NF.5.a 5.NF.5.a 13.b, 13.c 5.NF.B.5b Math.5.NF.5b 5.NF.5.b 5.NR.3.5 5.NF.5.b 5.NF.B.5.b 5.NF.5b 5.NF.b 5.NF.5.b 5.NF.5.b 5.NR.5

Factors & Products 5th Grade

Alabama Course of Study Standards: 13.a
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. Example: Use reasoning to determine which expression is greater? 255 or 3/4 × 225; 11/50 or 3/2 × 11/50
Arizona Academic Standards: 5.NF.B.5a Common Core State Standards: Math.5.NF.5a or 5.NF.5.a Kentucky Academic Standards (KAS): 5.NF.5.a Mississippi College- and Career-Readiness Standards: 5.NF.5a
Comparing 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.
New York State Next Generation Learning Standards: 5.NF.a
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. e.g., In the case of 10 × 1/2 = 5, 5 is half of 10 and 5 is 10 times larger than 1/2.
Tennessee Academic Standards: 5.NF.5.a
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. For example, know if the product will be greater than, less than, or equal to the factors.
Wisconsin Academic Standards: 5.NF.5.a
Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
Alabama Course of Study Standards: 13.b, 13.c
Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and relate the principle of fraction equivalence. 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.
Arizona Academic Standards: 5.NF.B.5b
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Common Core State Standards: Math.5.NF.5b or 5.NF.5.b Kentucky Academic Standards (KAS): 5.NF.5.b Mississippi College- and Career-Readiness Standards: 5.NF.5b
Explaining 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); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Georgia Standards of Excellence (GSE): 5.NR.3.5
Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.
Louisiana Academic Standards: 5.NF.B.5.b
Explaining 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)
New York State Next Generation Learning Standards: 5.NF.b
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 × n/n to the effect of multiplying a/b by 1. e.g., Explain why 4 × 3/2 is greater than 4. Explain why 4 × 1/2 is less than 4. 1/3 is equivalent to 2/6 because 1/3 × 2/2 = 2/6. .
Tennessee Academic Standards: 5.NF.5.b
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 less than the given number; and relate the principle of fraction equivalence a/b = (a × n)/(b × n) to the effect of multiplying a/b by 1.
Wisconsin Academic Standards: 5.NF.5.b
Relate the principle of fraction equivalence to the effect of multiplying or dividing a fraction by 1 or an equivalent form of 1 (e.g., 3/3, 5/5).
Georgia Standards of Excellence (GSE): 5.NR.5
Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.

EFFECTS OF MULTIPLICATION

Does the operation of multiplication on a number result in a larger number?
The answer is sometimes. Let's look at some cases.

When a number is multiplied by a fraction equivalent to 1,
the product is equal to the number.

Example:	$3$ × $\frac{2}{2}$ = $\frac{6}{2}$ = $3$
Example:	$\frac{1}{3}$ × $\frac{4}{4}$ = $\frac{4}{12}$ = $\frac{1}{3}$

When a positive whole number is multiplied by a fraction greater than 1,
the product is greater than the whole number.

Example:

3

1 \frac{1}{4}

3

\frac{5}{4}

\frac{15}{4}

3 \frac{3}{4}

When a positive whole number is multiplied by a fraction between 0 and 1,
the product is less than the whole number.

Example:	$3$ × $\frac{1}{3}$ = $\frac{3}{3}$ = $1$
Example:	$3$ × $\frac{1}{6}$ = $\frac{3}{6}$ = $\frac{1}{2}$

When a number greater than 1 is multiplied by a number greater than 1,
the product is greater than both numbers.

Example:	$3$ × $2$ = $6$
Example:	$3$ × $2 \frac{1}{3}$ = $3$ × $\frac{7}{3}$ = $\frac{21}{3}$ = $7$
Example:	$1 \frac{1}{2}$ × $1 \frac{1}{3}$ = $\frac{3}{2}$ × $\frac{4}{3}$ = $\frac{12}{6}$ = $2$

Factors & Products

Alabama Course of Study Standards: 13.a

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.
Example: Use reasoning to determine which expression is greater? 255 or 3/4 × 225; 11/50 or 3/2 × 11/50

Arizona Academic Standards: 5.NF.B.5a

Common Core State Standards: Math.5.NF.5a or 5.NF.5.a

Kentucky Academic Standards (KAS): 5.NF.5.a

Mississippi College- and Career-Readiness Standards: 5.NF.5a

Comparing 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.

New York State Next Generation Learning Standards: 5.NF.a

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.
e.g., In the case of 10 × 1/2 = 5, 5 is half of 10 and 5 is 10 times larger than 1/2.

Tennessee Academic Standards: 5.NF.5.a

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. For example, know if the product will be greater than, less than, or equal to the factors.

Wisconsin Academic Standards: 5.NF.5.a

Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

Alabama Course of Study Standards: 13.b, 13.c

Arizona Academic Standards: 5.NF.B.5b

Common Core State Standards: Math.5.NF.5b or 5.NF.5.b

Kentucky Academic Standards (KAS): 5.NF.5.b

Mississippi College- and Career-Readiness Standards: 5.NF.5b

Georgia Standards of Excellence (GSE): 5.NR.3.5

Louisiana Academic Standards: 5.NF.B.5.b

Explaining 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)

New York State Next Generation Learning Standards: 5.NF.b

Tennessee Academic Standards: 5.NF.5.b

Wisconsin Academic Standards: 5.NF.5.b

Relate the principle of fraction equivalence to the effect of multiplying or dividing a fraction by 1 or an equivalent form of 1 (e.g., 3/3, 5/5).

Georgia Standards of Excellence (GSE): 5.NR.5

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