Major Clusters

NF – Number and
Operations  Fractions

Apply and extend previous
understandings of multiplication and division to multiply and divide
fractions.

5.NF.4

Apply
and extend previous understandings of multiplication to multiply a fraction
or whole number by a fraction.
Interpret
the product of (a/b) × q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a × q ÷ b. For
example, use a visual fraction model to show (2/3 × 4 = 8/3, and create a
story context for this equation. Do
the same with (2/3) × (4/5) = 8/15.
(In general, (a/b) × (c/d) = ac/bd.)

5.NF.5

Interpret
multiplication as scaling (resizing), by:
a. 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.
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); 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.

5.NF.6

Solve
real world problems involving multiplication of fractions and mixed
numbers, e.g., by using visual fraction models or equations to represent
the problem.

5.NF.7

Apply
and extend previous understandings of division to divide unit fractions by
whole numbers and whole numbers by unit fractions. (Students able to multiple fractions in
general can develop strategies to divide fractions in general, by reasoning
about the relationship between multiplication and division. But division of a fraction by a fraction
is not a requirement at this grade level.)
a. Interpret
division of a unit fraction by a nonzero whole number, and compute such
quotients. For example, create a
story context for (1/3) ÷ 4, and use a visual fraction model to show the
quotient. Use the relationship
between multiplication and division to explain that (1/3) ÷ 4 = 1/12
because (1/12) × 4 = 1/3.
b. Interpret division of a whole number by a
unit fraction, and compute such quotients.
For example, create a story context for 4 ÷ (1/5), and use a visual
fraction model to show the quotient.
Use the relationship between multiplication and division to explain
that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
c. Solve real world problems involving
division of unit fractions by non‐zero whole numbers and division of whole numbers by
unit fractions, e.g., by using visual fraction models and equations to
represent the problem. For example,
how much chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 1/3cup
servings are in 2 cups of raisins?

Supporting
Clusters

Measurement and
Data

Convert like measurement units
within a given measurement system.

5.MD.2

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. For
example, given different measurements of liquid in identical beakers, find
the amount of liquid each beaker would contain if the total amount in all
the beakers were redistributed equally.

Additional
Clusters

Operations
and Algebraic Thinking

Write and interpret numerical
expressions.

5.OA.A.1

Use parentheses,
brackets, or braces in numerical expressions, and evaluate expressions with
these symbols.

5.OA.A.2

Write
simple expressions that record calculations with numbers, and interpret
numerical expressions without evaluating them. For
example, express the calculation “add 8 and 7, then multiply by 2” as 2 ×
(8 +7). Recognize that 3 × (18932 +
921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Foundational
Standards


3.OA.A.1

Interpret products of whole numbers, e.g., interpret 5 × 7
as the total number of objects in 5 groups of 7 objects each. For
example, describe a context in which a total number of objects can be
expressed as 5 × 7.

3.OA.A.2

Interpret wholenumber quotients of whole numbers, e.g.,
interpret 56 ÷ 8 as the number of objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of shares when 56 objects
are partitioned into equal shares of 8 objects each. For example,
describe a context in which a number of shares or a number of groups can be
expressed as 56 ÷ 8.

3.OA.B.6

Understand division as an unknown‐factor problem. For example, find 32 ÷ 8 by finding the
number that makes 32 when multiplied by 8.

4.OA.A.1

Interpret
a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many
as 7 and 7 times as many as 5. Represent verbal statements of
multiplicative comparisons as multiplication equations.

4.OA.A.2

Multiply or divide to solve word
problems involving multiplicative comparison, e.g., by using drawings and
equations with a symbol for the unknown number to represent the problem,
distinguishing multiplicative comparison from additive comparison.

3.NF.A.1

Understand
a fraction 1/b as the quantity formed
by 1 part when a whole is partitioned into b
equal parts; understand a fraction a/b
as the quantity formed by a parts of size 1/b.

4.NF.A.1

Explain why a fraction a/b is equivalent to a
fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts
differ even though the two fractions themselves are the same size. Use this
principle to recognize and generate equivalent fractions.

4.NF.B.4

Apply and extend previous
understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b.
For example, use a visual fraction model to represent 5/4 as the product
5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use
this understanding to multiply a fraction by a whole number. For
example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5),
recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
c. Solve word problems involving multiplication of a fraction
by a whole number, e.g., by using visual fraction models and equations to
represent the problem. For example, if each person at a party will eat
3/8 of a pound of roast beef, and there will be 5 people at the party, how
many pounds of roast beef will be needed? Between what two whole numbers
does your answer lie?

4.OA.A.1

Interpret a multiplication equation as a comparison, e.g.,
interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7
times as many as 5. Represent verbal statements of multiplicative
comparisons as multiplication equations.

4.OA.A.2

Multiply or divide to solve word problems involving
multiplicative comparison, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem, distinguishing
multiplicative comparison from additive comparison.

4.MD.A.2

Use the four operations to solve word problems involving
distances, intervals of time, liquid volumes, masses of objects, and money,
including problems involving simple fractions or decimals, and problems
that require expressing measurements given in a larger unit in terms of a
smaller unit. Represent measurement quantities using diagrams such as number
line diagrams that feature a measurement scale.

4.MD.B.4

Make
a line plot to display a data set of measurements in fractions of a unit
(1/2, 1/4, 1/8). Solve problems involving addition and subtraction of
fractions by using information presented in line plots. For
example, from a line plot find and interpret the difference in length
between the longest and shortest specimens in an insect collection.

5.MD.B.2

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. For
example, given different measurements of liquid in identical beakers, find
the amount of liquid each beaker would contain if the total amount in all
the beakers were redistributed equally.

5.NF.B.3

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.

Standards for
Mathematical Practices

1.
Make sense of problems and persevere
in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and
critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in
repeated reasoning.

Standards: Instructional Outcomes
·
5.NF.B.4:
o I can multiply fractions.
o I can determine the sequence of operations when multiplying a fraction
to a whole number.
o I can determine the sequence of opertions when multiplying two
fractions.
o I can multiply fractional side lengths to find areas of a rectangle.
o I can prove multiplying fractional side lengths to find the area is
the same as tiling a rectangle with unit squares.
o I can model the area of rectangles with fractional side lengths with
unit squares.
·
5.NF.B.5:
o
I can tell about the size of a product based on the
factors (relative to 2).
o
I can explain the relationship between two multiplication
problems that share a common factor ( and ).
o
I can compare the product of two factors without multiplying.
Example: 2 x ? = < 1 Answer must be less than ½.
o
I can explain why multiplying a number by a fraction greater
than one will result in a product greater than the given number.
o
I can explain why multiplying a fraction by one (which can be
written as various fractions, ex. , etc.) results in an equivalent fraction.
o I can explain
why multiplying a fraction by a fraction will result in a product smaller
than the given number.
·
5.NF.B.6:
o I can solve real world problems involving multiplication of fractions
and mixed numbers using models or equations.
o I can explain or illustrate my solution using fraction models or equations.
·
5.NF.B.7:
o
I can represent division of a unit fraction by a nonzero
whole number in a variety of ways.
o
I can represent division of a whole number by a unit fraction
in a variety of ways.
o
I can represent division of a unit fraction by a nonzero whole
number and a whole number by a unit fraction in a variety of ways to solve
real world problems.
·
5.MD.B.2
o
I can solve problems using line plots with halves, fourths,
and eighths using any operation.
o
I can make a line plot for measurements of fourths, halves,
and eighths.
·
5.OA.A.1
o
I can evaluate expressions using the order of operations
including parenthesis (), brackets [], or braces {}.
o
I can write expressions using the order of operations
including parenthesis (), brackets [], or braces {}.
·
5.OA.A.2
o
I can write simple expressions that record calculations with
numbers.
o
I can interpret numerical expressions without evaluating them.



