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 (m/n) q as parts of a partition of q into n equal
parts; equivalently, as the result of a sequence of operations m × q ÷ n. For
example, use a visual fraction model to show understanding, and create
a story context for (m/n) q.
 Construct a model to develop understanding of
the concept of multiplying two fractions and create a story context
for the equation. [in general,
(m/n) x (c/d) = (mc)/(n/d).]
 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.
 Multiply fractional side lengths to find areas
of rectangles, and represent fraction products as rectangular areas.

5.NF.5

Interpret multiplication as
scaling (resizing), by:
 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.
 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.
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.A.1

Convert among differentsized
standard measurement units within a given measurement system and use these
conversions in solving multistep, real world problems. (e.g., convert 5 cm
to 0.05 m; 9 ft to 108 in).

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

5.OA.A.2

Write
simple expressions that record calculations with whole numbers, fractions,
and decimals, 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 ×
(18,932 + 9.21) is three times as large as 18,932 + 9.21, without having to calculate the indicated sum or product.



