NBT  Number and
Operation in Base Ten

Use
equivalent fractions as a strategy to add and subtract fractions.

5.NF.A.1

Add and subtract fractions with unlike
denominators (including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent sum or
difference of fractions with like denominators.
For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.
(in general, a/b + c/d = (ab + bc)/bd.)

5.NF.A.2

Solve
word problems involving addition and subtraction of fractions referring to
the same whole, including cases of unlike denominators, e.g., by using
visual fraction models or equations to represent the problem. Use benchmark
fractions and number sense of fractions to estimate mentally and assess the
reasonableness of answers.
For
example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that
3/7 < 1/2.

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

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, e.g., by using visual fraction models or equations to
represent the problem. For example, interpret 3/4 as the result
of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when
3 wholes are shared equally among 4 people each person has a share of size
3/4. If 9 people want to share a 50‐pound sack of rice
equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your
answer lie?

5.NF.B.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.

Foundational
Standards


Represent and solve problems
involving multiplication and division.

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.

Understand properties of
multiplication and the relationship between multiplication and division.

3.OA.B.6


Geometric measurement: understand
concepts of area and relate area to multiplication and to addition.

3.MD.C.7b

Multiply side lengths to find areas of rectangles with
wholenumber side lengths in the context of solving real world and
mathematical problems, and represent wholenumber products as rectangular
areas in mathematical reasoning.

Extend understanding of fraction
equivalence and ordering.

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.A.2

Compare two fractions with different numerators and
different denominators, e.g., by creating common denominators or
numerators, or by comparing to a benchmark fraction such as 1/2. Recognize
that comparisons are valid only when the two fractions refer to the same
whole. Record the results of comparisons with symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model.

Build fractions from unit
fractions.

4.NF.B.3

Understand a fraction a/b with a > 1
as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining
and separating parts referring to the same whole.
b. Understand a fraction a/b with a > 1
as a sum of fractions 1/b.
Decompose a fraction into a sum of fractions with the same
denominator in more than one way, recording each decomposition by an
equation. Justify decompositions, e.g., by using a visual fraction model. Examples:
3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 +
1/8.
c. Understand a fraction a/b with a > 1
as a sum of fractions 1/b. Add and subtract mixed numbers with like
denominators, e.g., by replacing each mixed number with an equivalent
fraction, and/or by using properties of operations and the relationship
between addition and subtraction.
d. Understand a fraction a/b with a > 1
as a sum of fractions 1/b. Solve word problems involving addition
and subtraction of fractions referring to the same whole and having like
denominators, e.g., by using visual fraction models and equations to
represent the problem.

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?

Use the four operations with whole numbers to solve
problems.

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.

Solve problems involving
measurement and conversion of measurements.

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.

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.

Instructional Outcomes
·
5.NF.A.1:
o I can find equivalent fractions.
o I can add and subtract fractions with unlike denominators using
equivalent fractions.
o I can add and subtract mixed numbers with unlike denominators using
equivalent fractions.
·
5.NF.A.2:
o I can solve word problems using addition and subtraction of fractions
with like and unlike denominators referring to the same whole.
o I can use benchmark fractions and number sense of fractions to check
for reasonableness of answers.
·
5.NF.B.3
o I can interpret a fraction as division of the numerator by the
denominator
o I can solve word problems involving division of whole numbers with
quotients as fractions or mixed numbers.
o I can recognize the remainder as a fractional part of the problem.
·
5.NF.B.5
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.
