Description:
In Unit 3, fourthgrade students understand, recognize and
generate equivalent fractions.
Students will compare fractions with different numerators and
denominators. Students will create
line plots and solve simple word problems involving the fractions found on
the line plot.
Students will add and subtract fractions with like denominators,
for example, 3 fifths + 1 fifth = 4 fifths.
Students begin with models such as the area model, manipulatives, and
number lines, then progress to an equation. During this unit, students will multiply
a fraction by a whole number. Students
will use models and equations to solve word problems involving addition and
subtraction of fractions with like denominators and multiplication of a
fraction by a whole number.

Major
Cluster: Number and OperationsFractions

Extend understanding of fraction
equivalence and ordering.

4.NF.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. (Denominators are limited to
2, 3, 4, 5, 6, 8, 10, 12, and 100.)

4.NF.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. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10,
12, and 100.)

Build
fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers.

4.NF.3

Understand
a fraction a/b with a > 1 as a sum of fractions 1/b.
(Denominators
are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
 Understand addition and subtraction of fractions
as joining and separating parts referring to the same whole.
Example:
3/4 = 1/4 + 1/4 + 1/4.
 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.
 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.
 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.4

Multiply a fraction by a whole number. (Denominators are limited
to 2, 3, 4, 5, 6, 8, 10, 12,
and 100.)
 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).
 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.)
 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?

Supporting
Cluster: Measurement and Data

Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit

4.MD.2

Use the four operations to solve
word problems involving distances, intervals of time, liquid volumes,
masses of objects, and money, including problems involving whole numbers
and/or simple fractions (addition and subtraction of fractions with like
denominators and multiplying a fraction times a fraction or a whole
number), 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.
*Note: Students in grade 4 will be assessed on
multiplying a fraction and a whole number as indicated in the NF domain.
Some students may be able to multiply a fraction by a fraction as a result
of generating equivalent fractions; however, mastery of multiplying two
fractions occurs in Grade 5.

Represent
and interpret data

4.MD.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.

Operations and Algebraic
Thinking

Generate and analyze patterns.

4.OA.5

Generate a number or shape pattern that follows a given
rule. Identify apparent features of the
pattern that were not
explicit in
the rule itself. For
example, given the
rule “Add 3”
and the starting number 1, generate terms in the resulting
sequence and observe that
the terms
appear to alternate between odd and even numbers. Explain informally why
the numbers will
continue to alternate in
this way.





Enduring Understandings:
·
Fractions
can be composed and decomposed from unit fractions.
·
Mixed
numbers and improper fractions can be used interchangeably.
·
Fractions
can be represented visually and in written form.
·
Fractions
of the same whole can be compared.
·
Fractional numbers and mixed numbers can be added,
subtracted, and multiplied.

Essential Questions:
·
What is a fraction, what does it represent, and how can
it be represented?
·
What is a mixed number and how can it be represented?
·
How can common numerators or denominators be created?
·
How can equivalent fractions be identified?
·
How can fractions with different numerators and
different denominators be compared?
·
How can fractions and mixed numbers be used
interchangeably?
·
How do we apply our understanding of fractions in
everyday life?
·
How can you use fractions to solve addition,
subtraction, and multiplication problems?
·
How do we add fractions with like denominators?
