3rd Grade Mathematics
Instructional Week 31
Equivalent Fractions
Paced Standards:
3.NS.6: Understand two fractions as equivalent (equal) if they are the same size, based on the same
whole or the same point on a number line. –
3.NS.7: Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why
the fractions are equivalent (e.g., by using a visual fraction model). +
3.NS.8: Compare two fractions with the same numerator or the same denominator by reasoning
about their size based on the same whole. Record the results of comparisons with the symbols >, =,
or <, and justify the conclusions (e.g., by using a visual fraction model). 
Connections to other 3rd Grade Standards:
3.NS.3: 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. [In grade 3,
limit denominators of fractions to 2, 3, 4, 6, 8.]
3.NS.4: Represent a fraction, 1/b, on a number line by defining the interval from 0 to 1 as the whole,
and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of
the part based at 0 locates the number 1/b on the number line.
3.NS.5: Represent a fraction, a/b, on a number line by marking off lengths 1/b from 0. Recognize that
the resulting interval has size a/b, and that its endpoint locates the number a/b on the number line.
3.G.4: Partition shapes into parts with equal areas. Express the area of each part as a unit
fraction of the whole (1/2, 1/3, 1/4, 1/6, 1/8).
3.M.2: Choose and use appropriate units and tools to estimate and measure length, weight, and
temperature. Estimate and measure length to a quarter-inch, weight in pounds, and temperature in
degrees Celsius and Fahrenheit. 
3.DA.2: Generate measurement data by measuring lengths with rulers to the nearest quarter of an
inch. Display the data by making a line plot, where the horizontal scale is marked off in appropriate
units, such as whole numbers, halves, or quarters. 
Prerequisite/Foundational Standards:
2.G.5: Partition circles and rectangles into two, three, or four equal parts; describe the shares using
the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds,
four fourths. Recognize that equal parts of identical wholes need not have the same shape.
1.G.4: Partition circles and rectangles into two and four equal parts; describe the parts using the
words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of. Describe
the whole as two of, or four of, the parts. Understand for partitioning circles and rectangles into two
and four equal parts that decomposing into equal parts creates smaller parts.
3rd Grade ISTEP+ Toolkit
Indianapolis Public Schools
Curriculum and Instruction
3.NS.6
Standard: 3.NS.6: Understand two fractions as equivalent (equal) if they are the same size, based on the same whole or
the same point on a number line.
Teacher Background Information:
All students should eventually be able to write an equivalent fraction for a given fraction. At the same time, the
procedures should never be taught or used until the students understand what the result means. Consider how
different the procedure and the concept appear to be:
Concept: Two fractions are equivalent if they are representations for the same amount or quantity—if they are the
same number.
Procedure: To get an equivalent fraction, multiply (or divide) the top and bottom numbers by the same nonzero
number.
In 3rd grade, students will base their understanding of equivalent fractions completely on models and not on a
procedure. The general approach to helping students create an understanding of equivalent fractions is to have
them use contexts and models to find different names for a fraction. Consider that this is the first time in their
experience that a fixed quantity can have multiple names (actually an infinite number of names). Area models are a
good place to begin understanding equivalence.
Indianapolis Public Schools
Curriculum and Instruction
3.NS.6
Standard: 3.NS.6: Understand two fractions as equivalent (equal) if they are the same size, based on the same whole or
the same point on a number line.
Teacher Background Information:
Process Standards to Emphasize with Instruction of 3.NS.6:
3.PS.1: Make sense of problems and persevere in solving them.
3.PS.2: Reason abstractly and quantitatively.
3.PS.3: Construct viable arguments and critique the reasoning of others.
3.PS.4: Model with mathematics.
3.PS.6: Attend to precision.
3.PS.7: Look for and make use of structure.
3.PS.8: Look for and express regularity in repeated reasoning.
Indianapolis Public Schools
Curriculum and Instruction
3.NS.7
Standard: 3.NS.7: Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the
fractions are equivalent (e.g., by using a visual fraction model).
Teacher Background Information:
Grade 3 students do some preliminary reasoning about equivalent fractions, in preparation for work in Grade 4. As
students experiment on number line diagrams, they discover that many fractions label the same point on the number
1
2
line, and are therefore equal; that is, they are equivalent fractions. For example, the fraction is equal to and also to
2
4
3
.
6
Process Standards to Emphasize with Instruction of 3.NS.7:
3.PS.1: Make sense of problems and persevere in solving them.
3.PS.2: Reason abstractly and quantitatively.
3.PS.3: Construct viable arguments and critique the reasoning of others.
3.PS.4: Model with mathematics.
3.PS.6: Attend to precision.
3.PS.7: Look for and make use of structure.
3.PS.8: Look for and express regularity in repeated reasoning.
Indianapolis Public Schools
Curriculum and Instruction
3.NS.8
Standard: 3.NS.8: Compare two fractions with the same numerator or the same denominator by reasoning about their
size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions
(e.g., by using a visual fraction model).
Teacher Background Information:
Experiences should encourage students to reason about the size of pieces when dealing with fractions… the fact
1
1
that of a cake is larger than of the same cake. Since the same cake (the whole) is split into equal pieces, thirds
4
3
are larger than fourths.
Students recognize when examining fractions with common denominators, the wholes have been divided into the same
number of equal parts. So the fraction with the larger numerator has the larger number of equal parts.
2
5
<
6
6
Previously, in second grade, students compared lengths using a standard measurement unit. In third grade they
build on this idea to compare fractions with the same denominator. They see that for fractions that have the same
denominator, the underlying unit fractions are the same size, so the fraction with the greater numerator is greater
3
because it is made of more unit fractions. For example, the segment from 0 to
is shorter than the segment from
4
5
1
1
3
5
0 to because it measures 3 units of as opposed to 5 units of , therefore
< .
4
4
4
4
4
To compare fractions that have the same numerator but different denominators, students understand that each
fraction has the same number of equal parts but the size of the parts are different. They can infer that the same number
of smaller pieces is less than the same number of bigger pieces.
3 3
<
8 4
This standard involves comparing fractions with or without visual fraction models including number lines.
In this standard, students should also reason that comparisons are only valid if the wholes are identical. For
1
1
example,
of a large pizza is a different amount than
of a small pizza. Students should be given
2
2
1
opportunities to discuss and reason about which
is larger.
2
Indianapolis Public Schools
Curriculum and Instruction
3.NS.8
Standard: 3.NS.8: Compare two fractions with the same numerator or the same denominator by reasoning about their
size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions
(e.g., by using a visual fraction model).
Teacher Background Information:
Students also see that for unit fractions, the one with the larger denominator is smaller, by reasoning, for example, that
in order for more (identical) pieces to make the same whole, the pieces must be smaller. From this they reason that for
2 2
fractions that have the same numerator, the fraction with the smaller denominator is greater. For example, > ,
5 7
1 1
1
1
because < , so 2 lengths of is less than 2 lengths of . As with equivalence of fractions, it is important in
7 5
7
5
comparing fractions to make sure that each fraction refers to the same whole.
Process Standards to Emphasize with Instruction of 3.NS.8:
3.PS.1: Make sense of problems and persevere in solving them.
3.PS.2: Reason abstractly and quantitatively.
3.PS.3: Construct viable arguments and critique the reasoning of others.
3.PS.4: Model with mathematics.
3.PS.6: Attend to precision.
3.PS.7: Look for and make use of structure.
3.PS.8: Look for and express regularity in repeated reasoning.
Indianapolis Public Schools
Curriculum and Instruction
Instructional Week 31
3rd Grade Mathematics Assessment
Name: _____________________________
1.
4
4
of the figure above is shaded. Which fraction below is equivalent to
?
12
12
1
6
1
B.
4
1
C.
3
1
D.
2
A.
2. Megan and three of her friends ordered the same sized personal pan pizzas. The shaded part shows the
fraction of pizza that each person ate.
Megan
Tia
Lola
Polly
Which two people ate the same fraction of pizza?
A. Megan and Tia
B. Tia and Lola
C. Lola and Polly
D. Megan and Polly
Indianapolis Public Schools
Curriculum and Instruction
3. The fractions below are based on the same whole. Which comparison is true?
A.
1
1
is greater than
.
8
21
B.
7
7
is greater than .
9
8
C.
10
8
is less than
.
18
18
D.
11
10
is less than
.
14
14
4.
1
cups of sugar. Which of the following ways describes how the measuring cups shown can be
3
1
used to measure 1 cups of sugar accurately?
3
A recipe requires 1
I. Use the
II. Use the
III. Use the
IV. Use the
V. Use the
1
3
1
2
1
2
1
3
1
4
cup four times.
cup three times.
1
cup once.
3
1
cup twice and the cup once.
2
1
cup four times and the cup once.
3
cup twice and the
A. I, II, III, and IV only
B. I, III, and V only
C. II, and IV only
D. I only
Indianapolis Public Schools
Curriculum and Instruction
5. Look at the pattern blocks below.
hexagon
rhombus
triangle
trapezoid
Which statement is NOT true?
A. One rhombus is
B. One triangle is
1
of the hexagon.
3
1
of the trapezoid.
3
C. Two triangles are
1
of the hexagon.
3
D. Two rhombuses are
1
of the hexagon.
3
6. Use the number line to compare the given fractions. Which number sentence is true?
0
1
12
1
6
A.
2 1
<
3 3
B.
5 4
<
6 6
C.
3
3
>
4 12
D.
1 1
>
3 2
1
4
Indianapolis Public Schools
1
3
1
2
1
Curriculum and Instruction
Instructional Week 31
3 Grade Assessment Answer Key
Correct Answer
C
D
A
B
D
C
rd
Question
1
2
3
4
5
6
Indianapolis Public Schools
Standard(s)
3.NS.6
3.NS.7
3.NS.8
3.NS.7
3.NS.6
3.NS.8
Curriculum and Instruction