Developing Fractions Sense
Grade 3 Standards
What wording would your students use
to explain why the red block is a half?
Grade 3: 36/39
Which shapes have parts that are of
Dear Workshop Participant:
their whole shape?
This handout is designed to enable you to better follow the
presentation by entering notes next to specific problems.
Additionally, it is intended as a resource for you once you return
to the classroom.
Copyright © 2014 by Borenson and Associates, Inc.
1
Please write down a statement you can
make to your students to explain the
2
3
What fractional part of the rectangular
figure is shaded?
meaning of the fraction .
A flower garden is divided into equal parts. The color
of the flowers planted in each part is shown.
Select the three statements that are true:
Choose one:
.
4
PARCC Grade 3:13/15
.
5
.
a.
b.
c.
d.
e.
f.
There are red or yellow flowers in 1/6 of the garden.
Purple flowers are planted in 7/8 of the garden.
Pink flowers are planted in 1/8 of the garden.
Each part of the garden is 1/8 of the whole garden.
There are yellow flowers in 3/6 of the garden.
Red flowers are planted in 3/8 of the garden.
6
Given the rectangular bar below,
Given the rectangular bar below,
How many rectangles are colored red?
How many rectangles are colored blue?
How many rectangles are colored red or blue?
What fraction of the grid is colored red or blue?
How many rectangles are colored red and blue?
What fraction of the rectangles are colored red and
blue?
display the fraction .
display the fraction .
7
8
9
In the rectangular grid below, one of the 8 equal
rectangles has been partitioned into two parts.
a.
b.
c.
d.
e.
f.
What do you think of displaying as shown below?
Example: Mrs. Jones brought two cakes for Sean’s
birthday party. The cakes were divided into six slices
each. A total of 7 slices were eaten. What fraction of
Mrs. Jones’ cakes was consumed?
How can we represent a segment of
length 1/3 on a number line?
Please discuss with a colleague
10
11
12
Locate a segment of length on the
number line.
Here is a different question.
Locate the point 7/9 on the number line.
Locate the number on the number line.
13
14
15
What are the names of points A and B?
Label each point with its distance from the
zero mark.
PARCC Grade 3: 8/39
16
17
Plot the point that shows
on the number line.
18
PARCC Grade 3: 23/39
Plot a point on the number line that shows
the location .
Using the fraction blocks, please see what other
equivalent fractions you can generate which are
less than or equal to 1.
=
Use your knowledge of equivalent
fractions, or generate equivalent fractions,
to find the value of the question mark.
=
=
19
Draw two 4 by 2 rectangular grid on graph
paper. Illustrate one equivalent fraction other
than = .
20
21
Use your knowledge of equivalent
fractions, or generate equivalent fractions,
to find the value of the question mark.
=
=
22
=
=
23
?
?
Enrichment
Use the figure below to come up with one pair of
equivalent fractions involving the denominator of 12:
?
?
?
?
24
PARCC Grade 3:30/39
Which three comparisons are true?
A.
PARCC: Grade 3
Part A:
=
B.
=
C.
=
D.
=
E.
=
of the field has been planted with soybeans.
25
Part B
Type a fraction different than in the boxes that also represents the
fractional part of the farmer’s field that is plated with soybeans.
26
27
PARCC: Grade 3
Part B: The grid below shows how much wall space the art teacher can
use. Use the grid to create a rectangular array showing how the art
teacher might arrange the tiles on the wall.
An art teacher will tile a section of the wall with painted tiles made by
students in three art classes.
 Class A made 18 tiles
 Class B made 14 tiles
 Class C made 16 tiles
Select the boxes to shade them. Each tile should be shown by one
shaded box.
Part A: What is the total number of tiles that are used?
Explain why the two fractions above are equal.
28
29
30
Part C
Andy created a rectangular array showing how he would place 56. He
placed 7 tiles in each row. He wrote a multiplication equation using R
to stand for the number of rows to be used.
Write an equation using R that Andy could have written.
PARCC G3: 17/39
PARCC Grade 3:36/39
Use the More or Fewer buttons as many times as needed to divide the
circle into 6 equal parts.
Which three figures have an area of 12 square inches?
Select three correct answers.
Then shade 1/6 of the area of the circle. Divide the figure into the
correct number of equal parts by using the More and Fewer buttons.
Then shade by selecting the part or parts.
Fewer
More
Reset
31
32
33
PARCC Grade 3: 27/39
PARCC Grade 3: 19/39
Smarter Balanced Grade 3
Ken draws a rectangle with an area of 35-square
inches. The width of the rectangle is 5 inches.
What is the length of Ken’s rectangle?
Drag and drop the correct area into the box below each shaded
rectangle.
Find the numbers that go in the boxes. Draw a line to
make two 5 feet by 2 feet rectangles.
34
35
Then, find the total area.
36
Smarter Balanced
are equivalent fraction.
Look at the diagram below. Write an
equation between two equivalent
fractions. Justify your response.
37
38
39
PARCC Grade 3: 28/39
PARCC Grade 3: 33/39
SB Grade 3:3
A fraction is shown on the number line.
Eric measures 10 oak leaves with a ruler. He records the lengths as shown. For
each oak leave drop an x onto the line plot to show the length.
Drag each fraction to the correct point on the number
line.
Show on the number line that and
Plot a point on this number line to show a fraction that
is equivalent to the fraction shown on the other
number line.
40
,
,
,
,
,
41
,
,
,
,
42
Let’s consider these 4 circles as the whole.
How many circles form one-third of the whole?
Let’s consider these 6 circles as the whole.
What fraction of the whole is shown in each case?
By definition, one-third is the part formed by 1 part
when the whole is partitioned into three equal parts.
How many circles form two-thirds of the whole?
43
44
45
Michelle has 15 dolls in her toy collection. Twothirds of the dolls have blond hair. How many of
her dolls have blond hair?
Enrichment
Let’s consider these 6 circles as the whole.
How many circles form five-thirds of the whole?
46
47
Rashid showed us 9 of his collector coins, which
is three-fourths of his coin collection. How many
coins are in his collection?
48
Enrichment
Let’s define the perimeter of a rectangle
PARCC Grade 3: 21/39
Lavina wants to place a fence around a rectangular play
area for her rabbits. The play area will be 7-feet long and 4feet wide.
Ten counters are five halves of a set. How
many counters does the set have?
What is the total length of fence, in feet, Lavina needs to
place around the play area?
The perimeter, , of a rectangle is the sum of all four sides.
= +
49
Let’s compare fractions:
Use the correct symbol to show the
relationship: “<”, “=” or “>”
=
+
or
+ +
or
50
= ( +
)
Symbolically,
> , ℎ
> .
51
Use the correct symbol to show the
relationship: “<”, “=” or “>”
How would you verbalize the above statement?
a.
b.
Justify your answer visually
Justify your answer with a statement of explanation
52
53
54
“If you like a cake, would you rather have
one-third of the cake or one-hundredth of
the cake? Which is larger?”
Symbolically,
> , ℎ
< .
Use the correct symbol to show the
relationship: “<”, “=” or “>”
How would you verbalize the above statement?
Justify your response.
55
56
Symbolically,
PARCC Grade 3: 3/39
> , ℎ
< ,
for any whole number
57
<
Select the three fractions that make this comparison true.
> .
How would you verbalize the above statement?
a.
b.
c.
d.
e.
58
59
60