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3rd Grade
Fractions
www.njctl.org
2015-03-31
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· Whole Number Fractions
· Equal Parts
· Fractions of a Group
· Comparing Fractions with Same D enominators or Numerators
· Equivalent Fractions
Table of Contents
· Fractions on a Number Line
Click title to go to that section
· Measurement to Nearest H alf and Quarter Inch
· Benchmarks
· Exploring Fractions with Pattern Blocks
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Links to PARCC sample questions
Non-Calculator #3
Non-Calculator #4
End of Year
Performance Based Assessment
Non-Calculator #5Non-Calculator #7Non-Calculator #17
Non-Calculator #8Non-Calculator #13Non-Calculator #17Non-Calculator #23Non-Calculator #28Non-Calculator #30Non-Calculator #35
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Equal Parts
Return toTable of Contents
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Fraction - An expression that indicates the quotient ( ) of two quantities.
Numerator - The number above the fraction bar. The numerator answers the question"How many parts?"
Denominator - The number below the fraction bar. The denominator answers the question "How many total?"
Key Terms
Numerator 3 Denominator 7
Fraction = =
÷
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Where have you seen fractions? How do we use fractions?
96/100= A+
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These are halves.
How do you write one half?
numerator
denominator
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These are thirds.
How do you write one third?
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These are Fourths.
How do you show and write two fourths?
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Sixths
How do you show and write two sixths?
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Eighths
How do you show and write eight eighths?
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What fractions are represented below?
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Internet links for more practice
Fractions Naming Model
Fractions Parts of a Whole Model
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1 Does this show ?
YesNo
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2 What fraction of the whole is shaded?
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2 What fraction of the whole is shaded?
[This object is a pull tab]
Teac
her N
otes Note: To enter a fraction,
enter the number for the numerator, then press the fraction key. Next,
enter the number for the denominator.
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3 What fraction of the whole is white?
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4 What fraction could this picture show?
A
B
C Both A and B
D Neither A nor B
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5 How many more yellow pieces do I need to make this fraction ?
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6 Which of the following could be used to show ?
A B C
D
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7 Bella cut her ribbon into 4 pieces that are the same length. The length of one piece of ribbon is what fraction of the length of the ribbon?
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8 A whole is divided into 4 equal parts. Write the fraction that represents 3 parts of the whole.
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9 A whole is divided into 6 equal parts. Write the fraction that represents 1 part of the whole.
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10 A whole is divided into 7 equal parts. Write the fraction that represents 4 parts of the whole.
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11 Lee needs of a cup of sugar to make cookies. He
will measure the sugar using a cup scoop. How
many times will Lee need to fill the cup scoop in
order to measure of a cup of sugar?
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12 Sasha needs of a cup of mix to make pancakes
She will measure the mix using a cup scoop.
How many times will Sasha need to fill the cup
scoop in order to measure of a cup of mix?
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13 Which three shapes have parts that are the area of their whole shape.
A B C D E
Drag and drop the correct three shapes into the box.
From PARCC sample test
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13 Which three shapes have parts that are the area of their whole shape.
A B C D E
Drag and drop the correct three shapes into the box.
From PARCC sample test
[This object is a pull tab]
Ans
wer
B, C, & D
Once students have answered this question, have a volunteer come to the board to drag the three shapes into the shaded
box.
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14 Select the two shapes that have parts that are each
of the area of the whole shape.
A
B
C
D
E
From PARCC sample test
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14 Select the two shapes that have parts that are each
of the area of the whole shape.
A
B
C
D
E
From PARCC sample test
[This object is a pull tab]
Ans
wer
D & E
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15 A flower garden is divided into equal parts. The color of the flowers planted in each part of the garden is shown.
Select the three statements that are true.A There are red or yellow flowers in of the garden.
B Purple flowers are planted in of the garden.
C Pinks flowers are planted in of the garden.
D Each part of the garden is of the whole garden.
E There are yellow flowers in of the garden.
F Red flowers are planted in of the garden.From PARCC sample test
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15 A flower garden is divided into equal parts. The color of the flowers planted in each part of the garden is shown.
Select the three statements that are true.A There are red or yellow flowers in of the garden.
B Purple flowers are planted in of the garden.
C Pinks flowers are planted in of the garden.
D Each part of the garden is of the whole garden.
E There are yellow flowers in of the garden.
F Red flowers are planted in of the garden.From PARCC sample test
[This object is a pull tab]
Ans
wer
C, D, & F
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16 Each model equals one whole divided into equal parts. Which models show shaded?
Select the three correct answers.
A
B
C
D
E
F
From PARCC sample test
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16 Each model equals one whole divided into equal parts. Which models show shaded?
Select the three correct answers.
A
B
C
D
E
F
From PARCC sample test
[This object is a pull tab]
Ans
wer
A, C & E
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17 An artist plans to paint a wall in a room. The wall is divided into 6 equal parts so that each part can be painted a different color.
Part A
The artist goes to the store to buy brushes and small cans of paint. He pays a total of $94.· He buys 8 brushes that cost $5 each.· The rest of the money is used for the 6 cans of paint.
Each can of paint costs the same amount.
How much does each can of paint cost? (Show your work on paper at your desk and be ready to explain)
From PARCC sample test
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17 An artist plans to paint a wall in a room. The wall is divided into 6 equal parts so that each part can be painted a different color.
Part A
The artist goes to the store to buy brushes and small cans of paint. He pays a total of $94.· He buys 8 brushes that cost $5 each.· The rest of the money is used for the 6 cans of paint.
Each can of paint costs the same amount.
How much does each can of paint cost? (Show your work on paper at your desk and be ready to explain)
From PARCC sample test
[This object is a pull tab]
Ans
wer
Work:
8 brushes x $5 each = $40
$94 - $40 = $54
$54 6 = $9
Each can of paint costs $9.
÷
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18 Part B
The artist starts painting the wall. The parts of the wall that look white are not painted yet.
Which statements about the wall are correct?
Select the two correct statements.A Each painted part it of the whole wall.B Each painted part it of the whole wall.C Each painted part it of the whole wall.D The fraction of the wall not yet painted is .E The fraction of the wall not yet painted is .F The fraction of the wall not yet painted is .
From PARCC sample test
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18 Part B
The artist starts painting the wall. The parts of the wall that look white are not painted yet.
Which statements about the wall are correct?
Select the two correct statements.A Each painted part it of the whole wall.B Each painted part it of the whole wall.C Each painted part it of the whole wall.D The fraction of the wall not yet painted is .E The fraction of the wall not yet painted is .F The fraction of the wall not yet painted is .
From PARCC sample test
[This object is a pull tab]
Ans
wer
B and F
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Fractions of a Group
Return toTable of Contents
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The last lesson focused on dividing a whole shape into fractions.This lesson focuses on fractions of group of objects.
12
12
1 of the group of apples2
1 of the whole2
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What fraction of the shapes are circles?
Step 1: Count the circles. This is your numerator.
Step 2: Count all of the shapes. This is the denominator.
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What fraction of the nickels are heads up?
What fraction of the nickels are on tails?
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What fraction of the faces are happy?
What fraction of the faces are sad?
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Circle of the mice.
Circle of the frogs.
Circle of the lions.
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Click the cookie to practice fractions of a group.
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19 Are of the lions in the triangle?
Yes
No
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20 What fraction of the frogs are boxed below?
A
B
C
D
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21 What fraction is not circled?
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22 of the dogs are wearing a bow.
True
False
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23 What fraction of the flowers are not in the vase?
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Exploring Fractions with Pattern Blocks
Return toTable of Contents
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Groups of students need:
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Groups of students need:
[This object is a pull tab]
Teac
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otes
Have students work in groups to explore
the relationships between the blocks.
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How many are in one ?
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How many are in one ?
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Teac
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otes
Blocks are infinitely cloned.
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The is what fraction of the ?
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The is what fraction of the ?
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Teac
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Blocks are infinitely cloned.
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24 How many green triangles are in one red trapezoid?
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24 How many green triangles are in one red trapezoid?
[This object is a pull tab]
Teac
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otes
Trapezoid is locked in place, triangles are
infinitely cloned.
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25 The green triangle is what fraction of the red trapezoid?
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25 The green triangle is what fraction of the red trapezoid?
[This object is a pull tab]
Teac
her N
otes
Trapezoid is locked in place, triangles are
infinitely cloned.
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26 How many green triangles are in one yellow hexagon?
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26 How many green triangles are in one yellow hexagon?
[This object is a pull tab]
Teac
her N
otes
Hexagon is locked in place, triangles are
infinitely cloned.
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27 The green triangle is what fraction of the yellow hexagon?
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27 The green triangle is what fraction of the yellow hexagon?
[This object is a pull tab]
Teac
her N
otes
Hexagon is locked in place, triangles are
infinitely cloned.
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28 How many blue rhombuses are in one yellow hexagon?
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28 How many blue rhombuses are in one yellow hexagon?
[This object is a pull tab]
Teac
her N
otes
Hexagon is locked in place, rhombus is
infinitely cloned.
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29 The blue rhombus is what fraction of the yellow hexagon?
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29 The blue rhombus is what fraction of the yellow hexagon?
[This object is a pull tab]
Teac
her N
otes
Hexagon is locked in place, rhombus is
infinitely cloned.
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30 How many red trapezoids are in one yellow hexagon?
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30 How many red trapezoids are in one yellow hexagon?
[This object is a pull tab]
Teac
her N
otes
Hexagon is locked in place, trapezoid is
infinitely cloned.
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31 The red trapezoid is what fraction of the yellow hexagon?
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31 The red trapezoid is what fraction of the yellow hexagon?
[This object is a pull tab]
Teac
her N
otes
Hexagon is locked in place, trapezoid is
infinitely cloned.
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Small group/ individual practice with online pattern blocks.
Click for web site.
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Pattern block activity
Groups need a container of pattern blocks and will use pattern blocks to represent
fractions of a group.
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In this group of 8 pattern blocks, 3 of
them are triangles.
Drag blocks needed down into work space.
WORK SPACE
of the group is triangles
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Make a group of 5 pattern
blocks, with 2 of them squares.
Drag blocks needed down into work space.
WORK SPACE
Fraction =
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Make a group of 7 pattern
blocks, with 6 of them trapezoids.
Drag blocks needed down into work space.
WORK SPACE
Fraction =
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Make a group of 3 pattern
blocks, with 2 of them hexagons.
Drag blocks needed down into work space.
WORK SPACE
Fraction =
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32 What fraction of this group of pattern blocks is squares?
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33 What fraction of this group of pattern blocks is triangles?
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34 What fraction of this group of pattern blocks is hexagons?
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35 What fraction of this group of pattern blocks is trapezoids?
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36 What fraction of this group of pattern blocks is triangles?
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Fractions on a Number Line
Return toTable of Contents
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There are numbers between 0 and 1.
0 1
What is a number that is greater than 0 but less than 1?
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0 1
How did you know what the number was?
The number line was divided into 2 equal sections.
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What denominator would you use if the number line was divided into 3 equal parts?
0 1
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What denominator would you use if the number line was divided into 4 equal parts?
0 1
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37 Should you use a 6 in the denominator for this number line?
YesNo
10
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38 What denominator would you use to represent the lines on this number line?
0 1
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39 What denominator would you use to represent the lines on this number line?
0 1
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40 What denominator would you use to represent the lines on this number line?
0 1
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41 What denominator would you use to represent the lines on this number line?
0 1
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0 1
Move the fractions to label the lines on the number line.
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0 1
Divide the number line into 7 equal parts and label it.
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0 1
Divide the number line into 5 equal parts and label it.
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Click for Number Line Game
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42 What fraction is missing from the number line?
A
B
C
D
0 1 3 4 1 5 5 5
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43 What is the fraction for the red dot?
0 1?
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44 What is the fraction for the red dot?
0 1?
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45 What is the fraction for the red dot?
0 1?
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46 Where should be placed?
A B C0 1
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47 What fraction should be placed with point Z?
A B C
0 1X Y Z
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48 The point on the number line below represents the fraction . Which point shows ?
A B C D
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49 The point on the number line below represents the fraction . Which point shows 1?
A B C D
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50 The point on the number line below represents the fraction . Which point shows 0?
A B C D
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51 Which letter shows where would be plotted on the number line?
A B C D
From PARCC sample test
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51 Which letter shows where would be plotted on the number line?
A B C D
From PARCC sample test
[This object is a pull tab]
Ans
wer
C
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52 Which letter is positioned at ?
A B C D
From PARCC sample test
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52 Which letter is positioned at ?
A B C D
From PARCC sample test
[This object is a pull tab]
Ans
wer
D
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53 A fraction is shown on the number line.
Which letter is positioned on the number line to show a fraction that is equivalent to the fraction shown on the other number line?
A B C D
From PARCC sample test
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53 A fraction is shown on the number line.
Which letter is positioned on the number line to show a fraction that is equivalent to the fraction shown on the other number line?
A B C D
From PARCC sample test
[This object is a pull tab]
Ans
wer
C
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54 Which letter is positioned at ?
A B C D
From PARCC sample test
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54 Which letter is positioned at ?
A B C D
From PARCC sample test
[This object is a pull tab]
Ans
wer
B
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55 Mia placed point P on the number line.
What is the value of P as a fraction?
A
B
C
D
What does the denominator of your fraction represent on the number line?
What does the numerator of your fraction represent on the number line?
From PARCC sample test
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55 Mia placed point P on the number line.
What is the value of P as a fraction?
A
B
C
D
What does the denominator of your fraction represent on the number line?
What does the numerator of your fraction represent on the number line?
From PARCC sample test
[This object is a pull tab]
Ans
wer
C
The first question can be answered with responders.
The bottom two questions are to be answered on paper or
as a class discussion.
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Comparing Fractions
Return toTable of Contents
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To compare fractions, you could use pictures or number lines to determine which fractions are greater. By using these strategies,
you will come up with some rules to remember.
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Let's compare 4/5 and 2/5. Which one is greater? How do you know?
15 0 1
What rule could you use when comparing fractions with the same denominator?
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Let's compare 4/5 and 2/5. Which one is greater? How do you know?
15 0 1
What rule could you use when comparing fractions with the same denominator?
[This object is a pull tab]
Teac
her N
otes
The fraction pieces are infinitely cloned.
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Slide each problem over to the blue side to see if you are correct.
1 < 22 2
2 < 46 6
4 > 25 5
3 > 24 4
1 < 23 3
Compare each set of fractions. (Drag fraction to box on right to see the inequality symbol)
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56
A <
B >
C =
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57
A <
B >
C =
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58
A <
B >
C =
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59
A <
B >
C =
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60 Classroom A has of the students buying school lunch. Classroom B has of the students buying lunch. Which classroom has the larger fraction of the students buying lunch?
A Classroom A
B Classroom B
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12
Let's compare 1/5 and 1/2. Which one is greater? How do you know?
0 1
What rule could you use when comparing fractions with the same numerator?
15
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12
Let's compare 1/5 and 1/2. Which one is greater? How do you know?
0 1
What rule could you use when comparing fractions with the same numerator?
15
[This object is a pull tab]
Teac
her N
otes
The fraction pieces are infinitely cloned.
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Compare each set of fractions. Move the magnifying glass to see if you are correct.
1 > 12 3 6 < 6
12 10
3 > 34 5
4 > 46 8
5 < 59 7
2 < 25 2
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61 is less than .
Yes
No
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62 Which fraction is greater than ?
A
B
C Both A and B
D Neither A Nor B
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63
A <
B >
C =
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64
A <
B >
C =
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65
A <
B >
C =
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Click the fish to practice comparing fractions with the same denominators or
the same numerators.
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66 Enter a fraction larger than .
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67 Enter a fraction larger than .
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68 Enter a fraction less than .
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69 Enter a fraction less than .
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70 Which three comparisons are true?
A =
B =
C =
D =
E =
From PARCC sample test
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70 Which three comparisons are true?
A =
B =
C =
D =
E =
From PARCC sample test
[This object is a pull tab]
Ans
wer
B, C, & E
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71
A
B
C
D
E
<Select the three fractions that make this comparison true.
From PARCC sample test
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71
A
B
C
D
E
<Select the three fractions that make this comparison true.
From PARCC sample test
[This object is a pull tab]
Ans
wer
A, C & E
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Benchmark F ractions
Return toTable of Contents
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0 1
This circle has of it shaded. This is very close to zero.
This circle has of it shaded. This is very close to one.
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0 1
<
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0 1
This rectangle has of it shaded. This is very close to zero.
This rectangle has of it shaded. This is very close to one.
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0 1
<
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0 1
This group has of it sharks. This is very close to zero (or none of the group).
This group has of it dogs. This is very close to one (or the whole group).
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0 1
<
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72 Which fraction is closest to zero?
A B C D
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73 Which fraction is closest to zero?
A B C D
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74 Which fraction is closest to one?
A B C D
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75 Which fraction is closest to one?
A B C D
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0 1
We can also see if a fraction is equal to or close to .
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0 1
< <
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0 1
Very close to zero.
Very close to .
Very close to onewhole.
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0 1
< <
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0 1
This group has of it pinkhearts, thisis very close to of the group.
This group has of it blue triangles, this is very close to the whole group.
This group has of it purple stars, this is very close tozero.
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0 1
< <
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Move the magnifier to find the fractions that are close to half.
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79 Which fraction is closest to ?
A B C D
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80 Which fraction is closest to ?
A B C D
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81 Which fraction is closest to ?
A B C D
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82 Which group shows about of it as stars?
A B C
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83 Which group shows about of it as circles?
A B C
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Equivalent Fractions
Return toTable of Contents
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Key Term
Equivalent Fractions- Fractions that represent the same number or are equal to one another.
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1/4 pieces 1/6 pieces 1/8 pieces
1/2
How many 1/4 pieces fit in the 1/2 piece? Write as a fraction.
How many 1/6 pieces fit in the 1/2 piece?
How many 1/8 pieces fit in the 1/2 piece?
These fractions are equivalent.
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1/3 1/6 pieces
How many 1/6 pieces fit in a 1/3?
We show equivalence by writing both fractions with an equal sign.
=
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19
19
19
What do you notice about the denominators in each set of equivalent fractions?
The fraction bars below are equivalent because they are the same size.
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Drag the red rectangle to see equivalent fractions on number lines.
What do you notice about the numerators and denominators?
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To create equivalent fractions, multiply(or divide) the numerator and denominator by the same number.
2 x 3 = 6 4 x 3 = 12
6 ÷ 3 = 2 21 ÷ 3 = 7
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To create equivalent fractions, multiply(or divide) the numerator and denominator by the same number.
2 x 3 = 6 4 x 3 = 12
6 ÷ 3 = 2 21 ÷ 3 = 7
[This object is a pull tab]
Teac
her N
otes
Discuss the reason this works. 3/3 = 1 whole and any number (even fractions) multiplied or divided by one is the same
number.
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Practice finding equivalent fractions with this game. Click the star to play!
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84 Are the shaded areas equivalent?
Yes
No
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85 Which fraction is equivalent to ?
A
B
C
D
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86 Write a fraction equivalent to . 1 3
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87 Which set of fractions is equivalent?
A
B
C
D
1 2 2 2
=
4 1 8 4
1 3 3 6
3 9 7 21
=
=
=
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88 Write a fraction equivalent to . 5 9
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Whole Number Fractions
Return toTable of Contents
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Numerator = How many parts?
Denominator = How many total?
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This is read as 3 over 1.
It is 3 parts of 1 total.
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If each circle is one whole, then this picture shows that
3 wholes are shaded.
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The fraction bar means division. If you take the whole number 3 and divide it by 1. What would your answer be?
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89 What whole number is equal to?
A
B
C 4
D 1
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90 What whole number is equal to?
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91 What whole number is equal to?
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92 What fraction is equal to the whole number 7?
A
B
C
D 7
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93 What fraction is equal to the whole number 8?
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94 What fraction is equal to the whole number 3?
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Measurement to the Nearest Half and Quarter
Inch
Return toTable of Contents
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Inch
Small units of length are called inches.
Depending on how big your thumb is,your thumbnail can be about 1 inch.
The abbreviation of inch is in.
Can you think of some things you could measure in inches?
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Follow these steps to measure something correctly:
· Determine the unit you are measuring in.
· Choose the correct tool.
· Correctly line up the measuring tool.
· Measure to the nearest unit.
· Label your measurement.
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Let's measure this line in inches.
Determine the unit you are measuring in.
Choose the correct tool.
Correctly line up the measuring tool.
Measure to the nearest unit.
Label your measurement.
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Let's measure this line in inches.
Determine the unit you are measuring in.
Choose the correct tool.
Correctly line up the measuring tool.
Measure to the nearest unit.
Label your measurement.
x
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Let's measure this line in inches.
Determine the unit you are measuring in.
Choose the correct tool.
Correctly line up the measuring tool.
Measure to the nearest unit.
Label your measurement.
xx
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Let's measure this line in inches.
Determine the unit you are measuring in.
Choose the correct tool.
Correctly line up the measuring tool.
Measure to the nearest unit.
Label your measurement.
xxx
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Let's measure this line in inches.
Determine the unit you are measuring in.
Choose the correct tool.
Correctly line up the measuring tool.
Measure to the nearest unit.
Label your measurement.
xxxx
3 in.
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Click on The Ruler Game to practice measuring in inches.
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95 This line is 4 inches long.
Yes
No
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96 How long is this line?
_____ in.
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97 How many inches is this pencil?
_____ in.
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98 How many inches is this crayon?
_____ in.
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In between each of the numbers on a ruler are 1/2 inches.
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Let's measure in half inches.
Correctly line up the measuring tool.
Measure to the nearest half inch.
Label your measurement.
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Let's measure in half inches.
Correctly line up the measuring tool.
Measure to the nearest half inch.
Label your measurement.
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Let's measure in half inches.
Correctly line up the measuring tool.
Measure to the nearest half inch.
Label your measurement.
3 1/2 in.
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Let's measure in half inches.
Correctly line up the measuring tool.
Measure to the nearest half inch.
Label your measurement.
3 1/2 in.
Slide 188 / 215
Click on The Ruler Game to practice measuring in half inches.
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100 This line is inch long.
Yes
No
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101 How many inches is this comb?
_____ in.
A 3 1/2 in.
B 2 in.
C 2 1/2 in.
D 1/2 in.
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102 How many inches is this card?
_____ in.
A 3 1/2 in.
B 2 in.
C 2 1/2 in.
D 1/2 in.
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103 How long is this line?
_____ in.
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When measuring an object, we can get a more exact measurement using inch increments.
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What do you notice about inch?
in.
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What do you notice about inch?
in.
[This object is a pull tab]
Teac
her N
otes inch is equal to inch.
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104 Is inches equivalent to inches?
Yes
No
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105 Is in. equivalent to in.?
Yes
No
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Let's measure in quarter inches.
Correctly line up the measuring tool.
Measure to the nearest quarter inch.
Label your measurement.
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Let's measure in quarter inches.
Correctly line up the measuring tool.
Measure to the nearest quarter inch.
Label your measurement.
Slide 199 / 215
Let's measure in quarter inches.
Correctly line up the measuring tool.
Measure to the nearest quarter inch.
Label your measurement.
in.
Slide 200 / 215
Click to practice measuring in quarter inches.
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106 Measure the line. Students type their answers here
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107 Measure the line. Students type their answers here
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108 Measure the line. Students type their answers here
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109 Measure the line. Students type their answers here
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110 Measure the object. Students type their answers here
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111 Measure this object. Students type their answers here
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112 Measure this object. Students type their answers here
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113 Measure this object. Students type their answers here
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114 Measure this object. Students type their answers here
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115 Measure this object. Students type their answers here
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116 Measure this object. Students type their answers here
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117 Measure this object. Students type their answers here
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118 Measure this object. Students type their answers here
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119 Measure this object. Students type their answers here
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