Math Gr4 Ch13

Chapter 13
Fractions
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Lesson 13-1 Parts of a Whole
Lesson 13-2 Parts of a Set
Lesson 13-3 Problem-Solving Strategy: Draw
a Picture
Lesson 13-4 Equivalent Fractions
Lesson 13-5 Simplest Form
Lesson 13-6 Problem-Solving Investigation:
Choose a Strategy
Lesson 13-7 Compare and Order Fractions
Lesson 13-8 Add and Subtract Like Fractions
Lesson 13-9 Mixed Numbers
13
Fractions

Five-Minute Check (over Chapter 12)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
13-1 Parts of a Whole

• I will identify, write, and read fractions for parts
of a whole.
• fraction
• numerator
• denominator

Standard 4NS1.5 Explain different
interpretations of fractions, for example, parts
of a whole, parts of a set, and division of whole
numbers by whole numbers; explain equivalence
of fractions.

Standard 4NS1.7 Write the fraction represented
by a drawing of parts of a figure; represent a given
fraction by using drawings; and relate a fraction to
a simple decimal on a number line.

Write blue pieces
What fraction of the
circle is blue?
5
total pieces in all 8
Read five-eighths or five divided by eight
Answer: So, of the whole circle is blue.
5
8

What fraction of the circle is red?
A.
1
2
B.
3
5
C.
3
8
D.
3
4

What fraction of the figure is shaded?
Write parts shaded 3
total equal pieces in all 6
Read three-sixths or three divided by six
Answer: So, of the whole figure is shaded.
3
6

What fraction of the figure is shaded?
A.
1
6
B.
5
6
C.
7
8
D.
3
4

Gina is decorating a card for her mother’s birthday.
She decides to put glitter on of the card. Draw a
picture to show this fraction.
2
3
Divide a rectangle into 3 equal parts. Shade one
part to show two-thirds.

After Melinda’s party, she had of a pie left. Draw
a picture to show this fraction.
1
6
D.
A. B.
C.

Five-Minute Check (over Lesson 13-1)
Main Idea
Example 1
Example 2
Example 3
13-2 Parts of a Set

13-2 Parts of a Set
• I will identify, read, write, and model fractions for
parts of a set.

13-2 Parts of a Set
Standard 4NS1.5 Explain different interpretations
of fractions, for example, parts of a whole, parts
of a set, and division of whole numbers by whole
numbers; explain equivalence of fractions.

13-2 Parts of a Set
Standard 4NS1.7 Write the fraction represented
by a drawing of parts of a figure; represent a
given fraction by using drawings; and relate a
fraction to a simple decimal on a number line.

bicycles are red?
13-2 Parts of a Set
Write red bicycles 3
total cars 5
Read three-fifths or three divided by five
Answer: So, of the bicycles are red.
3
5
numerator
denominator

13-2 Parts of a Set
What fraction of the triangles are orange?
A.
3
7
B.
2
7
C.
4
7
D.
3
5

13-2 Parts of a Set
helmets are not black?
Write helmets not black 5
total helmets 7
Read five-sevenths or five divided by seven
Answer: So, of the helmets are not black.
5
7
numerator
denominator

13-2 Parts of a Set
What fraction of the circles are not blue?
A.
5
7
B.
3
5
C.
2
5
D.
1
2

Lane has 6 pets. Four-sixths of her pets are fish.
Draw a picture to model this fraction.
Answer: Four of Lane’s 6 pets are fish. You need to
draw a picture of four fish and two of any
other type of pet.
13-2 Parts of a Set

13-2 Parts of a Set
Which shaded figure represents one-third?
D.
A.
B.
C.

Main Idea
Example 1: Problem-Solving Strategy
13-3 Problem-Solving Strategy: Draw a Picture

• I will solve problems by drawing a picture.

Standard 4MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to explain
mathematical reasoning.

Standard 4NS1.7 Write the fraction represented by
a drawing of parts of a figure; represent a given
fraction by using drawings; and relate a fraction
to a simple decimal on a number line.

Brandi and her mom are at a pet store. The pet
store has 15 reptiles. One-third of the reptiles
are turtles. Two are snakes, and the rest are
lizards. How many of each reptile are there?

Understand
What facts do you know?
• There are 15 reptiles at the store.
• One-third are turtles.
• Two are snakes.
• The rest are lizards.

Understand
What do you need to find?
• Find the number of each reptile.

Plan
Draw a picture to solve the problem.

Solve
• Draw 15 circles to show
the 15 reptiles. Since the
fraction is used, place
the circles in 3 equal
groups.
1
3

Solve
• To show the turtles, shade
of the circles. That is,
one of the three equal
groups. So, there are 5
turtles. There are 2
snakes, so shade 2 circles
to show the snakes.
1
3

Solve
Answer: So, there are 5
turtles, 2 snakes,
and 8 lizards at
the pet store.
• There are 8 circles not
shaded. This is the
number of lizards.

Check
Look back at the problem. 5 turtles + 2 snakes + 8
lizards = 15 reptiles. The pet store has 15 reptiles. So,
the answer is correct.

Example 1
13-4 Equivalent Fractions

• I will find equivalent fractions.
• equivalent fractions

Standard 4NS1.5 Explain different interpretations of
fractions, for example, parts of a whole, parts of a
set, and division of whole numbers by whole
numbers; explain equivalence of fractions.

To find equivalent fractions, you can use
multiplication or division.
Find three fractions that are equivalent to .
4
6

One Way: Multiply
Multiply the numerator
and the denominator by
the same number.
4 2
×
6 2
8
=
12
4 3
×
6 3
=
18
12

Another Way: Divide
Divide the numerator
and the denominator by
the same number.
4 2
÷
6 2
2
=
3
Answer: So, , , or could be used to
represent .
8
12
2
3
12
18
4
6

Find two fractions that are equivalent to .3
6
D. ,
4
6
5
7
C. ,
1
2
6
12
B. ,
1
2
8
12
A. ,
4
6
8
12

Key Concept: Simplest Form
Example 1
Example 2
13-5 Simplest Form

13-5 Simplest Form
• I will write a fraction in simplest form.
• simplest form

13-5 Simplest Form
Standard 4NS1.5 Explain different
interpretations of fractions, for example, parts
of a whole, parts of a set, and division of whole
numbers by whole numbers; explain
equivalence of fractions.

Step 1 Find the common factors.
13-5 Simplest Form
Write in simplest form.
20
24
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, and 4

Step 2 Divide by the greatest common factor, 4.
13-5 Simplest Form
÷
20
24
4
4
=
5
6
Answer: So, in simplest form is .
20
24
5
6
The numbers 5 and 6 have no common factor
other than 1.

13-5 Simplest Form
Write in simplest form.
25
35
A.
5
6
B.
5
7
C.
4
5
D.
1
5

Stanley and his family spent 15 hours on a train ride
to visit his grandparents. Write what part of one day
he spent on the train as a fraction in simplest form.
Step 1 First, write a fraction.
13-5 Simplest Form
15 hours spent on train
24 total hours in a day

Step 2 Divide by common factors.
13-5 Simplest Form
÷
15
24
3
3
=
5
8
A common factor of
15 and 24 is 3.
The only common factor of 5 and 8 is 1.
Answer: So, simplifies to . Stanley and his
family spent of a day on the train.
15
24
5
8
5
8

13-5 Simplest Form
Dion spent 3 hours of his day playing basketball.
Write what part of one day he spent playing
basketball as a fraction in simplest form.
A.
2
8
B.
5
8
C.
1
8
D.
3
24

Main Idea
Example 1: Problem-Solving Investigation
13-6 Problem-Solving Investigation: Choose a Strategy

• I will choose the best strategy to solve a problem.

Standard 4MR2.2 Apply strategies and results from
simpler problems to more complex problems.
Standard 4NS1.7 Write the fraction represented by a
drawing of parts of a figure; represent a given
fraction by using drawings; and relate a fraction to
a simple decimal on a number line.

ANICA: My class visited the zoo. I
learned that one-sixth of the
animals at the zoo are reptiles.
There are 420 animals at the zoo.
How many animals are reptiles?
YOUR MISSION: Find how many animals
are reptiles.

Understand
What facts do you know?
• There are 420 animals at the zoo.
• One-sixth of the animals are reptiles.
What do you need to find?
• Find how many animals are reptiles.

Plan
Solve a simpler problem. First, find one-sixth of a
smaller number. Then, multiply to find one-sixth
of 420.

Solve
Find one-sixth of 42.
Draw 42 circles in 6
equal rows. Circle
one of the six equal
groups.

Solve
So, one-sixth of 42 equals 7. Now multiply.
THINK What number
can you multiply 42
by to equal 420?
Then multiply 7 by
the same number.
42
× 10
420
7
× 10
70
Answer: So, 70 of the animals at the zoo are
reptiles.

Check
Since 70 × 6 = 420, then 70 is one-sixth of 420.
The answer is correct.

Main Idea
Example 1
Example 2
Example 3
13-7 Compare and Order Fractions

• I will compare and order simple fractions.

Standard 4NS1.9 Identify on a number line
the relative position of positive fractions, positive
mixed numbers, and positive decimals to two decimal
places.

Use the data table
shown. Which insect is
longer, a mosquito or a
whirligig beetle?
You can use models to compare
and . First, you want the
denominators to be the same. So,
find an equivalent fraction for
that will give it a denominator of 2.
1
4
1
4
3
8

×
1
4
2
2
2
8
=
mosquito
2
8
whirligig
beetle
5
8
Answer: The model shows that < . So,
the whirligig beetle is longer.
2
8
5
8

Which measurement is longer, in. or in.?2
6
2
3
A.
2
6
B.
2
3

Use the data table shown.
Which insect is longer, a
field cricket or a lightning
bug?

You need to compare
and .
5
8
1
2
Answer: So, the field cricket is longer
than the lightning bug.

Which is the shorter length, or ?1
2
1
3
A.
1
2
B.
1
3

Order , , from least to greatest.
1
2
5
6
1
3
One Way: Number Lines
Use a number line.

1
3
<
1
2
<
5
6

1
2
× 3
3
,3
6
Another Way: Equivalent Fractions
,5
6
= 1
3
× 2
2
= 2
6
Compare the numerators. Order from least to
greatest.

,2
6
,3
6
5
6
,1
3
,1
2
5
6
Answer: So, the order from least to greatest is
, , .1
3
1
2
5
6

Order , , from least to greatest.
1
4
1
6
2
3
A. , ,
1
4
1
6
2
3
B. , ,
1
6
2
3
1
4
C. , ,
2
3
1
4
1
6
D. , ,
1
6
1
4
2
3

Key Concept: Add Fractions
Key Concept: Subtract Fractions
Example 1
Example 2
13-8 Add and Subtract Like Fractions

• I will add and subtract fractions.
• like fractions
• like denominators

Reinforcement of Standard 3NS3.2 Add
and subtract simple fractions (e.g., determine
the + is the same as ).1
8
3
8
1
2

Step 1 Add the numerators. Keep the same
denominator.
Rex spent hour reading Saturday morning and
hour reading Saturday evening. How much time did
he spend reading in all?
1
4
2
4
1
4
+
2
4
=
2 + 1
4
=
3
4

Step 2 Write in simplest form.
is in simplest form.
3
4
Answer: So, Rex spent of an hour reading on
Saturday.
3
4

Sherita spent of the day writing emails to her
friends in the morning and of the day writing
letters to more of her friends in the evening.
How much time did Sherita spend writing in all?
1
5
1
5
A.
1
5
B.
2
5
C.
3
5
D.
5
5

Levi ran of a mile
before football practice
and of a mile after
football practice. How
much farther did he run
before practice?
2
3
1
3
You need to subtract and .
2
3
1
3

2
3
–
1
3
=
1
3
Subtract the numerators.
Keep the same denominator.
The answer is in simplest form, so you don’t need
to reduce.
Answer: So, Levi ran of a mile more before practice.
1
3

Janice ate of a bag of chips on Monday. On
Tuesday, she ate more of that bag of chips.
How much more did she eat on Monday than
Tuesday?
6
10
3
10
A.
3
10
B.
4
10
C.
5
10
D.
9
10

Example 1
Example 2
Example 3
Example 4
13-9 Mixed Numbers

13-9 Mixed Numbers
• I will write mixed numbers and improper
fractions.
• mixed number
• improper fraction

13-9 Mixed Numbers
Standard 4NS1.5 Explain different interpretations
of fractions, for example, parts of a whole, parts of
a set, and division of whole numbers by whole
numbers; explain equivalents of fractions.

13-9 Mixed Numbers
Standard 4NS1.9 Identify on a number line
the relative position of positive fractions,
positive mixed numbers, and positive decimals to
two decimal places.

Each lasagna has 10 slices. There are 13 slices left.
What fraction of the lasagna is left?
13-9 Mixed Numbers

13-9 Mixed Numbers
One Way: Mixed Number
Count the wholes and the parts.
10
10
3
10
+ =
13
10
or 1
3
10

13-9 Mixed Numbers
Another Way: Improper Fraction
Count the parts.
13
10
Answer: So, or 1 of the lasagna is left.
13
10
3
10

13-9 Mixed Numbers
What fraction of the pizza is left?
A. 1
3
8
B.
3
8
C. 1
5
8
D. 1
1
2

13-9 Mixed Numbers
Write 1 as an improper fraction.
3
5
Write the mixed number as the
sum of a whole and part.
1
3
5
= 1 +
3
5
Write the whole number as a
fraction.
=
3
5
5
5
+
Add.=
5 + 3
5
=
8
5

13-9 Mixed Numbers
Write 1 as an improper fraction.
5
9
A.
13
9
B.
9
15
C.
14
9
D.
15
9

Divide the numerator by the denominator.
13-9 Mixed Numbers
Write as a mixed number.
10
3
3 10
3
9–
1
R1
Answer: So, = 3 .
1
3
10
3

13-9 Mixed Numbers
Write as a mixed number.
13
4
A. 4
1
3
B. 2
5
4
C. 3
4
1
D. 3
1
4

13-9 Mixed Numbers
Identify point A on the number line. Write it as a
mixed number and an improper fraction.
The number is 1 . You need to write it as an
improper fraction.
1
2

13-9 Mixed Numbers
1
1
2
= 1 +
1
2
=
1
2
2
2
+
=
2 + 1
2
=
3
2
Answer: So, the number on the number line is 1
or .
1
2
3
2

13-9 Mixed Numbers
Identify point A on the number line. Write it as an
improper fraction.
A.
3
2
B.
5
2
C.
5
4
D.
2
3

13
Fractions
Five-Minute Checks

13
Fractions
Lesson 13-1 (over Chapter 12)
Lesson 13-2 (over Lesson 13-1)

13
Fractions
(over Chapter 12)
Haddie spends $24 on 3 tickets to play miniature
golf. At this rate, how much will 10 tickets cost?
A. $70
B. $90
C. $80
D. $72

13
Fractions
(over Lesson 13-1)
Write the fraction that names part of the whole.
A.
2
4
B.
3
4
C.
1
4
D. 4

13
Fractions
(over Lesson 13-1)
Write the fraction that names part of the whole.
A.
1
3
B. 1
D.
1
4
C.
2
3

13
Fractions
(over Lesson 13-1)
Which picture correctly shows ?
2
5
A.
B.
C.
D.

13
Fractions
(over Lesson 13-1)
Which picture correctly shows ?
5
6
C.A.
D.B.

13
Fractions
(over Lesson 13-2)
Find the fraction that represents red eggs.
A.
9
12
B.
12
3
C.
3
12
D.
12
9

13
Fractions
(over Lesson 13-2)
Find the fraction that represents yellow eggs.
A.
4
12
B.
8
12
C.
12
4
D.
3
12

13
Fractions
(over Lesson 13-2)
Find the fraction that represents blue eggs.
A.
7
12
B.
12
5
C.
4
12
D.
5
12

13
Fractions
(over Lesson 13-2)
Find the fraction that represents not blue eggs.
A.
12
12
B.
7
12
C.
3
12
D.
4
12

13
Fractions
(over Lesson 13-2)
Find the fraction that represents blue and red eggs.
A.
4
12
B.
7
12
C.
8
12
D.
9
12

13
Fractions
(over Lesson 13-2)
Find the fraction that represents blue, red and
yellow eggs.
A.
8
12
B.
12
12
C.
5
12
D.
11
12

13
Fractions
(over Lesson 13-3)
Solve. Use the Draw a Picture
strategy. A pizza is cut into 12
equal slices. Half of the pizza has
sausage and peppers on it, two
slices have eggplant, and the rest
of the pizza is plain cheese. What
fraction of the pizza is plain?
A.
1
2
B.
2
3
C.
3
4
D.
1
3

13
Fractions
(over Lesson 13-4)
Write an equivalent fraction for .
2
4
A.
4
7
D.
2
3
C.
4
8
B.
2
8

13
Fractions
(over Lesson 13-4)
5
15
A.
1
3
D.
1
4
C.
2
3
B.
3
4

13
Fractions
(over Lesson 13-4)
8
10
A.
4
8
C.
2
3
B.
9
12
D.
12
15

13
Fractions
(over Lesson 13-4)
12
16
A.
4
3
D.
1
2
C.
3
4
B.
3
5

13
Fractions
(over Lesson 13-5)
Write in simplest form. If it is in simplest form,
write simplest form.
2
5
A.
1
5
D. simplest form
B.
1
2
C.
4
10

13
Fractions
(over Lesson 13-5)
2
8
A.
2
4
D. simplest form
B.
1
4
C.
1
2

13
Fractions
(over Lesson 13-5)
3
3
A.
1
3
D. simplest form
B.
1
6
C. 1

13
Fractions
(over Lesson 13-5)
3
5
A.
1
3
D. simplest form
B.
1
5
C.
2
5

13
Fractions
(over Lesson 13-5)
3
9
A.
1
3
D. simplest form
B.
1
9
C.
1
2

13
Fractions
(over Lesson 13-6)
Julio and Alvino are doing yard work to raise money
for a class field trip. Julio works 1 hours and
Alvino works 2 hours every day for a week. If they
each make $4 per hour, how much did they make
that week?
1
2
A. $84
B. $96
C. $98
D. $100

13
Fractions
(over Lesson 13-7)
A. <
B. >
C. =
2
5
1
3
Compare. Write <, >, or =.

13
Fractions
A. <
B. >
C. =
(over Lesson 13-7)
3
4
3
5

13
Fractions
A. <
B. >
C. =
(over Lesson 13-7)
4
6
2
3

13
Fractions
A. <
B. >
C. =
(over Lesson 13-7)
1
4
5
6

13
Fractions
A. <
B. >
C. =
(over Lesson 13-7)
5
7
5
8

13
Fractions
(over Lesson 13-8)
Find each sum or difference. Write in simplest form.
+ = ___3
9
3
9
A.
6
9
D.
1
3
B.
2
3
C.
6
18

13
Fractions
(over Lesson 13-8)
+ = ___1
7
4
7
D.
5
7
B. 1
A.
5
14
C.
5
12

13
Fractions
(over Lesson 13-8)
+ = ___2
4
2
4
A.
4
2
D.
2
8
C. 1
B.
4
8

13
Fractions
(over Lesson 13-8)
– = ___6
9
3
9
A.
1
3
D.
1
6
C.
3
9
B.
9
9

13
Fractions
(over Lesson 13-8)
– = ___5
10
1
10
D.
4
5
C.
2
5
B.
3
5
A.
4
10

13
Fractions
(over Lesson 13-8)
– = ___4
5
2
5
A.
1
2
D.
2
5
B.
6
5
C.
2
10

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Math Gr4 Ch13

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Math Gr4 Ch13