Transcript Gr03_Ch_12 - Etiwanda E

Chapter 12
Fractions
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12
Fractions
Lesson 12-1
Parts of a Whole
Lesson 12-2
Problem-Solving Investigation:
Choose a Strategy
Lesson 12-3
Find Equivalent Fractions
Lesson 12-4
Problem-Solving Strategy: Draw
a Picture
Lesson 12-5
Compare Fractions
Lesson 12-6
Add Like Fractions
Lesson 12-7
Subtract Like Fractions
12-1
Parts of a Whole
Five-Minute Check (over Chapter 11)
Main Idea and Vocabulary
California Standards
Example 1: Write and Read Fractions
Example 2: Write and Read Fractions
Example 3: Real-World Example
12-1
Parts of a Whole
• I will read and write fractions for part of a whole.
• fraction
• numerator
• denominator
12-1
Parts of a Whole
Standard 3NS3.1 Compare fractions represented by
drawings or concrete materials to show equivalency
and to add and subtract simple fractions in context (e.g.,
of a pizza is the same amount as
that is the same size; show that
of another pizza
is larger than
).
12-1
Parts of a Whole
What fraction of the spinner is yellow?
12-1
Parts of a Whole
One Way: Models
The spinner represents one whole. There are 5
equal parts. A whole can be divided into 5 equal
parts, or fifths.
12-1
Parts of a Whole
Another Way: Paper and Pencil
The spinner has 5 equal parts. One part is yellow.
1
part that is yellow
5
total number of equal parts
Write
Read
1
5
One-fifth
1
Answer: So, one-fifth or 5 of the spinner is yellow.
12-1
Parts of a Whole
What fraction of the figure is shaded green?
A.
2
3
B.
10
7
C.
7
10
D.
3
10
12-1
Parts of a Whole
What fraction of the figure
is shaded?
3
4
parts that are blue
total number of equal parts
The figure above represents one whole. There are
4 equal parts. A whole can be divided into 4 equal
parts or fourths. Three of the four parts are shaded.
Answer: 3
4
12-1
Parts of a Whole
What fraction of the figure is shaded green?
A.
8
15
B.
15
8
C.
7
15
D.
3
10
12-1
Parts of a Whole
The figure shows the part of the yard that has
been raked. What fraction of the yard has been
raked?
12-1
5
6
Parts of a Whole
parts that are blue
total number of equal parts
The figure above represents one whole. There are
6 equal parts. A whole can be divided into 6 equal
parts or sixths. Five of the six parts are shaded.
Answer: 5
6
12-1
Parts of a Whole
The figure shows a circle with a missing piece.
What fraction of the circle is shown?
A.
1
5
B.
1
4
C.
3
4
D.
2
5
12-2
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 12-1)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
12-2
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
12-2
Problem-Solving Investigation: Choose a Strategy
Standard 3MR2.3 Use a variety of methods, such
as words, numbers, symbols, charts, graphs,
tables, diagrams, and models, to explain
mathematical reasoning.
Standard 3NS2.1 Find the sum or difference
of two whole numbers between 0 and 10,000.
12-2
Problem-Solving Investigation: Choose a Strategy
CARLOTA: Last night, I played a
board game. On one turn, I rolled
two number cubes. The sum of the
numbers was 9. The difference was 3.
YOUR MISSION: Find the two numbers
Carlota rolled.
12-2
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• Carlota rolled two number cubes.
• The sum of the numbers was 9.
• The difference was 3.
What do you need to find?
• Find the two numbers rolled.
12-2
Problem-Solving Investigation: Choose a Strategy
Plan
Make a table to show all of the possible rolls and
their sums.
12-2
Problem-Solving Investigation: Choose a Strategy
Solve
The table shows that to
get a sum of 9, Carlota
must have rolled 5 and
4 or 6 and 3.
6+3=9
5+4=9
12-2
Problem-Solving Investigation: Choose a Strategy
Solve
Find the difference.
6–3=3
5–4=1
Answer: Since 6 + 3 = 9 and 6 – 3 = 3, Carlota
must have rolled 6 and 3.
12-2
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. Since 3 + 6 = 9 and
6 – 3 = 3, you know that the answer is correct.
12-3
Find Equivalent Fractions
Five-Minute Check (over Lesson 12-2)
Main Idea and Vocabulary
California Standards
Example 1: Find Equivalent Fractions
Equivalent Fractions
12-3
Find Equivalent Fractions
• I will find equivalent fractions.
• equivalent fractions
12-3
Find Equivalent Fractions
Standard 3NS3.1 Compare fractions represented by
drawings or concrete materials to show equivalency
and to add and subtract simple fractions in context (e.g.,
of a pizza is the same amount as
that is the same size; show that
of another pizza
is larger than
).
12-3
Find Equivalent Fractions
3
Complete 4 = 8 to find equivalent fractions.
12-3
Find Equivalent Fractions
One Way: Fraction Models
Think about the number of equal parts in
fraction models.
3
There are 6 eighths in 4 .
12-3
Find Equivalent Fractions
Another Way: Picture
The circle is divided into fourths.
Three parts are shaded.
12-3
Find Equivalent Fractions
Another Way: Picture
Another equal circle is divided
into eighths. The same part is
shaded.
3
There are 6 eighths in 4 .
3
6
Answer: So, 4 = 8 .
12-3
Find Equivalent Fractions
1
Complete 2 = 6 to find equivalent fractions.
A. 2
B. 3
C. 4
D. 5
12-4
Problem-Solving Strategy: Draw a Picture
Five-Minute Check (over Lesson 12-3)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
12-4
Problem-Solving Strategy: Draw a Picture
• I will draw a picture to solve problems.
12-4
Problem-Solving Strategy: Draw a Picture
Standard 3MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
12-4
Problem-Solving Strategy: Draw a Picture
Standard 3NS3.1 Compare fractions
represented by drawings or concrete materials
to show equivalency and to add and subtract
simple fractions in context.
12-4
Problem-Solving Strategy: Draw a Picture
Ana and her brother have 8 insects in a jar.
One-half of the insects are beetles. One is a
firefly, and the rest are crickets. How many of
the insects are crickets?
12-4
Problem-Solving Strategy: Draw a Picture
Understand
What facts do you know?
• There are 8 insects.
• One is a firefly.
• One-half are beetles.
• The rest are crickets.
What do you need to find?
• Find how many of the insects are crickets.
12-4
Problem-Solving Strategy: Draw a Picture
Plan
You can draw a picture to solve the problem.
12-4
Problem-Solving Strategy: Draw a Picture
Solve
• First draw a figure that is
divided into 8 equal parts.
This shows 8 insects.
• To show the beetles,
shade 1 of the figure.
2
Shade 1 part to show
the firefly.
12-4
Problem-Solving Strategy: Draw a Picture
Solve
• There are 3 parts not
shaded. This is the
number of crickets.
Answer: So, 3 of the insects are crickets.
12-4
Problem-Solving Strategy: Draw a Picture
Check
Look back at the problem.
4 beetles + 1 firefly + 3 crickets = 8 insects
There are 8 insects. So, the answer is correct.
12-5
Compare Fractions
Five-Minute Check (over Lesson 12-4)
Main Idea and Vocabulary
California Standards
Example 1: Compare Fractions
Example 2: Compare Fractions
12-5
Compare Fractions
• I will compare fractions.
• is greater than (>)
• is less than (<)
12-5
Compare Fractions
Standard 3NS3.1 Compare fractions represented by
drawings or concrete materials to show equivalency
and to add and subtract simple fractions in context (e.g.,
of a pizza is the same amount as
that is the same size; show that
of another pizza
is larger than
).
12-5
Compare Fractions
Compare 2 and 4 .
5
5
One Way: Fraction Models
2
4
is less than .
5
5
12-5
Compare Fractions
Another Way: Number Line
2
4
is to the left of .
5
5
Answer: So,
2 4
4 2
< or > .
5 5
5 5
12-5
Compare Fractions
Compare 4 to 6 .
7
7
A.
4< 6
7 7
B.
4> 6
7 7
C.
4= 6
7 7
12-5
Compare Fractions
Bill’s family ate 1 of an apple pie. Laureana’s family
3
ate 2 of an apple pie. Which family ate more?
4
You need to compare 1 and 2 .
3
4
12-5
Compare Fractions
One Way: Number Line
1
is less than 2 .
3
4
1 2
2 1
So, < or > .
3 4
4 3
12-5
Compare Fractions
Another Way: Drawing
1
is less than 2 .
3
4
1 2
2 1
So, < or > .
3 4
4 3
12-5
Compare Fractions
Answer: So, Laureana’s family ate more of the pie
because 2 > 1 .
4 3
12-5
Compare Fractions
Monica and her sister had pizza for dinner. Monica
ate 1 of the pizza, while her sister ate 1 of the
3
2
pizza. Who ate more?
A.
Monica
B.
Monica’s sister
12-6
Add Like Fractions
Five-Minute Check (over Lesson 12-5)
Main Idea and Vocabulary
California Standards
Key Concept: Add Like Fractions
Example 1: Add Like Fractions
Example 2: Add Like Fractions
Add Like Fractions
12-6
Add Like Fractions
• I will add like fractions.
• like fractions
12-6
Add Like Fractions
Standard 3NS3.2 Add and subtract simple
fractions (e.g., determine that
as
).
+
is the same
12-6
Add Like Fractions
12-6
Add Like Fractions
Lynn painted 1 of her wall green and 1 of her wall
3
3
blue. The rest she left white. What fraction of her
wall has color?
12-6
Add Like Fractions
One Way: Models
1
3
+
1
3
=
2
3
12-6
Add Like Fractions
Another Way: Paper and Pencil
1
1
+
=
3
3
1 + 1
=
3
2
3
Add the numerators.
Use the same denominator.
12-6
Add Like Fractions
Answer: So, 2 of Lynn’s wall has color.
3
12-6
Add Like Fractions
Nikki noticed that she only had 1 tank of gas left in
4
her car. She went to the gas station and filled her
car with another 2 tank of gas. How much gas is
4
now in Nikki’s car?
A.
1
2 tank
C.
3
tank
4
B.
2
tank
4
D.
1 tank
4
12-6
Add Like Fractions
From January to March, Sancha grew 5 of an inch.
8
From March to June, Sancha grew another 3 of an
8
inch. How much did she grow in all?
You need to find 5 + 3 .
8
8
12-6
Add Like Fractions
5
3
+
=
8
8
5 + 3
=
8
8
8
3
8
+
5
8
=
= 1 whole
Answer: So, Sancha grew a total of 8 of an inch
8
or 1 inch.
8
8
12-6
Add Like Fractions
Bob ate 2 of the sweet potato pie, and Sandy ate
5
3 of the same sweet potato pie. How much of
5
the pie did Bob and Sandy eat altogether?
A.
B.
5
, or the whole pie
5
5 pie
10
C.
3
pie
5
D.
2 pie
5
12-7
Subtract Like Fractions
Five-Minute Check (over Lesson 12-6)
Main Idea
California Standards
Key Concept: Subtract Like Fractions
Example 1: Subtract Like Fractions
Example 2: Subtract Like Fractions
Subtract Like Fractions
12-7
Subtract Like Fractions
• I will subtract like fractions.
12-7
Subtract Like Fractions
Standard 3NS3.2 Add and subtract simple
fractions (e.g., determine that
as
).
+
is the same
12-7
Subtract Like Fractions
12-7
Subtract Like Fractions
Laura found 5 of a pizza in the refrigerator.
6
She ate 2 . How much pizza is left?
6
You need to find 5 – 2 .
6
6
12-7
Subtract Like Fractions
One Way: Models
12-7
Subtract Like Fractions
Another Way: Paper and Pencil
5
2
–
=
6
6
5–2
=
6
3
6
Subtract the numerators.
Use the same denominator.
12-7
Subtract Like Fractions
Answer: So, there is 3 of the pizza left.
6
12-7
Subtract Like Fractions
Sarah had 3 of an interesting book left to read.
4
Today Sarah read 2 of the book, how much more
4
will she have to read to finish the book?
1
A.
of the book
3
2
C.
of the book
4
3
of the book
4
D. 1 of the book
4
B.
12-7
Subtract Like Fractions
Maximo read an entire book over the weekend.
On Saturday he read 1 . How much did he read
3
on Sunday?
Find 1 – 1 .
3
12-7
Subtract Like Fractions
1 – 1
3
3 – 1 = 3–1 = 2
3
3
3
3
2
3
Answer: So, Maximo read 2 of the book on Sunday.
3
12-7
Subtract Like Fractions
Natalie was preparing a six-course meal for her
family, 2 of which she had completed. How much
6
more of the meal does Natalie have to prepare?
A. 2 of the meal
6
C. 5 of the meal
6
B. 4 of the meal
6
D. 3 of the meal
6
12
Fractions
Five-Minute Checks
Math Tool Chest
Image Bank
Equivalent Fractions
Add Like Fractions
Subtract Like Fractions
12
Fractions
To use the images that are on the
following four slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
12
Fractions
12
Fractions
12
Fractions
12
Fractions
12
Fractions
Lesson 12-1 (over Chapter 11)
Lesson 12-2 (over Lesson 12-1)
Lesson 12-3 (over Lesson 12-2)
Lesson 12-4 (over Lesson 12-3)
Lesson 12-5 (over Lesson 12-4)
Lesson 12-6 (over Lesson 12-5)
Lesson 12-7 (over Lesson 12-6)
12
Fractions
(over Chapter 11)
Each time Jason picked a marble from a bag, he
recorded the color and replaced the marble. He
picked 40 red, 4 blue, 2 yellow, and 4 green marbles.
How many times did he pick a marble from the bag?
A. 45
B. 50
C. 25
D. 15
12
Fractions
(over Chapter 11)
Each time Jason picked a marble from a bag, he
recorded the color and replaced the marble. He
picked 40 red, 4 blue, 2 yellow, and 4 green marbles.
What color marble is most likely to be picked next?
A. red
B. yellow
C. green
D. blue
12
Fractions
(over Chapter 11)
Each time Jason picked a marble from a bag, he
recorded the color and replaced the marble. He
picked 40 red, 4 blue, 2 yellow, and 4 green marbles.
What two colors are equally likely to be picked?
A. blue and green
B. yellow and green
C. red and yellow
12
Fractions
(over Lesson 12-1)
Draw a picture for 1 . Shade the fraction.
2
A.
B.
C.
D.
12
Fractions
(over Lesson 12-1)
Draw a picture for 2 . Shade the fraction.
3
A.
B.
C.
D.
12
Fractions
(over Lesson 12-1)
Draw a picture for 1 . Shade the fraction.
5
A.
B.
C.
D.
12
Fractions
(over Lesson 12-1)
Draw a picture for 5 . Shade the fraction.
6
A.
B.
C.
D.
12
Fractions
(over Lesson 12-2)
Choose a strategy to solve the problem. Zach has
a rectangular fence around his back yard. The
perimeter of the fence is 78 feet. The length of one
side of the fence is 18 feet. What are the lengths of
the other sides?
A. 2 sides are 18 feet and 2 sides are 21 feet.
B. 2 sides are 14 feet and 2 sides are 24 feet.
C. 2 sides are 11 feet and 2 sides are 20 feet.
12
Fractions
(over Lesson 12-3)
Complete 1 = to find equivalent fractions.
2 8
A. 2
B. 6
C. 4
D. 8
12
Fractions
(over Lesson 12-3)
Complete 3 =
to find equivalent fractions.
4 12
A. 4
B. 9
C. 3
D. 10
12
Fractions
(over Lesson 12-3)
Complete
A. 3
B. 10
C. 15
D. 4
= 6 to find equivalent fractions.
5 10
12
Fractions
(over Lesson 12-3)
Complete
A.
6
B.
8
C.
10
D.
2
= 4 to find equivalent fractions.
3 6
12
Fractions
(over Lesson 12-4)
Solve. Use the draw a picture strategy. There are
four siblings: Bob, Arlo, Claudia and Diego. Claudia
is taller than Arlo. Diego is taller than Claudia. Bob is
the shortest. List the siblings in order from tallest to
shortest.
A. Diego, Claudia, Arlo, Bob
B. Bob, Diego, Claudia, Arlo
C. Claudia, Diego, Arlo, Bob
D. Caludia, Arlo, Diego, Bob
12
Fractions
(over Lesson 12-5)
Compare 2 1 . Write <, >, or =. Use fraction
4 4
strips, a number line, or a drawing if needed.
A. <
B. >
C. =
12
Fractions
(over Lesson 12-5)
4 . Write <, >, or =. Use fraction
Compare 3
10 10
strips, a number line, or a drawing if needed.
A. >
B. =
C. <
12
Fractions
(over Lesson 12-5)
1 . Write <, >, or =. Use fraction
Compare 4
8
4
strips, a number line, or a drawing if needed.
A. >
B. <
C. =
12
Fractions
(over Lesson 12-5)
5 . Write <, >, or =. Use fraction
Compare 1
2 10
strips, a number line, or a drawing if needed.
A. >
B. =
C. <
12
Fractions
(over Lesson 12-6)
Add.
3
4
+
12 12
A.
B.
C.
D.
12
12
7
24
1
12
7
12
12
Fractions
(over Lesson 12-6)
Add.
2
4
+
6
6
A.
B.
C.
D.
6 or 1
6
2
6
6
12
5
12
12
Fractions
(over Lesson 12-6)
Add.
2
5
+
8
8
A.
B.
C.
D.
13
8
5
16
7
8
1
7
12
Fractions
(over Lesson 12-6)
Add.
1
2
+
5
5
A.
B.
C.
D.
3
5
6
10
2
5
1
5
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