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Transcript
Lesson 11
Use after Ready Instruction page 97
Add and Subtract Fractions in
Word Problems
Name: Use Benchmark Fractions
Study the example problem showing comparing numbers by using the
benchmark fraction ​ 1 ​ . Then solve problems 1–5.
2
··
Example
Ricci and his brother Lorenzo both have to practice for an
upcoming karate tournament. Ricci practices for ​ 3 ​ hour,
8
··
3
and Lorenzo practices for ​   ​hour. Which brother practices
4
··
for a longer time?
Compare both numbers to the benchmark fraction ​ 1 ​ .
2
··
3
8
0
3
4
1
1
2
Look at the number line. It shows that ​ 3 ​is less than ​ 1 ​
8
··
and ​ 3 ​is greater than ​ 1 ​ .
4
2
··
··
3
3
3
3
So, ​   ​ , ​   ​ and ​   ​ . ​   ​ .
8 ··
4
4 ··
8
··
··
2
··
Lorenzo practices for a longer time.
1 Use the number line in the example problem to
compare each fraction below to ​ 1 ​ . Write each fraction
2
··
in the correct box.
​  6 ​
8
··
3
1
​   ​
4
··
​   ​
4
··
Less than ​ 1 ​
2
··
​ 5 ​
​ 2 ​
8
··
4
··
Equal to ​ 1 ​
2
··
​ 7 ​
8
··
2
​   ​
8
··
Greater than ​ 1 ​
2
··
Vocabulary
benchmark fraction a common fraction you
can judge other
numbers against
​1 example: ​ 1 ​ , ​ 1 ​ , ​ 3 ​   2.​
4 ··
2 ··
4
··
©Curriculum Associates, LLC Copying is not permitted.
Lesson 11 Add and Subtract Fractions in Word Problems
113
Solve.
2 You can also use the number 1 as a benchmark. Use
​ 1 ​
the fractions from the box.
​ 4 ​
3
··
Write each fraction that is
​  3  ​ 
3
​   ​
3
··
b. less than 1. 15
··
7
​   ​
5
··
10
··
a. greater than 1. ​ 12 ​  
3
··
2
​   ​
5
··
16
​   ​ 
10
··
c. equal to 1. 3 Which fraction from problem 2 is greater than 1 ​ 1 ​ ?
2
··
Explain how you know.
4 You can also model comparisons to ​ 1 ​using fraction
2
··
strips. Write ., 5, or , to compare each set of
2
3
fractions below.
​  2 ​ ​ 1 ​
3
2
··
··
So, ​ 2 ​ ​ 2 ​ .
3
6
··
··
​ 2 ​ ​ 1 ​
6
2
··
··
1
2
2
6
5 Josan and Andrea are on a long-distance bike ride.
They decide they will stop for water if either of their
water bottles is less than half full. Josan’s bottle is
​ 2 ​full. Andrea’s bottle is ​ 5 ​full. Should they stop?
5
··
6
··
Explain.
Show your work.
Solution: 114
Lesson 11 Add and Subtract Fractions in Word Problems
©Curriculum Associates, LLC Copying is not permitted.
Lesson 11 • Use after Ready Instruction page 99
Name: Estimate using Benchmark Fractions
Study the example problem showing how to estimate a
sum using benchmark fractions. Then solve problems 1–5.
Example
David grew 1 ​ 3 ​inches last year and 1 ​ 5 ​inches this year.
4
··
8
··
Estimate how much he grew in the two years.
You can estimate 1 ​ 3 ​ 1 1 ​ 5 ​using benchmark fractions.
4
··
8
··
The number line below shows common fractions used as
benchmark fractions to estimate sums and differences.
0
1
4
1
2
3
4
1
1
1
3
14 12 14
2
1 ​ 3 ​is already one of the benchmark fractions, so just
4
··
estimate 1 ​ 5 ​ .
8
··
1 ​ 5 ​is a little greater than 1 ​ 1 ​ . Estimate using 1 ​ 1 ​ .
8
··
2
··
2
··
1 ​  3 ​ 1 1 ​ 1 ​ 5 1 ​ 3 ​ 1 1 ​ 2 ​ 5 2 ​ 5 ​ , or 3 ​ 1 ​ .
4
··
2
··
4
··
4
··
4
··
4
··
The sum is a little greater than 3 ​ 1 ​ , so David grew a little
more than 3 ​ 1 ​ inches.
4
··
4
··
1 Look at the example problem. Explain how you know
1 ​ 5 ​is a little greater than 1 ​ 1 ​ .
8
2
··
··
2 Find the actual sum of 1 ​ 3 ​ 1 1 ​ 5 ​to determine how
4
8
··
··
much David grew in two years. Explain how you know
your answer is reasonable.
Show your work.
Solution: ©Curriculum Associates, LLC Copying is not permitted.
Lesson 11 Add and Subtract Fractions in Word Problems
115
Solve.
Irene makes 4 ​ 2 ​cups of pancake batter. She splits the
3
··
batter into 2 bowls. She mixes blueberries into
2 ​  1 ​cups of batter and walnuts into the rest of the
4
··
batter.
3 Estimate how much of the batter has walnuts in it.
Explain your estimate.
4 Find the actual amount of batter that has walnuts in it.
Explain how you know your answer is reasonable.
Show your work.
Solution: 5 Irene makes a second batch of 3 ​ 1 ​cups of pancake
4
··
batter. She wants to know how much more batter she
made in the first batch. She estimates that the
difference between the sizes of the two batches
4 ​ 2 ​ 2 3 ​ 1 ​is 2 ​  1  ​  . Explain why this estimate is not
3
··
4
··
12
··
reasonable.
116
Lesson 11 Add and Subtract Fractions in Word Problems
©Curriculum Associates, LLC Copying is not permitted.
Lesson 11 • Use after Ready Instruction page 101
Name: Add and Subtract Fractions in Word Problems
Solve the problems.
1 Write the missing numbers to show equivalent
Remember to
multiply both the
numerator and
denominator by the
same number to
show an equivalent
fraction.
fractions for some common numbers used as
benchmarks.
0
1
4
1
2
3
4
1
1
1
3
14 12 14
a.​ 1 ​ , ​ 
c.​ 3 ​ , ​ 
b.​ 1 ​ , ​ 
d. 2, ​ 
   ​ , ​    ​  
8 ····
12
4 ····
··
   ​ , ​    ​ 
8 ····
10
2 ····
··
2
   ​ , ​    ​  
8 ····
12
4 ····
··
   ​ , ​     ​
2 ····
4
····
2 The Graf family made two pizzas. They ate 1 ​ 1 ​ pizza
8
··
before watching a movie, and ​ 1 ​pizza more after the
2
··
movie. Which is a reasonable estimate for the amount
Where is 1 ··
​ 81 ​ located
on the number line?
of pizza left?
A less than ​ 1 ​
C less than 1 ​ 1 ​
B more than ​ 1 ​
D more than 1 ​ 1 ​
2
··
2
··
4
··
4
··
Tammy chose A as the correct answer. How did she
get that answer?
©Curriculum Associates, LLC Copying is not permitted.
Lesson 11 Add and Subtract Fractions in Word Problems
117
Solve.
3 Lexi bought 1 ​ 2 ​pounds of green grapes and
5
··
3
2 ​    ​ pounds of red grapes. Grapes are $2.99 a pound.
10
··
Did Lexi spend more or less than $12 on grapes?
Explain.
Do I need to find
the actual number
of pounds of grapes,
or can I answer the
question using an
estimate?
4 On Monday Marco practiced the piano for ​  7  ​ hour. On
10
··
Tuesday he practiced for 1 ​ 5 ​hours. He is supposed to
6
··
1
practice 1 ​   ​hours each day.
4
··
Use this information to write a question that involves
adding or subtracting fractions.
What fractions can
I use to write an
addition or
subtraction
question?
5 Look at the question you wrote in problem 4. Show
how to estimate the answer. Then find the actual
answer.
Show your work.
What benchmark
fractions could I use
to estimate?
Solution: 118
Lesson 11 Add and Subtract Fractions in Word Problems
©Curriculum Associates, LLC Copying is not permitted.
Practice Lesson 11 Add and Subtract Fractions in Word Problems
Lesson 11
Use after Ready Instruction page 97
Add and Subtract Fractions in
Word Problems
Solve.
Name:
M
Use Benchmark Fractions
2 You can also use the number 1 as a benchmark. Use
Write each fraction that is
benchmark fraction 1 . Then solve problems 1–5.
a. greater than 1.
Example
c.
Ricci and his brother Lorenzo both have to practice for an
4
··
8
··
2
So, 2
3
··
C
1
5
Less than 1
2
8
··
7
4
··
Equal to 1
2
··
2
3
.
6
··
,
1
2
1
2
··
2.
6
··
2
6
Show your work.
Students might use number lines, equations, or
8
··
Vocabulary
some other method to compare 2 and 5 to 1 .
5
··
can judge other
6
6
··
··
2 , or 4 , is less than 1 , or 5 .
10
2
10
···
··
···
1 example: ··14 , ··12 , ··34 2.
Lesson 11 Add and Subtract Fractions in Word Problems
Lesson 11 • Use after Ready Instruction page 99
6
··
2
··
Yes, they should stop. Possible explanation: Andrea’s bottle is more than half
Solution:
full because 5 is more than 3 and 3 5 1 , but Josan’s bottle is less than half full because
a common fraction you
5, 6, 3, 7
8 ··
8 ··
4 ··
8
··
Copying is not permitted.
2
2
··
2 full. Andrea’s bottle is 5 full. Should they stop?
6
··
numbers against
©Curriculum Associates, LLC
10
···
Explain.
2
··
2
4
··
2
··
water bottles is less than half full. Josan’s bottle is
benchmark fraction
2, 1
8 ··
4
··
10
···
5
··
Greater than 1
2
··
10 ···
10
···
They decide they will stop for water if either of their
2
8
··
10
···
5 Josan and Andrea are on a long-distance bike ride.
in the correct box.
4
··
1
.
3
··
1 Use the number line in the example problem to
compare each fraction below to 1 . Write each fraction
2
··
3
10
···
fractions below.
2
··
Lorenzo practices for a longer time.
4
··
10
···
strips. Write ., 5, or , to compare each set of
4
2
··
··
So, 3 , 3 and 3 . 3 .
8 ··
4
4 ··
8
··
··
6
10
···
4 You can also model comparisons to 1 using fraction
2
··
M
1
Look at the number line. It shows that 3 is less than 1
8
··
equal to 1.
2
··
3
4
and 3 is greater than 1 .
16
10
··
greater than 1 1 .
2
··
1
2
2
5
··
3
3
··
10
···
Compare both numbers to the benchmark fraction 1 .
0
15
··
7
5
··
Explain how you know.
16 ; Possible answer: 10 is 1. 16 is 10 1 6 , or 1 6 . 6 is more than 5 , or 1 , so 1 6 is
for a longer time?
3
8
3
3
··
3 ···
15 ···
10 ··
5
··
12
3
··
3
10
··
3 Which fraction from problem 2 is greater than 1 1 ?
2
··
M
8
··
and Lorenzo practices for 3 hour. Which brother practices
4
3
··
4 , 7 , 16
3 ··
5 ···
10
··
1 , 12 , 3 , 2
b. less than 1.
upcoming karate tournament. Ricci practices for 3 hour,
1
the fractions from the box.
Study the example problem showing comparing numbers by using the
2
··
M
Unit 1
6
··
2
··
5
··
113
113
114
114
Lesson 11 Add and Subtract Fractions in Word Problems
©Curriculum Associates, LLC
Copying is not permitted.
Name:
Solve.
Estimate using Benchmark Fractions
Irene makes 4 2 cups of pancake batter. She splits the
Study the example problem showing how to estimate a
sum using benchmark fractions. Then solve problems 1–5.
3
··
batter into 2 bowls. She mixes blueberries into
2 1 cups of batter and walnuts into the rest of the
4
··
Example
batter.
David grew 1 3 inches last year and 1 5 inches this year.
4
··
8
··
Estimate how much he grew in the two years.
C
You can estimate 1 3 1 1 5 using benchmark fractions.
4
··
8
··
3 Estimate how much of the batter has walnuts in it.
Explain your estimate.
Estimates and explanations will vary, but the estimate should be about 2 1 cups.
2
··
The number line below shows common fractions used as
benchmark fractions to estimate sums and differences.
0
1
4
1
2
1
3
4
1
1
3
14 12 14
2
M
1 3 is already one of the benchmark fractions, so just
4
··
estimate 1 5 .
8
··
1 5 is a little greater than 1 1 . Estimate using 1 1 .
8
2
2
··
··
··
1 3 1 1 1 5 1 3 1 1 2 5 2 5 , or 3 1 .
4
2
4
4
4
4
··
··
··
··
··
··
The sum is a little greater than 3 1 , so David grew a little
4
··
more than 3 1 inches.
4
··
B
4 Find the actual amount of batter that has walnuts in it.
Explain how you know your answer is reasonable.
Show your work.
Students might use fraction strips, equations, or
some other method to subtract 2 1 from 4 2 .
4
··
3
··
2 5 cups. Explanations will vary but should indicate that the answer 2 5 is
12
···
12
···
Solution:
close to the estimate from problem 3.
M
1 Look at the example problem. Explain how you know
1 5 is a little greater than 1 1 .
8
2
··
··
Possible answer: You can rewrite 1 1 as 1 4 . 1 5 is 1 more.
2
8
8 ··
8
··
··
··
5 Irene makes a second batch of 3 1 cups of pancake
4
··
batter. She wants to know how much more batter she
made in the first batch. She estimates that the
difference between the sizes of the two batches
M
2 Find the actual sum of 1 3 1 1 5 to determine how
4
8
··
··
4 2 2 3 1 is 2 1 . Explain why this estimate is not
3
··
much David grew in two years. Explain how you know
4
··
3
··
4
··
4
··
12
···
4
··
12
···
3
··
8
··
12
···
3 3 inches. The answer is a little greater than 3 1 , as estimated.
8
··
©Curriculum Associates, LLC
26
8
··
12
··
would also be true. But 3 1 2 5 5, so 3 1 1 2 1 is greater than 5.
Show your work.
Possible work: 1 3 1 1 5 5 3 3
Solution:
4
··
reasonable.
Answers will vary. Possible answer: If 4 2 2 3 1 5 2 1 is true, then 3 1 1 2 1 5 4 2
your answer is reasonable.
4
··
Copying is not permitted.
Practice and Problem Solving
Lesson 11 Add and Subtract Fractions in Word Problems
115
115
116
116
Lesson 11 Add and Subtract Fractions in Word Problems
©Curriculum Associates, LLC
Copying is not permitted.
Unit 2 Number and Operations—Fractions
©Curriculum Associates, LLC Copying is not permitted.
Practice Lesson 11 Add and Subtract Fractions in Word Problems
Lesson 11 • Use after Ready Instruction page 101
Unit 1
Name:
Solve.
Add and Subtract Fractions in Word Problems
Solve the problems.
B
M
1 Write the missing numbers to show equivalent
0
1
4
1
2
3
4
1
1
3
2
2
3
a. 1 ,
,
6
9
c. 3 ,
,
4
5
b. 1 ,
,
d. 2,
8 ····
12
4 ····
··
Explain.
less than $12; Possible explanation: Lexi bought
less than 1 1 pounds of green grapes and less
4
,
2
··
2
··
4 pounds altogether. Grapes are a little less than
$3 a pound. She spent less than 4 3 $3, or $12
8
for grapes.
2 ····
4
····
2 The Graf family made two pizzas. They ate 1 1 pizza
8
··
before watching a movie, and 1 pizza more after the
2
··
movie. Which is a reasonable estimate for the amount
M
1
Where is 1 ··
located
8
on the number line?
of pizza left?
A
less than 1
B
more than 1
C
2
··
4 On Monday Marco practiced the piano for 7 hour. On
10
··
Tuesday he practiced for 1 5 hours. He is supposed to
6
··
practice 1 1 hours each day.
4
··
Use this information to write a question that involves
adding or subtracting fractions.
less than 1 1
4
··
What fractions can
I use to write an
addition or
subtraction
question?
Possible answer: How much longer should
D more than 1 1
2
··
Do I need to find
the actual number
of pounds of grapes,
or can I answer the
question using an
estimate?
than 2 1 pounds of red grapes. That is less than
8 ····
12
4 ····
··
8 ····
10
2 ····
··
M
1
14 12 14
Did Lexi spend more or less than $12 on grapes?
Remember to
multiply both the
numerator and
denominator by the
same number to
show an equivalent
fraction.
fractions for some common numbers used as
benchmarks.
3 Lexi bought 1 2 pounds of green grapes and
5
··
2 3 pounds of red grapes. Grapes are $2.99 a pound.
10
··
4
··
Marco have practiced on Monday?
Tammy chose A as the correct answer. How did she
get that answer?
Answers will vary. Possible answer: She correctly
C
estimated that since 1 1 is a little greater than 1,
8
··
they ate a little more than 1 1 1 pizzas. So, there
2
··
5 Look at the question you wrote in problem 4. Show
how to estimate the answer. Then find the actual
answer.
Show your work.
Students might use benchmark fractions or
some other method to estimate; and fraction
strips, equations, or some other method to find
the actual answer.
is a little less than 1 of a pizza left.
2
··
What benchmark
fractions could I use
to estimate?
Solution: Estimates and answers will vary.
©Curriculum Associates, LLC
Copying is not permitted.
Lesson 11 Add and Subtract Fractions in Word Problems
117
117
118
118
Lesson 11 Add and Subtract Fractions in Word Problems
©Curriculum Associates, LLC
Copying is not permitted.
Key
B Basic
M Medium
C Challenge
Practice and Problem Solving
©Curriculum Associates, LLC Copying is not permitted.
Unit 2 Number and Operations—Fractions
27