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Arizona State University *
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Course
430
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
31
Uploaded by SargentResolve13180
Grade 4 January 23, 2024 Answer Key
Demonstration of Learning
1.
C. Exactly
of the eggs
1
2
2.
A. Sloane will have less than
of her sticker collection left.
1
4
3.
B. Less than
of the fruit snacks are left.
1
2
4.
Chase’s estimate is unreasonable. Explanations will vary.
5.
Monica is incorrect. Explanations will vary.
© Houston ISD Curriculum 2023-2024
Name: ________________________________________
Date: ____________
Learning
January 23, 2024 | TEK 4.3F
Student Objective
: SWBAT use benchmark fractions 0, ¼ , ½, ¾, and 1 to evaluate reasonableness
of sums and differences of fractions referring to the same whole.
Q1
Look at the fractions bars and write
1 thing you notice and 1 thing you
wonder.
Answers will vary.
I notice
I wonder
Q2
What patterns do you see in the numerators and denominators of these fractions?
Think-Pair-Share
Answers will vary.
© Houston ISD Curriculum 2023-2024
Q3
Name 2 fractions that are equivalent to
.
1
2
Write your answers in the space provided below.
Answers will vary.
Q4
Name 2 fractions that are
equivalent to
.
1
4
Answers will vary.
Write your answers in the space
provided below.
Use the fraction strips to answer questions 5-7.
True or false.
is about
.
2
3
1
2
Q5
Label the fraction strips.
Labeled correctly.
1 whole.
1
2
1
3
Q6
Shade in
.
1
2
Shade in
.
2
3
© Houston ISD Curriculum 2023-2024
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Q7
True or false.
False
is about
.
2
3
1
2
Write your answer in the space provided below.
Use the fraction strips to answer questions 8-10.
True or false.
is about
.
2
5
3
4
Q8
Label the fraction strips.
Labeled correctly.
1 whole.
3
4
2
5
Q9
Shaded correctly.
Shade in
.
3
4
Shade in
.
2
5
Q10
True or false.
False
is about
.
3
4
2
5
Write your answer in the space provided below.
© Houston ISD Curriculum 2023-2024
Use the fraction strips to answer questions 11-13.
True or false.
is about
.
2
8
1
4
Q11
Label the fraction strips.
Labeled correctly.
1 whole.
1
4
2
8
Q12
Shaded correctly
Shade in
.
1
4
Shade in
.
2
8
Q13
True or false.
True
is about
.
2
8
1
4
Write your answer in the space provided below.
© Houston ISD Curriculum 2023-2024
Q14
Chase and Jackson each had a candy bar that was
equal
in size.
●
Chase ate
of his candy bar.
4
6
●
Jackson ate
of his candy bar.
1
12
Chase believes that, together he and Jackson have almost eaten 1 whole candy bar.
Is Chase's estimate reasonable?
Chase
__________
Jackson
__________
Chase’s estimate is
A. Reasonable
B. Not reasonable
Answers will vary.
because ____________________________________________________________
___________________________________________________________________
© Houston ISD Curriculum 2023-2024
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Use the story problem below to answer questions
14-15.
Ellen and James painted a mural on a wall at the park.
Ellen painted
of the mural.
James painted
of the
4
10
2
5
mural. Ellen believes that James painted less than
of the
1
2
mural.
Q14
Partition and shade the strip
below to represent
.
2
5
Partition and shaded correctly.
Partition and shade the strip above to
represent
.
1
2
Partition and shaded correctly.
Q15
Do you agree with Ellen? Why or why not?
Yes, explanations will vary.
Q16
Manny’s mom told him he could spend
hour playing video games before lunch. So far, he
10
12
has spent
hour playing his video game. What is a reasonable estimate of the amount of time he
6
12
has remaining?
A. About
hour.
1
2
B. About
hour.
1
4
C. Exactly
hour.
1
2
D. Exactly
hour.
1
4
© Houston ISD Curriculum 2023-2024
Q17
Carlyn has a huge collection of pins.
She will give
of her pin collection to her cousin, Lauren.
1
3
She will give
of her pin collection to her brother, Ken.
3
6
Which statement is true?
A. Carlyn will have less than
of her pin collection left.
1
4
B. Carlyn will have more than
of her pin collection left.
1
4
C. Carlyn will have about
of her pin collection left.
1
2
D. Carlyn will have more than
of her pin collection left.
1
2
Q18
Draw fractions strips to justify your answer.
Fractions strips drawn correctly.
© Houston ISD Curriculum 2023-2024
Name: _____________________________
Date: ____________
Securing 1
January 23, 2024 | TEK 4.3F
Student Objective
: SWBAT use benchmark fractions 0, ¼ , ½, ¾, and 1 to evaluate
reasonableness of sums and differences of fractions referring to the same whole.
Use the fraction strips to answer questions 1-3.
True or false.
is less than
.
2
5
3
4
Q1
Label the fraction strips.
Labeled
correctly.
1 whole.
3
4
2
5
Q2
Shaded correctly
Shade in
.
3
4
Shade in
.
2
5
Q3
True or false.
True
is less than
.
2
5
3
4
Write your answer in the space provided below.
© Houston ISD Curriculum 2023-2024
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Use the fraction strips to answer questions 4-7.
True or false.
is about
.
6
8
1
2
Q4
Partition the strip below to represent
and
.
Strips partitioned and shaded
6
8
1
2
correctly.
Q5
True or false.
False
is about
.
6
8
1
2
Write your answer in the space provided
below.
Q6
True or false.
True
is less than
.
2
8
1
2
Write your answer in the space provided
below.
Q7
Fill in the blank to make the statement true.
4
8
Is exactly
.
1
2
© Houston ISD Curriculum 2023-2024
Use the fraction strips to answer questions 8-11.
True or false.
is about
.
2
10
1
4
Q8
Partition the strip below to represent
and
.
Strips partitioned and shaded
2
10
1
4
correctly.
Q9
True or false.
True
is about
.
2
10
1
4
Write your answer in the space provided
below.
Q10
True or false.
True
is about
.
8
10
3
4
Write your answer in the space provided
below.
Q11
Fill in the blank to make the statement true.
Answers will vary.
is more than
.
1
4
© Houston ISD Curriculum 2023-2024
Use the story problem below to answer questions 12-13.
Zack and Cody’s mom bought a carton of eggs. In one week, Zack and Cody had
eaten
of the eggs in the carton. What is a reasonable estimate of the amount of
9
12
eggs remaining in the carton?
Q12
Partition the strips into
halves, fourths and twelfths
.
Strips partitioned into halves, fourths and twelfths correctly.
Q13
What is a reasonable estimate of the amount of eggs remaining in the carton?
A. About
of the eggs
1
2
B. About
of the eggs
1
4
C. Exactly
of the eggs
1
2
D. Exactly
of the eggs
1
4
© Houston ISD Curriculum 2023-2024
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Use the story problem below to answer questions 14-15.
Lynn bought a box of chips. In one week, she ate
of chips.
2
7
Image by OpenClipart-Vectors from Pixabay
Find the true statement.
Q14
Draw fraction strips to help you
solve.
Strips partitioned and shaded
correctly to represent ½, ¼ and 2/7.
Q15
Which statement is true?
A. Lynn ate less than
of the chips.
1
4
B. Lynn ate more than
of the chips.
1
2
C. Lynn ate about
of the chips.
1
2
D. Lynn ate about
of the chips.
1
4
Use the story problem below to answer questions 16-17.
Phineas has a huge collection of rare rocks.
He will give
of his rock collection to his brother, Pherb.
1
3
He will give
of his rock collection to his sister, Candice.
3
6
Image by OpenClipart-Vectors from Pixabay
Q16
Draw fraction strips to help you
solve.
Strips partitioned and shaded
correctly to represent ⅓ , 3/6 and ¼,
½ .
Q17
Which statement is true?
A. Phineas will have less than
of his
1
4
rock collection left.
B. Phineas will have more than
of his
1
4
rock collection left.
C. Phineas will have about
of his rock
1
2
collection left.
D. Phineas will have more than
of his
1
2
rock collection left.
© Houston ISD Curriculum 2023-2024
Q18
Raven and Cory each had a candy bar that was equal in size. Raven ate
of
1
6
her candy bar. Cory ate
of his candy bar. Raven believes that, together, Corey and
2
12
her have eaten more than a whole candy bar.
Is Raven’s estimate reasonable? Why or why not?
Raven’s estimate is not
reasonable.
Use a benchmark fraction to explain your reasoning.
Explanations will vary.
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
© Houston ISD Curriculum 2023-2024
Name: _______________________________
Date: ____________
Securing 2
January 23, 2024 | TEK 4.3F
Student Objective
: SWBAT use benchmark fractions 0, ¼ , ½, ¾, and 1 to evaluate
reasonableness of sums and differences of fractions referring to the same whole.
Use the story problem below to answer questions 1-3.
Perla bought a box of chips. In one week, she ate
of chips.
2
7
Image by OpenClipart-Vectors from Pixabay
Q1
Which statement is true?
A.
Perla ate less than
of the chips
.
1
4
B. Perla ate more than
of the chips.
1
2
C. Perla ate about
of the chips.
1
2
D. Perla ate about
of the chips.
1
4
Q2
What is a reasonable estimate of the amount of chips Perla has left?
1
4
Q3
Use fraction strips to explain your reasoning.
Fraction strips drawn correctly.
© Houston ISD Curriculum 2023-2024
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Use the story problem below to answer questions 4-6.
Lee has a huge collection of fidget spinners.
He will give
of his fidget spinner collection to his brother, Fonzo.
1
3
He will give
of his fidget spinner to his sister, Reign.
3
6
Q4
Which statement is true?
A. Lee will have less than
of his fidget spinner collection left.
1
4
B. Lee will have more than
of his fidget spinner collection left.
1
4
C. Lee will have about
of his fidget spinner collection left.
1
2
D. Lee will have more than
of his fidget spinner collection left.
1
2
Q5
Use fraction strips to explain your reasoning.
Fraction strips drawn correctly.
Q6
What is a reasonable estimate of the amount of Lee’s fidget spinner collection he gave
away?
A. Less than
.
1
2
B. Less than
.
1
4
C. About
.
3
4
D. Less than
.
3
4
Explain. Explanations
will vary.
© Houston ISD Curriculum 2023-2024
Use the story below to answer questions 7-9.
Kim, Juan and Cecia painted a mural on a wall at a park. Kim painted
of the mural. Juan
4
10
painted
of the mural. Cecia painted the rest of the mural. Cecia believes the part of the
2
5
mural that Kim and Juan painted was less than
of the entire mural.
1
2
Q7
Do you agree with Cecia? Explain.
Answers will vary.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
Q8
Use fraction strips to explain your reasoning.
Fraction strips drawn correctly. Explanations
will vary.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
Q9
Kim painted
of the mural.
4
10
What is a reasonable estimate of the amount of wall Kim painted?
A. About
.
1
4
B. About
.
1
2
C. About
.
3
4
D. Less than
.
3
4
© Houston ISD Curriculum 2023-2024
Q10
Juan painted
of the mural.
2
5
Fill in the blank to make the statement true.
Juan painted about
.
½
Q11
Fedes’ mom bought a box of cookies for his family. In one week, Fedes’ family had eaten
of the cookies in the box. What is a reasonable estimate of the amount of cookies
6
10
remaining in the box?
A. About
of the box
1
2
B. About
of the box
1
4
C. Exactly
of the box
1
2
D. Exactly
of the box
1
4
Justify your answer.
Answers will vary.
Explain to a friend the strategy you used to solve question 11.
Q12
George used
of his notebook. George’s sister drew in
of his notebook. What is a
1
8
4
9
reasonable estimate for how much of George’s notebook was used?
A. About
of the notebook
1
4
B. About
of the notebook
1
2
C. About
of the notebook
3
4
D. About 1 notebook
© Houston ISD Curriculum 2023-2024
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Use pictures, words, and/or numbers to justify your solution.
Answers will vary.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Q13
List
TWO
fractions that are about
.
1
2
Write your answers in the space provided below.
Fractions will vary.
List
TWO
fractions that are about
.
1
4
Write your answers in the space provided below.
Fractions will vary.
List
TWO
fractions that are about
.
3
4
Write your answers in the space provided below.
Fractions will vary.
© Houston ISD Curriculum 2023-2024
Q14
Jack, Ronald, and Deborah painted a mural on the wall at City Hall. Jack painted
of
5
6
the mural. Ronald painted
of the mural. Deborah painted the rest of the mural. What is a
1
12
reasonable estimate for the amount of the mural painted by Ronald and Jack?
A.
Between
and 1
3
4
B.
Between
and
3
4
1
2
C.
Between
and
1
2
1
4
D.
More than 1
Use pictures, words, and/or numbers to justify your solution.
Answers will vary.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Q15
What is a reasonable estimate for the part of the mural painted by Deborah?
Less than
½.
© Houston ISD Curriculum 2023-2024
Q16
A store sells bags of chips.
●
of the bags are spicy-flavored chips.
1
3
●
of the bags are ranch-flavored chips.
3
5
●
The rest of the bags are plain chips.
Which statement is true?
A. More than
of the bags are plain chips.
1
2
B. There are no bags of plain chips.
C. Exactly
of the bags are plain chips.
1
2
D. Less than
of the bags are plain chips.
1
2
Q17
True or False.
of the bags are ranch-flavored chips are about
. __________
True
3
5
1
2
of the bags are spicy-flavored chips are more than
. ________
False
1
3
1
2
What is a reasonable estimate of the amount of ranch and spicy-flavored chips?
Answers will
vary. Acceptable answer; More than ¾ .
© Houston ISD Curriculum 2023-2024
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Q18
Cooper bought
pound of dog food and
pound of cat food. What is a reasonable
3
16
7
16 estimate of the total amount of dog and cat food Cooper bought?
A. About
lb
1
4
B. About
lb
3
4
C. Between
lb and 1 lb
3
4
D. Between
lb and
lb.
1
4
1
2
Which
TWO
strategies could use to solve the question above.
Answers will vary.
Using academic vocabulary, explain
each
strategy.
Answers will vary.
© Houston ISD Curriculum 2023-2024
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Name: _______________________________
Date: ____________
Advanced
January 23, 2024 | TEK 4.3F
Student Objective
: SWBAT use benchmark fractions 0, ¼ , ½, ¾, and 1 to evaluate
reasonableness of sums and differences of fractions referring to the same whole.
Q1
Paula, Gustavo, and Maddie painted a mural on the wall at City Hall. Paula painted
of
5
6
the mural. Gustavo painted
of the mural. Maddie painted the rest of the mural. What is a
1
12
reasonable estimate for the part of the mural painted by Gustavo and Paula?
A.
Between
and 1
3
4
B.
Between
and
3
4
1
2
C.
Between
and
1
2
1
4
D.
More than 1
Use pictures, words, and/or numbers to justify your solution.
Answers will vary.
Q2
What is a reasonable estimate for the part of the mural painted by Maddie?
.
Less than ½.
© Houston ISD Curriculum 2023-2024
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Q3
A store sells bags of chips.
●
of the bags are cheese-flavored chips.
1
3
●
of the bags are sourcream and onion-flavored chips.
3
5
●
The rest of the bags are plain chips.
Which statement is true?
E. More than
of the bags are plain chips.
1
2
F.
There are no bags of plain chips.
G. Exactly
of the bags are plain chips.
1
2
H. Less than
of the bags are plain chips.
1
2
Use pictures, words, and/or numbers to justify your solution.
Answers will vary
Q4
True or False.
More than
of the bags are sourcream and onion-flavored chips. __________
True
1
2
Less than
of the bags are cheese-flavored chips. ________
False
1
4
What is a reasonable estimate of the amount of sourcream and onion and cheese-flavored
chips? Why?
Answers will vary. Acceptable answer; More than ¾ .
© Houston ISD Curriculum 2023-2024
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Q5
Benny bought
pound of hamster food and
pound of cat food. What is a
3
16
7
16 reasonable estimate of the total amount of hamster and cat food Benny bought?
E. About
lb
1
4
F.
About
lb
3
4
G. Between
lb and 1 lb
3
4
H. Between
lb and
lb.
1
4
1
2
Which
TWO
strategies a student could use to solve the question above.
Answers will vary.
Using academic vocabulary, explain
each
strategy.
Answers will vary.
Q6
How can fraction bars help you decide if a fraction is closest to 0? Closest to
? Closest
1
4
to
? Closest to
? Closest to 1?
Answers will vary.
1
2
3
4
Part B on the next page.
© Houston ISD Curriculum 2023-2024
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Part B:
Label the fractions strips below and highlight the benchmark fractions of 0,
,
,
1
4
1
2
3
4
and 1.
Fractions labeled and highlighted correctly.
© Houston ISD Curriculum 2023-2024
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Q7
Which benchmark fraction is
closest? _____
¾
5
6
Which benchmark fraction is
closest? ______
½
3
8
Which benchmark fraction is
closest? _____
½
2
5
Which benchmark fraction is
closest? _____
¼
2
10
Q8
List a fraction that is about
. ______
Answers will vary.
1
4
List a fraction that is about
. _____
Answers will vary.
1
2
List a fraction that is about
. _____
Answers will vary.
3
4
Q9
Sara bought a box of oatmeal. In one week she ate
of the oatmeal.
4
9
Which is closest to the fraction of the cereal she had left?
A. Less than
of the oatmeal was left.
1
4
B. More than
of the oatmeal was left.
3
4
C. About
of the oatmeal was left.
1
2
D. About
of the oatmeal was left.
1
4
Use pictures, words, and/or numbers to justify your solution.
Answers will vary.
Answers will vary.
© Houston ISD Curriculum 2023-2024
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Q10
During cross country practice, Eve ran
mile, while Alo ran
mile. Which best
5
12
4
9
describes the total distance Eve and Alo ran?
A. Less than 1 mile
B. Exactly 1 mile
C. A little more than 1 mile
D. Less that
mile
1
2
Use pictures, words, and/or numbers to justify your solution.
Answers will vary.
Q11
Omar sorted his collection of football cards.
●
Omar will give
of his collection to his brother.
1
5
●
Omar will sell
of his collection to a card shop.
4
10
Which statement is true?
A. Omar will have exactly half of his collection left.
B. Omar will sell more than half his collection to a shop.
C.
Omar will have less than half his collection left.
D. Omar will give more than half his collection to his brother.
Use academic vocabulary to explain your solution.
Answers will vary.
© Houston ISD Curriculum 2023-2024
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Q12
Selena and Hailey painted an entire wall together. Selena painted
of the wall, and
3
7
Hailey painted the rest. Which statement is true?
A. Selena painted less than half the wall, and Hailey painted more than half of the wall.
B. Selena painted more than half of the wall, and Hailey painted less than half of the wall.
C. Each girl painted more than half of the wall.
D. Each girl painted less than half of the wall.
Justify your solution.
Answers will vary.
Justify your solution using pictures.
Answers will vary.
Q13
Pick an answer choice and explain why it is unreasonable.
Answers will vary.
© Houston ISD Curriculum 2023-2024
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Q14
Mr. Tyler presented the story problem below to his class.
Shelby and her brother shared a candy bar. Shelby are
of the candy bar. Her brother ate
4
9
1
8
of the candy bar. What is a reasonable estimate of the amount of the candy bar Shelby and
her brother ate?
He asked the class to use fraction strips to solve.
Amber drew the following:
However, Amber is struggling to interpret the information to find a reasonable estimate.
Answer
the following questions to help Amber understand.
Which benchmark fraction can you use to determine the reasonable estimate of the amount
of the candy bar Shelby and her brother ate?
½
Why did you choose that benchmark fraction?
Answers will vary.
How can she apply her understanding of benchmark fractions to estimate the fraction sum in
this problem type?
Answers will vary.
What operation(s) might she use to solve this problem?
Answers will vary.
Q15
Solve.
What is a reasonable estimate of the amount of the candy bar Shelby and her brother ate?
Shelby and her brother ate about ½ of a candy bar.
© Houston ISD Curriculum 2023-2024
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Q16
Create a story problem with the fractions
and
.
Answers will vary.
2
6
4
8
Story problem must include the following question:
What is a reasonable estimate for __________________________?
Q17
Provide the solution for your story problem.
Answers will vary.
Q18
Explain your answer.
Answers will vary.
© Houston ISD Curriculum 2023-2024
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