Answer Key • Lesson 10: Add Fractionsmtb4dev.kendallhunt.com/teacher/pdf/g5/u02/G5_TG_U... · 2. A. Answers will vary. The methods are alike in that they both reach the same answer.
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B. Yes. 1 pink is half a box, 3 blue is less thanhalf; together they will fit in one box.
C. 7–8 pizza; Possible explanation: One morepiece would make a whole pizza.
D. Number sentences will vary. Possibleresponses: 1–2 � 3–8 � 7–8 ; 4–8 � 3–8 � 7–8 ; 8–8 – 1–8 � 7–8
2. A. Answers will vary. The methods are alike inthat they both reach the same answer.Romesh exchanged pieces so he would haveall one color and then added. Kathyreasoned using benchmarks such as 1–2 and 1.The whole pizza is 8 eighths. One piece ismissing, so 7–8 remains.
B. Answers will vary.3. A.*
B. 5–6 ; Possible responses: I added 2–6 and 3–6 . Or,I saw that one one of the six pieces wasmissing, so I subtracted, 6–6 – 1–6 � 5–6 .
C. 2–6 � 3–6 � 5–6 or 6–6 – 1–6 � 5–6D. Answers will vary; Romesh used addition
1. A. Use fraction circle pieces to model the problem.
B. Is Kathy’s estimate correct? Explain your reasoning.
C. Exactly how much pizza is left over? Show or tell how you found youranswer.
D. Write a number sentence that shows how you solved the problem.
Kathy models the problem with circle pieces this way:
“Let’s put all the pieces together like we did with the pieces of pizza,” saidRomesh. “Now the model looks like this.”
“Now let’s solve the problem,” said Kathy. Romesh and Kathy both show adifferent way to solve the problem.
Romesh’s way Kathy’s way
I trade the pink piece for blue pieces so I just look at what’s missing from theall the pieces are the same color. whole. We need one more blue piece
to make a unit whole.
Eight blue pieces cover the whole unit, so each blue piece is 1�8 of the whole. If we have 1�8 less than a whole, thatThere are seven pieces, so we have makes 7�8 .7�8 of a pizza. The number sentence is: 8�8 � 1�8 � 7�8
2. A. How are Romesh’s and Kathy’s methods the same? How are theydifferent?
B. How do Romesh’s and Kathy’s strategies compare to yours?
Kathy’s Cookie
3. Kathy shared another large chocolate chip cookie. She cut the cookie into sixths. She gave Rosa 2�6 ofthe cookie and ate 3�6 herself. Kathy wants to knowhow much of the cookie they ate altogether.
A. Use fraction circle pieces to model the problem.
B. How much of the cookie did they eataltogether? Show how you solved the problem.
C. Write a number sentence that matches yoursolution.
D. Was your strategy more like Romesh’s solution or Kathy’s solution toQuestion 1?
Romesh and Kathy model the cookie problem with circle pieces this way:
A
AA
A
A
Rosa’spiecesKathy’s
pieces
The numerators tell the number of parts to add. The denominators tell the type of parts, such as sixths. I add the numerators together to find the sum.
2–63–6+
Rosa’s way
A A
sRosa’
piecessKathy’
A
A
s wayRosa’
piecessRosa’
A
rotaremud the ndal the typels trotinamodenels trotaremuhe nT
s wayRosa’
+ 6–3
6–2
d the suino fr ttheegos trh a, suctsre of pal the typ
ts tr of parmbeul the nel
.md the su I .s sixthsh ahe Td.do ats t
Student Guide - Page 91
*Answers and/or discussion are included in the lesson.
B. 7–12; Explanations will vary; see discussionand diagrams in the Student Guide.
C. Number sentences will vary. Possibleresponses: 3–12 � 4–12 � 7–12; 6–12 � 1–12 � 7–12
6. A. Answers will vary. Each problem involvesadding fractions; each can be solved inmore than one way; all three are solvedusing fraction circle pieces.
B. Each problem involves different fractionpieces; problems 1 and 5 involve fractionswith different denominators; problem 3involves fractions with the samedenominator.
C. Questions 1 and 5; he trades so he can addlike pieces.
D. Question 3; the pieces are already the same(sixths) so he can add the sixths.
Julia finds equivalent fractions with common denominators.
6. Discuss with a partner how the problems in Questions 1, 3, and 5 compareto each other.
A. What is the same about each problem?
B. What is different about each problem?
C. In which problem(s) does Romesh trade fraction pieces to get one color?Why does he have to trade them?
D. In which problem(s) does Romesh not have to trade any pieces? Whynot?
Use fraction circle pieces to solve the problems on the Find Fraction Sums 1pages in the Student Activity Book.
I solve + another way. It’s easier to add when all the pieces are the same color or when the denominators are the same. To find the same denominator, I replace the pieces with all the same color. Then I can add fractions with the same denominators.
1–31–4
Julia
Julia’s way
Julia’
Julia’
4e + an 41 –3 1 31 –
.srotinamodend frdan ahen I cT.rr.oolccaple, I rrr, I rotinamoden
e the samrs arotinamodene the samrs aec the piella
r watheo 1vI solJulia’
eth the samins wiotcad frl the samlth ais wece the piec
e d the samino fTTo f.ee the samhen the r wr ooole ce the sam
d wdo ar tsies ea It’s .yr was wayJulia’
e l the sam
hen the hen d w
ailuJ
Julia
To solve + , I find = and = .3—12
4—12+ 7—12=
1–4 1–3 1–43—12 1–3 4—12
1 � ?————3 � ?
?—4
= No
Can I rename as fourths?
1 � 2————3 � 2
2—6
= Yes
1 � ?————4 � ?
?—6
= No
Can I rename as sixths?
Can I rename as sixths?
1 � ?————4 � ?
?—12
= Yes
1 � ?————3 � ?
?—12
=
1 � 3————4 � 3
3—12
=
1 � 4————3 � 4
4—12
= Yes
Can I rename both and as twelfths?
BK BK
BK BK
BKBK
BK
1–3
1–3
1–4
1–4
1–3
3Can I r
=4—?
?�3 ———— ?�1
3 –– 11ename
as fourths?
No 4–1evolo sTTo s
3–
1—43d = 31 –12 a 123 —4d = 41 –3 ,–1 1 1n 3 1ni f I 3+
12 .—4 12
ename rCan I
ename rCan I
=6—?
?�4 ———— ?�1
=6—2
2�3 ———— 2�1
4 ?�3
4–1
3–1
as sixths?
as sixths?
No
sYe
4–
3–
BK
BKBK
BK
BK
BK
BK
= 12—7+ 12—
412—3
ailuJ
ename both rCan I
=12—?
?�3 ———— ?�1
=12—?
?�4 ———— ?�1
6 ?�4
as twelfths?andename both
sYe=12—4
4�3 ———— 4�1
=12—3
3�4 ———— 3�1 sYe
3–1
4–1
as twelfths?
s
s
Student Guide - Page 94
Answer Key • Lesson 10: Add Fractions
*Answers and/or discussion are included in the lesson.
Use fraction circle pieces or another method to solve the problems inQuestions 7–10.
7. Jackie rides her bicycle 1�4 of a mile from home to the park. She ridesanother 1�8 of a mile to the grocery store.
A. Is the distance more or less than 1�2 mile?
B. How far does she ride in all?
8. Luis spent 1�3 of his weekly allowance going to the movies. He spent another1�2 of it on a birthday present for his dad. How much of his total allowancedid he spend?
9. When playing Fraction Fill 1, the circles look like this:
A. Shannon spins a “ 1�2 ” on the spinner. She adds the entire 1�2 to thefourths circle. How much of the circle will be covered?
B. Jacob spins a “ 3�4 .” He adds the entire 3�4 to the eighths circle. Howmuch of the circle will be covered?
10. Mrs. Macintosh starts an apple orchard on her land by planting apple treescovering 3�10 of an acre. In the next two years she plants trees on
2�10 of anacre and then 4�10 of an acre.
A. Has she planted closer to 1�2 acre or 1 whole acre?
To make lemon-lime punch, Romesh mixes 2�3 of a gallon of lemonade, 1�6 of agallon of ginger ale, and 1�2 of a gallon of lemon-lime soda.
To find out how much punch he has, he writes the sum and shows it with fractioncircle pieces.
Romesh solves the problem this way:
11. A. Use circle pieces to solve the problem a different way from Romesh’sway. Write your answer both as a fraction and as a mixed number.
B. What color pieces did you use to solve the problem?
C. How is your method different from Romesh’s?
12. Julia notices that the denominators in 2�3 , 1�6 , and 1�2 are all factors of 12.“That is why Romesh could replace all the pieces with black pieces.” Thenshe notices that the denominators are also factors of 6.
Solve 2�3 + 1�6 + 1�2 using equivalent fractions with 6 as the fractions’denominators. Include a number sentence.
I replace all the circle pieces with black pieces. I count all the black pieces. Since there are 16 of them total, the answer is of a gallon.16——12
I can show my answer as a mixed number too. I put 12 black pieces together to make a unit whole. There are 4 black pieces left over. The answer is of a gallon.4——121
Use fraction circle pieces to solve the problems on the Find Fraction Sums 2pages in the Student Activity Book.
Check-In: Questions 13–18Use circle pieces or another method to solve the problems. Include numbersentences.
13. Linda sprints for 1�4 of a lap around the track, jogs for 3�4 of a lap, and walks
for 2�3 of a lap. How many total laps does Linda complete?
14. Frank writes these directions for Jacob to get to his house:
Go 2–5 of a mile on Elm Street toOak Street. Take a right on Oak Street and go 3–10 of a mile to MapleAvenue. Take a left on Maple Avenue and go 1–5 of a mile to my house.
How far is it from Jacob’s house to Frank’s house?
15. Jessie uses a rain gauge to measure rainfall in her yardfor 5 days. She recordeddata in the table.
• Use benchmarks of 0, 1�2 , and 1 to estimate the sum.• Use fraction circle pieces or another method to find an exact answer.• Write a number sentence to represent your solution.
A.5�12 �
1�4 B.2�6 �
3�6 C.2�4 �
2�3
D.11�12 �
2�3 E.1�3 �
5�6 �1�3 F.
1�2 �1�3 �
1�4
G. Use Julia’s method to solve Question 16E.
17. Jerome measures a stack of three tiles to be 3�8 of an inch tall. If he stacked10 tiles on top of each other, how tall would the stack be?
18. Use Julia’s method of finding equivalent fractions with commondenominators to solve 3�4 � 1�2 � 2�8 . Include a number sentence.
3_8
inch
Student Guide - Page 98
Answer Key • Lesson 10: Add Fractions
13. 12–3 laps14. 9–10 mile15. 13–12 inches or 11–12 inches16. Number sentences will vary. Two possible
solutions are given for each problem.A. Between 1–2 and 1; 5–12 � 1–4 � 8–12, 5–12 � 3–12 � 8–12B. Close to 1; 2–6 � 3–6 � 5–6 , 2–6 � 1–2 � 5–6 C. More than 1; 2–4 � 2–3 � 14–12 or 12–12 ,
6–12 � 8–12 � 14–12 or 12–12D. More than 1; 11–12 � 2–3 � 19–12 or 17–12 ,
11–12 � 8–12 � 19–12 or 17–12E.* More than 1; 1–3 � 5–6 � 1–3 � 9–6 or 13–6 ,
2–6 � 5–6 � 2–6 � 9–6 or 13–6 or 11–2F.* More than 1; 1–2 � 1–3 � 1–4 � 13–12 or 11–12 ,
3. A. trueB. trueC. false; 7–4D. trueE. false; 4–10 or 2–5F. trueG. trueH. false; 6–2I. Possible response: I knew 1–2 � 3–6 .
I multiplied 2–3 by 2–2 to get 4–6 . 2–6 � 3–6 � 4–6 � 9–6so the number sentence is true.
4. Word problems will vary. Sample problem:Jessie had a bag of mixed candy. 1–6 of the candywas peppermint, 1–4 of the candy was gumdrops,and 1–3 of the candy was butterscotch. The restof the bag was chocolate. How much of thebag was not chocolate? Solution: 2–12 � 3–12 � 4–12 � 9–12 or 3–4