6. A. 4 9, 2 3, 5 6 B. 1 4, 1 3, 3 8 C. 6 9, 5 6, D. 2 3, 3 4, 7 8 7, 5 8, F. 3 5, 7 10, 3 2

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1 Answer Key Lesson : Workshop: roblem Solving with Fractions Student uide Workshop: roblem Solving with Fractions (S pp ) Questions 7 A > ; ossible explanation: I know is almost, and is closer to < ; ossible explanation: is almost, but is C = ; ossible explanation: I used circle pieces blue pieces cover the same part of the circle as black pieces D < ; ossible explanation: I renamed as tenths = and < A,,,, C,, D Responses will vary ossible response: is closest to, and is the same as is closest to A There are equal parts We are interested in 7 of the parts C 7 is closer to ; ossible explanation: It is only away from D ossible response: is close to E is closer to ; ossible explanation: If there are equal pieces, is just a little bit of the whole Workshop: roblem Solving with Fractions Compare and Order Mr Moreno s class played the Comparing and Ordering Fractions ame Roberto had to compare to did common? I d not have time during the game to find mon denominators, so I thought about benchmarks like,, less and, and a is a little than one, d is a little more than, so o < Sam had to compare to? I thought about where the fractions were on the number less than but very, b t close Sam to, so > lines is is v Self-Check: Questions Use fraction circle pieces, the Fractions on Number Lines Chart in the Reference section, benchmarks, or your own strategies to compare the pairs of fractions For each problem: Use the symbols,, or to show your answer Show or tell how you decided A D C ut the following fractions in order from least to greatest A,,,, C,, D Show or tell how you ordered the fractions in Question C Workshop: roblem Solving with Fractions S rade Unit Lesson Student uide - age Use the Self-Check questions to choose practice with comparing and ordering fractions F ossible response: ossible response: is close to I looked on the Fractions on Number Lines Chart Can I Do This? Compare and order fractions Working On It! etting It! ot It! I could use I just need I m ready some extra help a some more practice for a challenge Q#,, Q#,, Q#, A > > C = D < 7 E < F > 7 A > < 7 C < ; = D ossible response: = > E ossible response: I used circle pieces is blacks is blues They cover the same amount of the red circle, so = For Questions, use fraction circle pieces, the Fractions on Number Lines Chart in the Reference section, benchmarks, or your own strategies A What does the denominator in the fraction 7 tell you? What does the numerator in the fraction 7 tell you? C Is 7 is closer to or to? How do you know? D Name a fraction close to E Is closer to or to? How do you know? F Name a fraction close to Name a fraction close to How did you decide? For each problem, first use number lines to compare the fractions Then use fraction circle pieces to compare Use the symbols >, <, or = in your answers A C E Student uide - age D 7 F 7 Compare each pair of fractions using the methods described below Use the symbols >, <, or = in your answers A Draw a number line to compare to Sketch the circle pieces you use to compare to 7 C Compare to Use multiplication or division to rename as sixths D Choose a strategy to compare to Show your work E Choose a strategy different from the one used in Question D to compare to Show your work S rade Unit Lesson Workshop: roblem Solving with Fractions T rade Unit Lesson Answer Key

2 Answer Key Lesson : Workshop: roblem Solving with Fractions Write the fractions in order from least to greatest A,,,,,, 7 D,, C 7 E,, F,, 7 7 A Choose two fractions with unlike denominators Compare them by using the symbols >, <, or = Choose three fractions with unlike denominators Order them from least to greatest Show or tell how you decided C Find two fractions greater than but less than Compare them by using the symbols >, <, or = D Find two fractions greater than but less than Compare them by using the symbols >, <, or = Darius hiked of a mile and Richard hiked 7 of a mile Whose hike was longer? Show or tell how you know by sketching a number line After their hikes, Darius drank liter of water and Richard drank liter of water Who drank more water? Show or tell how you know and include a number sentence This is the fraction set: questions below,, 7, 7 Use the number lines to answer the A,,,, C,, D,, 7 E 7,, F, 7, 7 Responses will vary Sample responses: A >,, C > D < Darius s hike was longer 7 A Which fraction is closest to? Which fraction is closest to? C Which fraction is equal to? D Which fraction is close to? E ut the fractions in order from least to greatest Workshop: roblem Solving with Fractions S rade Unit Lesson 7 Student uide - age 7 Richard drank more water ossible response: Richard drank liter = Darius drank litter > A closest to : closest to : 7 C equal to : D close to : 7 E,, 7, 7 This is the fraction set: A Which fraction is largest? Which fraction is smallest?,,, C Which fraction is equal to? D Which fraction is close to? E ut the fractions in order from least to greatest This is the fraction set:,, A Which fraction is largest? Which fraction is smallest?, C Which fraction is equivalent to? D Which fraction is closest to? 7, E ut the fractions in order from least to greatest Name three fractions between: A and C E and and D and and F and Estimate, Add, and Subtract Self-Check: Question For each problem, use the Fractions on Number Lines Chart in the Reference section, fraction circle pieces, or another strategy to estimate whether the sum or difference is greater than or less than Then solve the problem A C D E Show or tell how you solved Question D F Were your estimates close to your calculations? 7 S rade Unit Lesson Workshop: roblem Solving with Fractions Student uide - age T rade Unit Lesson Answer Key A C D E,,, A C D E,,, 7, Answers will vary Sample responses: A,,,, C,, D,, E,, 7 F,, A less than ; less than ; C greater than ; D less than ; E ossible response: = and =, so = F Answers will vary

3 Answer Key Lesson : Workshop: roblem Solving with Fractions Nicholas is not correct ossible explanation: is close to and 7 is close to, so a better estimate is a sum close to His sum,, is less than A She put a mark at and then added which is half of, so the mark is halfway between and green pieces and purple piece is half of a red circle C es, h er estimate was reasonable Use the Self-Check questions and the menu to choose practice with estimating, adding, and subtracting fractions Can I Do This? Solve the following problems Use tools such as number lines, two sets of fraction circle pieces, pictures, and your own strategies Show all your work Nicholas says, 7 = Use the number line below to estimate the sum Decide if you think Nicholas s answer is correct Show or tell why you think so Mara used the number line below to estimate the sum of She forgot to label her hops and the number line A Sketch and label the number line to show how Mara estimated Show how to solve using circle pieces C Was her estimate reasonable? Working On It! etting It! ot It! I could use I just need I m ready some extra help a some more practice for a challenge Estimate sums and differences ences in fraction Q#, 7 Q# 7 Q# problems Solve problems involving the addition and subtraction of Q#, 7,, Q#, 7, Q#,,, 7,,,,, fractions with like 7, 7 and unlike denominators Workshop: roblem Solving with Fractions S rade Unit Lesson Student uide - age 7 A close to close to C close to or D close to E close to F close to Students will choose different problems to solve, and their evaluations of their estimates will vary The sums and differences for Questions 7A F are A ; ; C ; D ; E ; F 7 Estimate the sum or difference for each problem below Choose the closest benchmark Close to Close to Close to A C E 7 D F 7 A close to close to C close to or D more than E more than F close to close to H close to I Students will choose different problems to solve, and their evaluations of their estimates will vary The sums and differences for Questions A H are A ; ; C ; D = ; E = ; F ; ; H Choose problems from Questions 7A F and find exact answers Show all of your work For each problem, tell if your estimate is close to your calculation Estimate the sum or difference for each problem below Choose the closest benchmark Close to Close to Close to Close to More than A C E 7 D F H I Choose problems from Questions A H and find exact answers For each problem, use a different strategy or tool, show your work, and tell if your estimate is close to your calculation S rade Unit Lesson Student uide - age Workshop: roblem Solving with Fractions T rade Unit Lesson Answer Key

4 Answer Key Lesson : Workshop: roblem Solving with Fractions Sharing Strategies Kim solved a problem this way: A Use circle pieces to show or tell if you agree or disagree with Kim s + = solution If you disagree, find the correct answer Kim Explain a strategy Kim can use to add fractions with unlike denominators Frank is solving Here is his thinking: FrankF A Can Frank rename as thirds? Why or why not? Which fraction can Frank rename to solve? Rename the fraction and solve the problem Chris are Tara are working together to solve They want to find fractions with common denominators a If I multiply the two I don t think that is correct r, fra r fo A Compare the students answers Do you agree with Chris or with Tara? Explain your thinking First solve Chris s way Then solve it Tara s way using aqua pieces Compare your solutions Does Chris s strategy work when solving? Show or tell how you know C Does Chris s strategy work when solving the problem? Show or tell how you know by solving the problem a second way Workshop: roblem Solving with Fractions S rade Unit Lesson Student uide - age Sharing Apples and Apple ie Find the sums or differences A pie pie = = C pie 7 pie = D = E pie pie = F = Emily solves pie pie this way: A Solve Emily s way Solve Emily s way Emily solves pie pie this way: = = Emily I think about circle pieces I can cut the pie this way or this way or Emily A Solve Emily s way Solve Emily s way Jessie s mom baked an pie for dessert The family ate of the pie the first night They ate of the pie the next night A Did they eat more or less than half of the pie? Model the problem with circle pieces to find out how much of the pie was eaten C Is your answer reasonable? How do you know? D What single color of circle pieces can you use to solve the problem? S rade Unit Lesson I look ok at the denominators first I can t t rename rename as as halves and I can t t e thirds a I know and are both factors of, so I will = rename both fractions as sixths is, so = =, so = = Workshop: roblem Solving with Fractions ra A Kim is incorrect; + = ossible response: Kim is adding unlike denominators She needs to find circle pieces that are all the same color like yellows or multiply to find an equivalent fraction with a common denominator like = A Frank cannot rename as thirds divided by is, but divided by is not a whole number ossible response: Frank could rename as = A oth Chris and Tara are correct is the same as Chris s way: is the same as and is the same as, so = Tara s way using circle pieces: aquas minus aquas is aquas or of the circle The solutions are equivalent, = es, Chris s strategy works C es, Chris s strategy works is the same as = = Using circle pieces, blue pieces ( ) minus blue piece ( ) is blue pieces ( ) A pie C pie D E pie F A = ; = = ; = A = and = ; = = and = ; = A more than of the pie C ossible response: es, because I estimated more than D blue Student uide - age T rade Unit Lesson Answer Key

5 Answer Key Lesson : Workshop: roblem Solving with Fractions A ; black C and ; 7 A about half of the ; Or Or k k k k k k k k k k k Jessie s mom used cup of white sugar and cup of brown sugar A Model the problem with circle pieces to find out how much sugar she used altogether What single color circle piece can you use to solve the problem? C Show how to use Emily s method to solve the problem a different way 7 Shannon and Emily shared an Shannon ate of the Emily ate of the A Did they eat close to half of the or almost all the? Model the problem with circle pieces to find out how much of the was eaten C Show how to use Emily s method to solve the problem a different way D Is your answer reasonable? How do you know? E How much of the is left? Write a number sentence Shannon, Emily, and Jessie shared two whole s Shannon ate of one, Emily ate of an, and Jessie ate of an A How much of the s did they eat? Write a number sentence and show or tell how you solved the problem Nicholas ate what was left of the two s About how much of an did he eat? Choose the closest estimate Close to About Close to whole C Exactly how much did Nicholas eat? Write a number sentence C ; D ossible response: es, because I got the same answer in both solutions Workshop: roblem Solving with Fractions S rade Unit Lesson E A s ossible strategy: When I added the pieces I got: Student uide - age K That is whole and of another I covered the pink with blue pieces and counted About C T rade Unit Lesson Answer Key

6 Answer Key Lesson : Workshop: roblem Solving with Fractions Snack Mix rofessor eabody wants to make a snack mix He has three bowls and three recipes Which recipe should he mix in which bowl? How did you decide? cup: Trail Mix; cups: Cereal Mix; cups: Monkey Mix ossible strategy: I used fraction circle pieces to show each recipe and compared them to the bowl size rofessor eabody had cup of pretzels he wanted to use to make a snack mix Which snack mix can he make? Explain your reasoning rofessor eabody brought one batch of Monkey Mix to a party One-half cup mix was eaten How many cups are left? rofessor eabody decided to make three batches of Monkey Mix How much of each ingredient will he need? Invent a new recipe for snack mix using the measurements and ingredients given in the three recipes above A What is the name of your new snack mix? Write a number sentence to show how much your recipe makes S rade Unit Lesson Workshop: roblem Solving with Fractions Student uide - age The Deli lanca and Lin bought one sandwich at the deli lanca ate of the sandwich and Lin ate of it A Did the girls eat close to a half or close to the whole sandwich? Model the problem with circle pieces to find out how much of the whole sandwich the two girls ate Write a number sentence C Is your answer reasonable? How do you know? D What single color circle piece can you use to solve the problem? E How much of the sandwich was left? Show how you know lanca and Lin s deli sandwich was made with the following ingredients: pound of turkey pound of cheese pound of mustard and onions pound of bread A Estimate the weight of the sandwich Choose one About pound Less than pound More than pound How much does the deli sandwich weigh? Lin and lanca also bought a pound container of potato salad lanca ate pound of the salad and Lin ate pound A How much of the salad did the girls eat? How much potato salad is left? C Could the girls have bought a pound container rather than the pound container of potato salad? Explain your thinking Workshop: roblem Solving with Fractions S rade Unit Lesson Student uide - age He can make up to batches of Trail Mix assuming he has the other ingredents There are no pretzels in Monkey Mix and he does not have enough pretzels to make Cereal Mix cups left; cups cup cups anana Chips cups Nuts cup Dried s cups Coconut cups A Answers will vary Answers will vary A Close to the whole sandwich 7 C ossible response: es, because 7 is close to a whole sandwich D blue E of the sandwich was left ossible response: 7 T rade Unit Lesson Answer Key

7 Answer Key Lesson : Workshop: roblem Solving with Fractions A Less than pound of a pound A A Money 7 randon saved of his babysitting earnings in his piggy bank A What fraction of his earnings did he have left to spend? randon spent of his earnings on baseball cards Does he have close to nothing left or close to of his earnings left? C Use circle piece or rename as tenths to find the exact fraction of randon s earnings that are left Shannon said, I spent of my allowance at the book store, of my allowance on a gift, and I saved the rest A How much of her allowance did she spend? How much of her allowance did she save? less than a whole pound A of a pound; + ; I traded the yellow for blacks and the aqua for blacks blacks is equal to 7 of a pound is left; = 7 C es, pound would have been enough The girls ate Half a pound would be 7 A of his earnings Close to half his earnings left C of his earnings are left to spend Shannon s mother spends of her monthly salary on rent (which includes heat) roceries for the month and her car payment add up to about of her salary A Do all these bills account for about of her salary, more than of her salary, or all of her salary ( whole salary)? What fraction of her salary is spent after paying for rent, groceries, and her car? Anna and race received the same amount of money as birthday gifts Each spent her money at the mall A How much of her gifts did each girl spend? Anna race How much does each girl have left? C Who spent more money? at the bookstore at the hobby store at the food court at the bookstore D What is the difference between what each girl spent? E race wants to buy a pin for her mother that is worth of her birthday gift Does she have enough money left to buy it? F Anna decides to give some of her money to race to pay for the pin Do Anna and race have enough money? Explain your thinking All his babysitting money saved A All of her allowance; whole She did not save anything because she had nothing left A More than of her salary of her salary is spent A Anna spent of her money, so race spent or of her money; I put pink ( ) and blue ( ) together and I recognize that as or yellow Anna has of her money left and race has of her money left C race; is more than D ; E No; she has only of her money left F es Anna can give race the she needs to buy a gift worth their birthday money left S rade Unit Lesson Student uide - age Workshop: roblem Solving with Fractions T rade Unit Lesson Answer Key 7

8 Answer Key Lesson : Workshop: roblem Solving with Fractions Walk and Run Roberto s older sister jogs every morning This morning, after running 7 of a kilometer, she met a friend She stopped to chat Then she jogged kilometer more A Did Roberto s sister jog more or less than kilometer? How far did she jog? After school, Maria walked mile to the park She then walked another block, or of a mile farther, to the store A How far did Maria walk? Maria tries to walk at least mile each day How much more does Maria need to walk to meet her goal? Shannon ran of a mile Then she walked mile A Did she go more or less than mile? How do you know? How many miles did Shannon run and walk together? Jerome used number lines to solve A Where did Jerome start? Why? Where did Jerome stop on the number line? C Compare Jerome s answer to your answer to Question Are they the same? D Nicholas compares his answer to Jerome s Do you agree with I got a different answer than Nicholas? Why or why not? Jerome Jerome got and I got One of our strategies did not work Workshop: roblem Solving with Fractions S rade Unit Lesson 7 Student uide - age 7 A Less than a kilometer green and 7 purple are less than one kilometer; 7 7 A mile; is the same as, so mile; A More than a mile; is close to whole and is more than, so is more than mile mile; I traded for A ; is the same as C Responses will vary D I do not agree with Nicholas and are the same A es, one yellow, one green, and one purple are more the of a whole circle vegetable plants lanning a arden Shannon is planning a garden She is planning a flower section and a vegetable section Look at the list of the things she would like to plant A Shannon wants at least her garden to be vegetable plants Does her garden plan have at least vegetable plants? How much of Shannon s garden will be flower plants? Shannon s arden lan Flower lants Vegetable lants petunias peppers roses lettuce tomatoes C How much of Shannon s garden will be vegetable plants? Shannon would like to plant some lilies A Does Shannon still have space in her garden for the lily plants? How much of her garden is not planned? 7 lan your own garden our garden should have flower and vegetable plants Choose plants that fit into each category A How much of your garden is flower plants? How much of your garden is vegetable plants? C How much of your garden is not planned? 7 ; 7 ossible strategy: Two greens cover the yellow ( ) and the purple ( ) but by a little piece too much That little piece is There are in each, so 7 C ossible strategy: A pink covers most of the pieces There is a little piece left, smaller than the smallest fraction circle pieces Two of these little pieces fit in so it must be There are in a pink A es Use the Sharing aper pages in the Student Activity ook to practice solving more problems with fractions is not planned 7 A C Responses will vary Workshop: roblem Solving with Fractions S rade Unit Lesson Student uide - age T rade Unit Lesson Answer Key