G6 U6 Constructed Response
Name: ________________________________________ Date:_______________
Grade 6 Unit 6 Constructed Response Rate and Ratio TASK 1: Word Problems using Unit Rates (MC: 6.RP.2, 3b; MP: 1, 2, 3, 4, 6, 7, 8) 1. The local market had a sale on fruit. These are their advertised prices. a. Which fruit has the lowest cost per pound? Explain how you know.
Fruit
Advertised Price
apples
3 lb/$1.80
tangerines
10 lb/$2.00
pears
2 lb/$1.50
grapes
4 lb/$3.20
watermelon
5 lb/$1.25
b. If you spent $1.00 on each kind of fruit, how many pounds of fruit would you buy? Explain how you know.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 1, Page 1
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c. What would it cost to buy 1 lb of apples, 3 lb of tangerines, 2 lb of 2 pears, 1 lb of grapes, and a 7-pound watermelon? Show your work.
2. Many of our family members drove from their hometowns to Las Vegas for a family reunion. Over dinner the first night, they compared their trips to see whose car has the best gas mileage. The miles the family members drove and the gallons of gas they used are listed in the table.
Family Member
Distance Driven (miles)
Great Uncle Emory Aunt Kathy Uncle Robert Mom Grandma Lou
576 294 276 434 405
Gas Used on the Drive to Las Vegas (gallons) 32 14 23 14 15
a. Whose car has the best gas mileage (went the farthest on one gallon of gas)? Explain how you found your answer.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 1, Page 2
b. Grandma Lou paid a unit price of $3.35 per gallon to fill up her gas tank before starting the trip. If she bought 17.2 gallons, how much did it cost?
c. It is 15 miles from Las Vegas to Henderson, where some of the family members want to visit an old friend. Both Great Uncle Emory and Uncle Robert will drive their own cars. Great Uncle Emory says his car will use less gas on the trip. Is he right? Explain.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 1, Page 3
Name: ________________________________________ Date:_______________
Grade 6 Unit 6 Constructed Response Rate and Ratio TASK 2: Word Problems using Equivalent Ratios (MC: 6.RP.1, 3a; MP: 1, 2, 4, 6, 7, 8) 3. Mrs. Frenza just went grocery shopping and filled the family’s fruit bowl. These are the fruits in the bowl.
a. What is the ratio of bananas to all fruits? Give your response as a ratio and in a complete sentence.
b. What is the ratio of oranges to apples? Give your response as a ratio and in a complete sentence.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 4
c. What is the ratio of apples to all other fruits? Give your response as a ratio and in a complete sentence.
d. Mr. Frenza was being helpful and also went to the grocery store for fruits. He came home with exactly the variety of fruits as his wife. If you had to answer questions a, b, and c again for all of the fruits together, would the ratios be equivalent? Explain.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 5
4. Mrs. Rush found this easy recipe in a magazine and decided she wanted to paint eggs with her twin boys.
Painted Eggs 12 hard-boiled eggs 1
a. She will mix four batches of Terrific Teal. Complete the table to find the number of drops of each color she will use.
Green
2
Blue
5
4
2
teaspoon of white vinegar food dye (see color mixes below)
Choose the color you want to make. Mix the vinegar and the food dye in a small bowl to get the desired color. Use a paintbrush to brush the color on the eggs. Popular Colors Dusty Pink: 14 drops red + 6 drops blue Deep Orange: 3 drops red + 17 drops yellow Energetic Yellow: 1 drop red + 45 drops yellow
b. She will mix five batches of Dusty Pink. Draw a double number line to find the number of drops of each color she will use.
Grass Green: 14 drops green + 6 drops yellow Terrific Teal: 2 drops green + 5 drops blue Purple Grape: 1 drop red + 7 drops blue
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 6
5. For every 3 eggs Ethan painted, Brian painted 5. a. If Brian painted 10 more eggs than Ethan, how many eggs did they paint altogether? Use a tape diagram or double number line to solve.
b. Explain how you solved the problem.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 7
c. Make a table of the equivalent ratios you found in Part A. Graph them on the coordinate grid. (Remember to include the scale labels and title.)
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 8
Name: ________________________________________ Date:_______________
Grade 6 Unit 6 Constructed Response Rate and Ratio TASK 3: Word Problems with Percentage and Measurement Ratios (MC: 6.RP.3cd; MP: 1, 2, 4, 6, 7, 8) 6. A week ago, Darwin planted seeds in his garden. The table shows the number of seeds he planted and the number of seeds that have already sprouted. Seed Type Broccoli Cauliflower Pumpkin Radish Tomato
Number of Seeds Planted 8 10 4 6 12
Number of Seeds Sprouted 6 7 1 3 9
a. Which seed has the greatest percentage of sprouts? Explain how you know.
b. Overall, what percentage of all the seeds has sprouted?
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 3, Page 9
7. Filipe shopped for a new outfit and found these items on sale.
SALE! 15% off! khakis
SALE! 30% off! jeans
SALE! 25% off! pullover
SALE! 50% off! t-shirt
a. Which pair of pants has the greatest dollar discount? Explain how you know.
b. Draw a percentage bar to find the sale price of the pullover.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 3, Page 10
8. The Hibner family is on a trip to Germany. To better understand volume and distance in the metric system, use ratios to convert the measurements to the US customary system. a. Omi’s old-country recipe for hasenpfeffer calls for a liter of white vinegar. About how many quarts is that? Show your work.
b. It is 380 km from Prague to Munich. About how many miles is that? Show your work.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 3, Page 11
Grade 6 Unit 6 Constructed Response Rate and Ratio TASK 1: Word Problems using Unit Rates (MC: 6.RP.2, 3b; MP: 1, 2, 3, 4, 6, 7, 8) 1. The local market had a sale on fruit. These are their advertised prices. a. Which fruit has the lowest cost per pound? Explain how you know.
Fruit
Advertised Price
apples
3 lb/$1.80
tangerines
10 lb/$2.00
pears
2 lb/$1.50
grapes
4 lb/$3.20
watermelon
5 lb/$1.25
b. If you spent $1.00 on each kind of fruit, how many pounds of fruit would you buy? Explain how you know.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 1, Page 1
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c. What would it cost to buy 1 lb of apples, 3 lb of tangerines, 2 lb of 2 pears, 1 lb of grapes, and a 7-pound watermelon? Show your work.
2. Many of our family members drove from their hometowns to Las Vegas for a family reunion. Over dinner the first night, they compared their trips to see whose car has the best gas mileage. The miles the family members drove and the gallons of gas they used are listed in the table.
Family Member
Distance Driven (miles)
Great Uncle Emory Aunt Kathy Uncle Robert Mom Grandma Lou
576 294 276 434 405
Gas Used on the Drive to Las Vegas (gallons) 32 14 23 14 15
a. Whose car has the best gas mileage (went the farthest on one gallon of gas)? Explain how you found your answer.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 1, Page 2
b. Grandma Lou paid a unit price of $3.35 per gallon to fill up her gas tank before starting the trip. If she bought 17.2 gallons, how much did it cost?
c. It is 15 miles from Las Vegas to Henderson, where some of the family members want to visit an old friend. Both Great Uncle Emory and Uncle Robert will drive their own cars. Great Uncle Emory says his car will use less gas on the trip. Is he right? Explain.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 1, Page 3
Name: ________________________________________ Date:_______________
Grade 6 Unit 6 Constructed Response Rate and Ratio TASK 2: Word Problems using Equivalent Ratios (MC: 6.RP.1, 3a; MP: 1, 2, 4, 6, 7, 8) 3. Mrs. Frenza just went grocery shopping and filled the family’s fruit bowl. These are the fruits in the bowl.
a. What is the ratio of bananas to all fruits? Give your response as a ratio and in a complete sentence.
b. What is the ratio of oranges to apples? Give your response as a ratio and in a complete sentence.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 4
c. What is the ratio of apples to all other fruits? Give your response as a ratio and in a complete sentence.
d. Mr. Frenza was being helpful and also went to the grocery store for fruits. He came home with exactly the variety of fruits as his wife. If you had to answer questions a, b, and c again for all of the fruits together, would the ratios be equivalent? Explain.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 5
4. Mrs. Rush found this easy recipe in a magazine and decided she wanted to paint eggs with her twin boys.
Painted Eggs 12 hard-boiled eggs 1
a. She will mix four batches of Terrific Teal. Complete the table to find the number of drops of each color she will use.
Green
2
Blue
5
4
2
teaspoon of white vinegar food dye (see color mixes below)
Choose the color you want to make. Mix the vinegar and the food dye in a small bowl to get the desired color. Use a paintbrush to brush the color on the eggs. Popular Colors Dusty Pink: 14 drops red + 6 drops blue Deep Orange: 3 drops red + 17 drops yellow Energetic Yellow: 1 drop red + 45 drops yellow
b. She will mix five batches of Dusty Pink. Draw a double number line to find the number of drops of each color she will use.
Grass Green: 14 drops green + 6 drops yellow Terrific Teal: 2 drops green + 5 drops blue Purple Grape: 1 drop red + 7 drops blue
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 6
5. For every 3 eggs Ethan painted, Brian painted 5. a. If Brian painted 10 more eggs than Ethan, how many eggs did they paint altogether? Use a tape diagram or double number line to solve.
b. Explain how you solved the problem.
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c. Make a table of the equivalent ratios you found in Part A. Graph them on the coordinate grid. (Remember to include the scale labels and title.)
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 2, Page 8
Name: ________________________________________ Date:_______________
Grade 6 Unit 6 Constructed Response Rate and Ratio TASK 3: Word Problems with Percentage and Measurement Ratios (MC: 6.RP.3cd; MP: 1, 2, 4, 6, 7, 8) 6. A week ago, Darwin planted seeds in his garden. The table shows the number of seeds he planted and the number of seeds that have already sprouted. Seed Type Broccoli Cauliflower Pumpkin Radish Tomato
Number of Seeds Planted 8 10 4 6 12
Number of Seeds Sprouted 6 7 1 3 9
a. Which seed has the greatest percentage of sprouts? Explain how you know.
b. Overall, what percentage of all the seeds has sprouted?
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 3, Page 9
7. Filipe shopped for a new outfit and found these items on sale.
SALE! 15% off! khakis
SALE! 30% off! jeans
SALE! 25% off! pullover
SALE! 50% off! t-shirt
a. Which pair of pants has the greatest dollar discount? Explain how you know.
b. Draw a percentage bar to find the sale price of the pullover.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 3, Page 10
8. The Hibner family is on a trip to Germany. To better understand volume and distance in the metric system, use ratios to convert the measurements to the US customary system. a. Omi’s old-country recipe for hasenpfeffer calls for a liter of white vinegar. About how many quarts is that? Show your work.
b. It is 380 km from Prague to Munich. About how many miles is that? Show your work.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response, Task 3, Page 11
