G6 U1 Constructed Response
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions TASK 1: GCF, LCM, and Ordering/Comparing Decimals (CCSS 6.NS.3, 6.NS.4, 6.NS.5; SMP 1, 2, 3, 4, 6, 8)
1. Chelsea and her friends are making small fruit baskets for their neighborhood. They have 90 pears, 45 peaches, and 75 apples. What is the greatest number of baskets they can make if each basket has the same number of contents? a. Explain what the meaning of the problem is and describe a starting point for solving this problem. Are there any math tools you could use in this situation?
b. Using your strategy, find the greatest number of baskets Chelsea and her friends can make. Show your work.
Answer: _____________________
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 1
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 2. Troy needs to rent tables and table covers for a birthday party, and he needs to have the same number of both. The company he is renting from has packages of 12 tables, and packages of 18 table covers. a. What is the least possible number of tables and table covers he needs to rent to have equal amounts of both at the birthday party? Show your work.
Answer: ____________________ b. What mathematical operation was important when solving this problem? How did you decide that this operation was appropriate to use in this situation?
c. How was the process for finding your solution in Question 1b similar and different to the process you used in Question 2a? Explain your reasoning.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 2
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 3. Five swimmers entered a competition. Four of the swimmers have already competed. The table shown below lists the time for each swimmer. Swimmer Number 1
Time (seconds) 9.15
2
9.17
3
9.25
4
9.10
5 a. Put the swimmer’s times in order from fastest to slowest. Answer: __________________________________________ b. What time must the fifth swimmer beat in order to win the race? What time must he beat to qualify in fourth place?
c. If swimmer 2 had gotten a time of 9.45 seconds how would this have changed the results?
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 3
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions TASK 2: Add, Subtract, and Multiply Decimals (CCSS: 6.NS.3; SMP: 1, 2, 3, 4, 6, 8)
4. Fulton is buying supplies for a hike with his friends. He has $110 to spend on his supplies. He needs to buy a water bottle, sun hat, and hiking boots. The table below shows the prices for each item at a local sporting goods store. Item Hiking Boots Water Bottle Backpack Hiking Socks Sun Hat Sunblock Sunglasses
Price $65.75 $12.36 $35.15 $9.86 $16.25 $4.75 $18.85
a. How much money will Fulton be spending on the three items? Show your work.
Answer: _____________________ b. With his left over money, would he be able to purchase more items? If so, what other items could he purchase?
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 4
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 5. Corey and his brother Sam are practicing discus throwing for track and field. The table below shows the distances each brother reached per throw. Throw 1 2
Corey 39.45 feet 43.86 feet
Sam 42.51 feet 40.34 feet
a. What is the total distance each brother reached for both throws? Show your work.
Answer: Corey _____________________ Sam _____________________ b. Based on your answers, determine which brother threw the farthest. Explain your reasoning.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 5
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions c. Determine how much farther the brother you identified threw the discus. Show your work.
Answer: ___________________ 6. Monica and her family take a trip to the zoo for her 10th birthday. She goes with her mom, dad, grandma, and her younger brother and sister. a. Each adult ticket cost $19.50 and each child’s ticket cost $14.50. How much money did they spend total on all the tickets. Show your work.
Answer: ________________________ b. At lunchtime, they buy kids meals for Monica and her brother and sister for $7.67 each, and regular meals for the adults for $9.86 each, plus drinks for each person for $2.75 each. How much money did they spend on food and drinks? Show your work.
Answer: ______________________ Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 6
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions c. What operations did you use for each part of this problem? How did you use them?
d. What did the family spend the most money on during this trip to the zoo? Explain your reasoning.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 7
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions TASK 3: Division of Whole Numbers, Decimals and Fractions (CCSS: 6.NS.1, 6.NS.2, 6..NS.3; SMP: 1, 3, 4, 5, 6, 8 )
7. Neil and Christian are training for a half marathon. They can both run a mile in an average time of 7.3 minute. a. With this average, how many miles would they run in 42 minutes? Show your work and round your answer to the nearest hundredth.
Answer: ____________________ b. What mathematical operation was important when solving this problem? How did you decide that this operation was appropriate to use in this situation?
Answer: _____________________________
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 8
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 8. Georgia, Christie, and Patricia are making bows for their rooms. Each bow 1 1 will require yard of ribbon. Each of the girls brought yard of ribbon to help 8 4 make the bows. a. How much ribbon do they have combined? Show you work.
Answer: ______________________ b. Determine how many bows they can make with the total yards of ribbon they have. Show your work.
Answer: ______________________ c. Construct a model to prove that your answer is correct and explain how your model proves that you are correct.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 9
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 9. A soccer club is selling cookie dough tubs to help raise money for new practice equipment. They have 9,360 tubs of cookie dough to sell. a. If there are 60 teams in the club, how many tubs of cookie dough does each team have to sell? Show your work.
Answer: ______________________ b. If there are 13 players on each team, how many cookie dough tubs does each player have to sell?
Answer: ______________________ c. Looking back at your answers for part A and part B, explain how you could prove that each of your answers is correct.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 10
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions d. Using the strategy you explained above, prove that your answers are correct.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 11
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions TASK 1: GCF, LCM, and Ordering/Comparing Decimals (CCSS 6.NS.3, 6.NS.4, 6.NS.5; SMP 1, 2, 3, 4, 6, 8)
1. Chelsea and her friends are making small fruit baskets for their neighborhood. They have 90 pears, 45 peaches, and 75 apples. What is the greatest number of baskets they can make if each basket has the same number of contents? a. Explain what the meaning of the problem is and describe a starting point for solving this problem. Are there any math tools you could use in this situation?
b. Using your strategy, find the greatest number of baskets Chelsea and her friends can make. Show your work.
Answer: _____________________
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 1
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 2. Troy needs to rent tables and table covers for a birthday party, and he needs to have the same number of both. The company he is renting from has packages of 12 tables, and packages of 18 table covers. a. What is the least possible number of tables and table covers he needs to rent to have equal amounts of both at the birthday party? Show your work.
Answer: ____________________ b. What mathematical operation was important when solving this problem? How did you decide that this operation was appropriate to use in this situation?
c. How was the process for finding your solution in Question 1b similar and different to the process you used in Question 2a? Explain your reasoning.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 2
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 3. Five swimmers entered a competition. Four of the swimmers have already competed. The table shown below lists the time for each swimmer. Swimmer Number 1
Time (seconds) 9.15
2
9.17
3
9.25
4
9.10
5 a. Put the swimmer’s times in order from fastest to slowest. Answer: __________________________________________ b. What time must the fifth swimmer beat in order to win the race? What time must he beat to qualify in fourth place?
c. If swimmer 2 had gotten a time of 9.45 seconds how would this have changed the results?
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 3
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions TASK 2: Add, Subtract, and Multiply Decimals (CCSS: 6.NS.3; SMP: 1, 2, 3, 4, 6, 8)
4. Fulton is buying supplies for a hike with his friends. He has $110 to spend on his supplies. He needs to buy a water bottle, sun hat, and hiking boots. The table below shows the prices for each item at a local sporting goods store. Item Hiking Boots Water Bottle Backpack Hiking Socks Sun Hat Sunblock Sunglasses
Price $65.75 $12.36 $35.15 $9.86 $16.25 $4.75 $18.85
a. How much money will Fulton be spending on the three items? Show your work.
Answer: _____________________ b. With his left over money, would he be able to purchase more items? If so, what other items could he purchase?
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 4
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 5. Corey and his brother Sam are practicing discus throwing for track and field. The table below shows the distances each brother reached per throw. Throw 1 2
Corey 39.45 feet 43.86 feet
Sam 42.51 feet 40.34 feet
a. What is the total distance each brother reached for both throws? Show your work.
Answer: Corey _____________________ Sam _____________________ b. Based on your answers, determine which brother threw the farthest. Explain your reasoning.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 5
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions c. Determine how much farther the brother you identified threw the discus. Show your work.
Answer: ___________________ 6. Monica and her family take a trip to the zoo for her 10th birthday. She goes with her mom, dad, grandma, and her younger brother and sister. a. Each adult ticket cost $19.50 and each child’s ticket cost $14.50. How much money did they spend total on all the tickets. Show your work.
Answer: ________________________ b. At lunchtime, they buy kids meals for Monica and her brother and sister for $7.67 each, and regular meals for the adults for $9.86 each, plus drinks for each person for $2.75 each. How much money did they spend on food and drinks? Show your work.
Answer: ______________________ Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 6
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions c. What operations did you use for each part of this problem? How did you use them?
d. What did the family spend the most money on during this trip to the zoo? Explain your reasoning.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 7
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions TASK 3: Division of Whole Numbers, Decimals and Fractions (CCSS: 6.NS.1, 6.NS.2, 6..NS.3; SMP: 1, 3, 4, 5, 6, 8 )
7. Neil and Christian are training for a half marathon. They can both run a mile in an average time of 7.3 minute. a. With this average, how many miles would they run in 42 minutes? Show your work and round your answer to the nearest hundredth.
Answer: ____________________ b. What mathematical operation was important when solving this problem? How did you decide that this operation was appropriate to use in this situation?
Answer: _____________________________
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 8
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 8. Georgia, Christie, and Patricia are making bows for their rooms. Each bow 1 1 will require yard of ribbon. Each of the girls brought yard of ribbon to help 8 4 make the bows. a. How much ribbon do they have combined? Show you work.
Answer: ______________________ b. Determine how many bows they can make with the total yards of ribbon they have. Show your work.
Answer: ______________________ c. Construct a model to prove that your answer is correct and explain how your model proves that you are correct.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 9
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions 9. A soccer club is selling cookie dough tubs to help raise money for new practice equipment. They have 9,360 tubs of cookie dough to sell. a. If there are 60 teams in the club, how many tubs of cookie dough does each team have to sell? Show your work.
Answer: ______________________ b. If there are 13 players on each team, how many cookie dough tubs does each player have to sell?
Answer: ______________________ c. Looking back at your answers for part A and part B, explain how you could prove that each of your answers is correct.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 10
Name: ________________________________________ Date:_______________
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions d. Using the strategy you explained above, prove that your answers are correct.
Copyright © Swun Math Grade 6 Unit 1 Constructed Response, Page 11
