G3 U7 Constructed Response Rubric
Grade 3 Unit 7 Constructed Response Two Step Word Problems Scoring Rubric Task
1. Addition and Subtraction Two Step Word Problems
2. Addition/ Subtraction/ Multiplication Two Step Word Problems
3. Addition/ Subtraction/ Division Two Step Word Problems
Common Core State Standard for Mathematical Content (MC) 3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) 3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) 3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)
Copyright © Swun Math Grade 3 Unit 7 Constructed Response Rubric, Page 1
Standards for Mathematical Practice (MP)
MP.1, MP.2, MP.4, MP.5, MP.7, MP.8
MP.1, MP.2, MP.4, MP.5, MP.7, MP.8
MP.1, MP.2, MP.4, MP.5, MP.7, MP.8
Grade 3 Unit 7 Constructed Response Two Step Word Problems Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked.
Scoring Rubric Question 1. a. Student gives correct answer: Jim has $575 saved. He earns $125 mowing lawns, so add 125. He spends $230 on his skiing trip, so subtract 230. b. Student gives correct answers: $575 +$125 - $230 = m; m = amount of money Jim has left in his savings c. Student gives correct answer and shows work using an accurate number line: (Check student’s number line for accuracy in the using strategy.); $470 Student gives an accurate explanation. Wording may vary. Sample explanation: 2. a. Student gives correct answer: 590 – 137 - 258 = s s=number of hours giving lessons in June b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the equation that best represents the situation I had to use several pieces of important information in the problem. I am told that in three months they spent 590 hours giving scuba diving lessons. I am also told in the month of May they spent 137 hours giving diving lessons, and in the month of July they spent 258 hours giving diving lessons. The month of June is unknown because they lost their time sheet, so my missing quantity is the hours they gave classes in June. Since I know the total hours they spent giving classes from the month of May to July, and I know the hours they gave classes in May and July, the best way to find the missing number of hours is to subtract these quantities. My equation would be the total hours minus the hours giving classes in May and minus the hours giving classes in July, or 590 – 137 – 258 = s. The difference between these quantities is the number of hours they gave classes in June. c. Student gives correct answer and shows work: 195 hours
Copyright © Swun Math Grade 3 Unit 7 Constructed Response Rubric, Page 2
Points 2
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Grade 3 Unit 7 Constructed Response Two Step Word Problems 3. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to solve this problem I first need to find the difference between the spools of blue yarn she has and the spools of pink yarn. I am told she has 7 spools of blue yarn and 12 spools of pink yarn and each has 6 yards in it. So I need to subtract 7 from 12 and multiply the difference by 6. The product of these two quantities is how many more yards of pink yarn she has than blue yarn. b. Student gives correct answers: (12 − 7) × 6 = 𝑦; y = how many more yards of pink yarn than blue yarn c. Student gives correct answer and shows work: 30 more yards of pink yarn than blue yarn 4. a. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: After analyzing Robby’s work, I determined his equation and his answer are both incorrect. His equation is incorrect because it does not represent the problem correctly. In his equation he adds up the total games he wants to buy and multiplies by the sum of the prices for new and pre-owned games. This is incorrect, mainly because the price of new and pre-owned games are not the same and there is no reason for the prices to be added. What he needed to do was first multiply the number of pre-owned he wants to purchase by the price of each preowned game, and then multiply the number of new games he wants to purchase by the price of each new game. His next step should have been to add these two quantities together to get the total for all the games. b. Student gives correct answers: ($15 x 3) + ($30 x 2) = g ; $105 5. a. Student gives correct answer: Juliana picks 64 apples. She decides to keep 19, so subtract 19. She places the left over apples in baskets that can hold 5 apples, so divide by 5. b. Student gives correct answers: (64 − 19) ÷ 5 = 𝑏; b= number of baskets c. Student gives correct answer and shows work using an accurate illustration: (Check student’s work in using the strategy); 9 baskets 6. a. Student gives correct answer: (64 + 56 + 48 + 24 + 96) ÷ 8 = 𝑘 ; k = number of kites sold b. Student gives an accurate explanation. Wording may vary. Sample explanation: Several pieces of information in the problem helped me to write the equation for this problem. In the table I am given the amount of money he made each day on kite sales, and in the passage I am told he sells each kite for $8. Based on this information I knew first I had to add up all the money he made from the kite sale during the week, so the first part Copyright © Swun Math Grade 3 Unit 7 Constructed Response Rubric, Page 3
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Grade 3 Unit 7 Constructed Response Two Step Word Problems of the equation needed to be 64 + 56 + 48 + 24 + 96. Since each kite has the same price of $8, I knew I had to divide the total profit he made from kite sales by 8 to find the number of kites sold. So my final equation was (64 + 56 + 48 + 24 + 96) ÷ 8 = 𝑘, where k equals the total number of kites he sold. c. Student gives correct answer and shows work: 36 kites 7. a. Student gives correct answer and shows work: 14 cupcakes each b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the solution to this problem, I had to use several pieces of information given to me. I am told Linda and her six cousins were in charge of making cupcakes at their bakery, so I know the total number of people working on the cupcakes is 7. I am also told each of the three orders was for 36 cupcakes. But in order to make the thirty-six cupcakes for each order 10 more will be needed. This piece of information meant that if each of them made an equal amount they would be short 10 cupcakes. So to start figuring out how many cupcakes they each made, the first thing I needed to find was the total number of cupcakes needed for the three orders. To do this I multiplied 36 by 3 which was equal to 108. However, since Linda’s mother needs to make ten more cupcakes to equal this amount, I needed to subtract ten from 108 to find out how many cupcakes Linda and her cousins actually made. This number was 98. The next step was to find how many cupcakes each person made, and to do this I divided 98 by 7 and got 14. So Linda and her cousins each made 14 cupcakes. Total
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1. Addition and Subtraction Two Step Word Problems
2. Addition/ Subtraction/ Multiplication Two Step Word Problems
3. Addition/ Subtraction/ Division Two Step Word Problems
Common Core State Standard for Mathematical Content (MC) 3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) 3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) 3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)
Copyright © Swun Math Grade 3 Unit 7 Constructed Response Rubric, Page 1
Standards for Mathematical Practice (MP)
MP.1, MP.2, MP.4, MP.5, MP.7, MP.8
MP.1, MP.2, MP.4, MP.5, MP.7, MP.8
MP.1, MP.2, MP.4, MP.5, MP.7, MP.8
Grade 3 Unit 7 Constructed Response Two Step Word Problems Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked.
Scoring Rubric Question 1. a. Student gives correct answer: Jim has $575 saved. He earns $125 mowing lawns, so add 125. He spends $230 on his skiing trip, so subtract 230. b. Student gives correct answers: $575 +$125 - $230 = m; m = amount of money Jim has left in his savings c. Student gives correct answer and shows work using an accurate number line: (Check student’s number line for accuracy in the using strategy.); $470 Student gives an accurate explanation. Wording may vary. Sample explanation: 2. a. Student gives correct answer: 590 – 137 - 258 = s s=number of hours giving lessons in June b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the equation that best represents the situation I had to use several pieces of important information in the problem. I am told that in three months they spent 590 hours giving scuba diving lessons. I am also told in the month of May they spent 137 hours giving diving lessons, and in the month of July they spent 258 hours giving diving lessons. The month of June is unknown because they lost their time sheet, so my missing quantity is the hours they gave classes in June. Since I know the total hours they spent giving classes from the month of May to July, and I know the hours they gave classes in May and July, the best way to find the missing number of hours is to subtract these quantities. My equation would be the total hours minus the hours giving classes in May and minus the hours giving classes in July, or 590 – 137 – 258 = s. The difference between these quantities is the number of hours they gave classes in June. c. Student gives correct answer and shows work: 195 hours
Copyright © Swun Math Grade 3 Unit 7 Constructed Response Rubric, Page 2
Points 2
1 2
1 2
1
Total
Grade 3 Unit 7 Constructed Response Two Step Word Problems 3. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to solve this problem I first need to find the difference between the spools of blue yarn she has and the spools of pink yarn. I am told she has 7 spools of blue yarn and 12 spools of pink yarn and each has 6 yards in it. So I need to subtract 7 from 12 and multiply the difference by 6. The product of these two quantities is how many more yards of pink yarn she has than blue yarn. b. Student gives correct answers: (12 − 7) × 6 = 𝑦; y = how many more yards of pink yarn than blue yarn c. Student gives correct answer and shows work: 30 more yards of pink yarn than blue yarn 4. a. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: After analyzing Robby’s work, I determined his equation and his answer are both incorrect. His equation is incorrect because it does not represent the problem correctly. In his equation he adds up the total games he wants to buy and multiplies by the sum of the prices for new and pre-owned games. This is incorrect, mainly because the price of new and pre-owned games are not the same and there is no reason for the prices to be added. What he needed to do was first multiply the number of pre-owned he wants to purchase by the price of each preowned game, and then multiply the number of new games he wants to purchase by the price of each new game. His next step should have been to add these two quantities together to get the total for all the games. b. Student gives correct answers: ($15 x 3) + ($30 x 2) = g ; $105 5. a. Student gives correct answer: Juliana picks 64 apples. She decides to keep 19, so subtract 19. She places the left over apples in baskets that can hold 5 apples, so divide by 5. b. Student gives correct answers: (64 − 19) ÷ 5 = 𝑏; b= number of baskets c. Student gives correct answer and shows work using an accurate illustration: (Check student’s work in using the strategy); 9 baskets 6. a. Student gives correct answer: (64 + 56 + 48 + 24 + 96) ÷ 8 = 𝑘 ; k = number of kites sold b. Student gives an accurate explanation. Wording may vary. Sample explanation: Several pieces of information in the problem helped me to write the equation for this problem. In the table I am given the amount of money he made each day on kite sales, and in the passage I am told he sells each kite for $8. Based on this information I knew first I had to add up all the money he made from the kite sale during the week, so the first part Copyright © Swun Math Grade 3 Unit 7 Constructed Response Rubric, Page 3
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Grade 3 Unit 7 Constructed Response Two Step Word Problems of the equation needed to be 64 + 56 + 48 + 24 + 96. Since each kite has the same price of $8, I knew I had to divide the total profit he made from kite sales by 8 to find the number of kites sold. So my final equation was (64 + 56 + 48 + 24 + 96) ÷ 8 = 𝑘, where k equals the total number of kites he sold. c. Student gives correct answer and shows work: 36 kites 7. a. Student gives correct answer and shows work: 14 cupcakes each b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the solution to this problem, I had to use several pieces of information given to me. I am told Linda and her six cousins were in charge of making cupcakes at their bakery, so I know the total number of people working on the cupcakes is 7. I am also told each of the three orders was for 36 cupcakes. But in order to make the thirty-six cupcakes for each order 10 more will be needed. This piece of information meant that if each of them made an equal amount they would be short 10 cupcakes. So to start figuring out how many cupcakes they each made, the first thing I needed to find was the total number of cupcakes needed for the three orders. To do this I multiplied 36 by 3 which was equal to 108. However, since Linda’s mother needs to make ten more cupcakes to equal this amount, I needed to subtract ten from 108 to find out how many cupcakes Linda and her cousins actually made. This number was 98. The next step was to find how many cupcakes each person made, and to do this I divided 98 by 7 and got 14. So Linda and her cousins each made 14 cupcakes. Total
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