G3 U1 Constructed Response Rubric
Grade 3 Unit 1 Constructed Response Understanding Division Scoring Rubric Task
Common Core State Standard
Standards for Mathematical Practice
1. Rounding to the Nearest 10 or 100
3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
SMP.1, SMP.3, SMP.5, SMP.6, SMP.7
2. Addition and Subtraction within 1000
3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100. 3.NBT.2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
SMP.2, SMP.4, SMP.5, SMP.6, SMP.8,
3. Multiply Multiples of 10
3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10 – 90 using strategies based on place value and properties of operations.
SMP.1, SMP.2, SMP.4, SMP.5, SMP.7, SMP.8
Note to Teacher: The following scoring rubric should be used as a guide to determine student points 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.
Copyright © Swun Math Grade 3 Unit 1 Constructed Response Rubric, Page 1
Grade 3 Unit 1 Constructed Response Understanding Division Scoring Rubric Question 1. a. Student gives explanation: A math tool I could use to solve this problem would be a number line. To solve this problem using a number line I would first need to identify two possible answers for the problem, and write them at the beginning and end of the number line. My next step would be to record where the number falls between the two possible answers. With these three numbers recorded on the number line I would need to decide whether the original number from the problem should be rounded up or down based on where it falls between the possible answers. b. Student draws number line and gives correct answr: 800
Points 0.5
0.5
778
700
800
2. a. Student gives correct answer and explanation: After reviewing both answers I was able to determine that Regina’s answer is correct. I know that her answer is correct because when you round 697 to the nearest ten, the number in the place value that needs to be rounded up is nine because the value of the number in the ones place is greater than 5. Since nine needs to round up to 10 it carries over into the hundreds place which raises the value of the 6 in that spot to a 7. This makes the new number 700, which makes sense because 697 is closer to 700. Samantha’s answer is incorrect because she rounded up the 9 in the tens place to 10 but she wrote the whole number in her answer (610).
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3. a. Student completes table: Cyclist Original Time (min) New Time (min) 1 79 80 2 83 80 3 90 90 4 78 80 5 86 90 6 89 90 b. Student gives explanation: Bella’s strategy was not effective in determining the place of each cyclist in the race. By rounding down the times she put cyclist 1, 2, and 4 tied for first place and cyclist 3, 4, and 5 tied
1
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Total
Grade 3 Unit 1 Constructed Response Understanding Division for second place. This makes Bella’s strategy very ineffective because the results need to be more accurate down to the minute, so 1st, 2nd, 3rd, 4th, 5th, and 6th place can be determined. 4. a. Student gives correct answer: 289 + x = 635 b. Student gives correct answer and shows work: 346 candles c. Student gives explanation: I know that my solution is reasonable because I can check my answer. To do this I can add my answer to the total candles sold during week 1. This would be 289 + 346 which is equal to 635. This is the total number of candles sold as stated in the problem, so I know that the number of candles I found for week 2 is correct. 5. a. Student gives correct explanation and shows work: After working out this problem, I was able to determine that Ruby does have enough money to buy all of the items. I know this because I estimated the price of each item, so the hat cost about $20, the snow jacket $80, the snow boots $70, and the glove $20. When I added these prices together the total came out to $190. Since Ruby has $200 to spend, she does not have enough to buy all 4 items. b. Student gives explanation and answer: After analyzing my answer, I was able to determine that Ruby has enough money to buy one more item. Since she is already spending $190 on the items she needs and she has $200 total that leaves her with $10 left to spend. That is enough money for her to also buy a pair of wool socks that cost $10. 6. a. 562 + 253 = 253 + 562 True Explanation: This answer is true because when I solved both sides of the equation I found that the sum of each side was 715. b. 279 – 215 = 215 - 279 False Explanation: This answer is false because when I solved both sides of the equation I found that the difference of each side was not equal. The left hand side of the equation is equal to 64, and the right hand side of the equation is equal to -50; therefore, the equation is false because 50 is not equal to -50. c. 865 – 210 = 395 + 260 True Explanation: The answer is true because both sides of the equation are equal to 655. I know this because when I found the difference of the left side of the equation I found the answer to be 655. When I did the opposite operation on the right side of the equation I also got an answer of 655. d. 354 + 125 = 125 + 275 False Explanation: The answer is false because both sides of the equation are not equal. When I found the sum of the left side of the equation to be 479, Copyright © Swun Math Grade 3 Unit 1 Constructed Response Rubric, Page 3
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Grade 3 Unit 1 Constructed Response Understanding Division and the sum of the right side of the equation was 400. Since the sums of both sides of the equation were not equal, the equation is false. 7. a. Student gives correct answer and shows work: These two sentences represent the same quantity. I know this because the number of groups in each is the same, and the number 90 is equal to 9 tens. b. Student creates illustration: 3 x 90 = X c. Student gives correct answer and illustration:
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0.25 0.50
3 x 90 = 270
8. a. Student gives correct answers: 30 x 3 = 90; 30 x 4 = 120; 30 x 5 =
150; 30 x 6 = 180; 30 x 7 = 210
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b. Student gives explanation: The pattern I noticed in each product was that they increased by 30 or 3 tens as I multiplied by each increasing number. 9. a. Student gives the correct answer and shows work: After reading the passage, I was able to determine that this problem involves working with multiplication and multiples of ten. In this problem I am told that the children are placed into groups labeled from A-H, so that means each group is assigned a letter A, B, C, D, E, F, G, or H. This is a total of 8 groups. I am also told that there are 20 kids per group. With this information I know that to find the total number of children at camp I need to multiply 8 groups by 20. b. Student gives correct answer and shows work: 160 children at camp c. Student creates illustration:
0.5 0.5
Test Total
15
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Common Core State Standard
Standards for Mathematical Practice
1. Rounding to the Nearest 10 or 100
3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
SMP.1, SMP.3, SMP.5, SMP.6, SMP.7
2. Addition and Subtraction within 1000
3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100. 3.NBT.2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
SMP.2, SMP.4, SMP.5, SMP.6, SMP.8,
3. Multiply Multiples of 10
3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10 – 90 using strategies based on place value and properties of operations.
SMP.1, SMP.2, SMP.4, SMP.5, SMP.7, SMP.8
Note to Teacher: The following scoring rubric should be used as a guide to determine student points 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.
Copyright © Swun Math Grade 3 Unit 1 Constructed Response Rubric, Page 1
Grade 3 Unit 1 Constructed Response Understanding Division Scoring Rubric Question 1. a. Student gives explanation: A math tool I could use to solve this problem would be a number line. To solve this problem using a number line I would first need to identify two possible answers for the problem, and write them at the beginning and end of the number line. My next step would be to record where the number falls between the two possible answers. With these three numbers recorded on the number line I would need to decide whether the original number from the problem should be rounded up or down based on where it falls between the possible answers. b. Student draws number line and gives correct answr: 800
Points 0.5
0.5
778
700
800
2. a. Student gives correct answer and explanation: After reviewing both answers I was able to determine that Regina’s answer is correct. I know that her answer is correct because when you round 697 to the nearest ten, the number in the place value that needs to be rounded up is nine because the value of the number in the ones place is greater than 5. Since nine needs to round up to 10 it carries over into the hundreds place which raises the value of the 6 in that spot to a 7. This makes the new number 700, which makes sense because 697 is closer to 700. Samantha’s answer is incorrect because she rounded up the 9 in the tens place to 10 but she wrote the whole number in her answer (610).
2
3. a. Student completes table: Cyclist Original Time (min) New Time (min) 1 79 80 2 83 80 3 90 90 4 78 80 5 86 90 6 89 90 b. Student gives explanation: Bella’s strategy was not effective in determining the place of each cyclist in the race. By rounding down the times she put cyclist 1, 2, and 4 tied for first place and cyclist 3, 4, and 5 tied
1
Copyright © Swun Math Grade 3 Unit 1 Constructed Response Rubric, Page 2
1
Total
Grade 3 Unit 1 Constructed Response Understanding Division for second place. This makes Bella’s strategy very ineffective because the results need to be more accurate down to the minute, so 1st, 2nd, 3rd, 4th, 5th, and 6th place can be determined. 4. a. Student gives correct answer: 289 + x = 635 b. Student gives correct answer and shows work: 346 candles c. Student gives explanation: I know that my solution is reasonable because I can check my answer. To do this I can add my answer to the total candles sold during week 1. This would be 289 + 346 which is equal to 635. This is the total number of candles sold as stated in the problem, so I know that the number of candles I found for week 2 is correct. 5. a. Student gives correct explanation and shows work: After working out this problem, I was able to determine that Ruby does have enough money to buy all of the items. I know this because I estimated the price of each item, so the hat cost about $20, the snow jacket $80, the snow boots $70, and the glove $20. When I added these prices together the total came out to $190. Since Ruby has $200 to spend, she does not have enough to buy all 4 items. b. Student gives explanation and answer: After analyzing my answer, I was able to determine that Ruby has enough money to buy one more item. Since she is already spending $190 on the items she needs and she has $200 total that leaves her with $10 left to spend. That is enough money for her to also buy a pair of wool socks that cost $10. 6. a. 562 + 253 = 253 + 562 True Explanation: This answer is true because when I solved both sides of the equation I found that the sum of each side was 715. b. 279 – 215 = 215 - 279 False Explanation: This answer is false because when I solved both sides of the equation I found that the difference of each side was not equal. The left hand side of the equation is equal to 64, and the right hand side of the equation is equal to -50; therefore, the equation is false because 50 is not equal to -50. c. 865 – 210 = 395 + 260 True Explanation: The answer is true because both sides of the equation are equal to 655. I know this because when I found the difference of the left side of the equation I found the answer to be 655. When I did the opposite operation on the right side of the equation I also got an answer of 655. d. 354 + 125 = 125 + 275 False Explanation: The answer is false because both sides of the equation are not equal. When I found the sum of the left side of the equation to be 479, Copyright © Swun Math Grade 3 Unit 1 Constructed Response Rubric, Page 3
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Grade 3 Unit 1 Constructed Response Understanding Division and the sum of the right side of the equation was 400. Since the sums of both sides of the equation were not equal, the equation is false. 7. a. Student gives correct answer and shows work: These two sentences represent the same quantity. I know this because the number of groups in each is the same, and the number 90 is equal to 9 tens. b. Student creates illustration: 3 x 90 = X c. Student gives correct answer and illustration:
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0.25 0.50
3 x 90 = 270
8. a. Student gives correct answers: 30 x 3 = 90; 30 x 4 = 120; 30 x 5 =
150; 30 x 6 = 180; 30 x 7 = 210
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b. Student gives explanation: The pattern I noticed in each product was that they increased by 30 or 3 tens as I multiplied by each increasing number. 9. a. Student gives the correct answer and shows work: After reading the passage, I was able to determine that this problem involves working with multiplication and multiples of ten. In this problem I am told that the children are placed into groups labeled from A-H, so that means each group is assigned a letter A, B, C, D, E, F, G, or H. This is a total of 8 groups. I am also told that there are 20 kids per group. With this information I know that to find the total number of children at camp I need to multiply 8 groups by 20. b. Student gives correct answer and shows work: 160 children at camp c. Student creates illustration:
0.5 0.5
Test Total
15
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