G3 U8 Constructed Response Rubric
Grade 3 Unit 8 Constructed Response Identifying Patterns Scoring Rubric Task
Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
1. Patterns on an Addition Table, and a Hundreds Chart
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
MP.1, MP.2, MP.3, MP.6, MP.7
2. Patterns on a Multiplication Table
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
MP.1, MP.2, MP.6, MP.7
3. Finding Patterns Using In and Out Tables, Finding Patterns to Solve Word Problems
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
MP.1, MP.2, MP.4, MP.6, MP.7
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.
Copyright © Swun Math Grade 3 Unit 8 Constructed Response Rubric, Page 1
Grade 3 Unit 8 Constructed Response Identifying Patterns Scoring Rubric Question 1. a. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: When two even numbers are added together you get an even number. The reason this happens is because the ones digit in the sum can be shared equally. For example, when you add 4 plus 8 you get an even sum of 12. Another example would be when you add 2 plus 6 you get an even sum of 8. b. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: When an even number and an odd number are added together you get an odd number. The reason this happens is because the ones digit in the sum cannot be shared equally. For example, when you add 7 plus 4 you get an odd sum of 11. Another example would be when you add 9 and 6 you get an odd sum of 15. 2. a. Student gives correct answers: 47, 51, 55, 59 b. Student gives an accurate explanation. Wording may vary. Sample explanation: The pattern present in the number set I completed is that each number is four more than the previous number in the set. So to each number I had to add four. I observed that each number in the pattern is an odd number which is a result of adding the even number four to each odd number in the pattern. 3. a. Student gives correct answers: 55, 40, 22, 1 b. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: The rule present in the pattern I completed is each number is subtracted by a multiple of 3. So each number is subtracted by 3, 6, 9, 12, and so on. For example, the first number in the pattern, 85, is subtracted by three to get the second number 82. And then 82 is subtracted by 6 to get the next number in the pattern 76. 4. a. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: When two odd numbers are multiplied together you get an odd number. The reason this happens is because the ones digit in the product cannot be shared equally. For example, when you multiply 9 by 3 you get an odd product of 27. Another example would be when you multiply 3 by 5 you get an odd product of 15. b. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: When an even number and an odd number Copyright © Swun Math Grade 3 Unit 8 Constructed Response Rubric, Page 2
Points 2
2
1 2
1 2
2
2
Total
Grade 3 Unit 8 Constructed Response Identifying Patterns are multiplied together you get an even number. The reason this happens is because the ones digit in the product can be shared equally. For example, when you multiply 6 by 9 you get an even product of 54. Another example would be when you multiply 3 and 8 you get an even product of 24.
5. a. Student gives correct answers: 18, 21 and 27, 30 b. Student gives an accurate explanation. Wording may vary. Sample explanation: The multiplication table helped me find the missing numbers in the pattern because once I identified the rule that represented the problem, I used the table to identify the next factors in the pattern. In this case I noticed 3 was added to each number in the pattern, so I knew these numbers were multiples of three. With this information I was able to go to the table to find what the next numbers would be. In this case the missing numbers I was looking for were the products of 6 × 3, and 7 × 3 for the first missing numbers and then the products of 9 × 3, and 10 × 3 for the second missing numbers in the pattern.
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6. a. Student gives correct answer: 18 b. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: The rule that best represents the pattern in this scenario is the numbers are increased by 3, so +3. I know this is the rule because I am told Brad makes 3 goals the first week, 6 goals the second week, and 9 goals the third week. As can be seen, each number increases by three, so if he continues this pattern each week he will make three more goals than the previous week.
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7. a. Student gives an accurate explanation. Wording may vary. Sample explanation: The rule that best represents the pattern in the table is the numbers are increased by 12, so +12. I know this is the rule because I am given an In value of 8 and an Out value of 20 in the table, and the difference between the two is twelve. The same happens with the In value of 24 and the Out value of 36; the difference between the two is 12. So the rule is 12 is added to each In value to get the Out value. b. Student gives correct answer and shows work: 16 and 44
2
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Grade 3 Unit 8 Constructed Response Identifying Patterns 8. a. Student gives an accurate explanation. Wording may vary. Sample explanation: The problem is asking me to find the number of pages she will read after four weeks, and the number of pages she should read per week, if she doubles the amount of pages she reads per week. I am told she reads 16 pages the first week and she wants to double the amount of pages she reads every week. So this means in the second week she needs to read twice as much as the first week, the third week she needs to read twice as much as the second week and finally the fourth week she needs to read twice as much as the third. Each value represents how much she needs to read each week. Then to find how many pages she has read total I need to add up all these weekly pages. Student gives correct answers: 240 pages, Week 1= 16, Week 2= 32, Week 3= 64, Week 4= 128; Rule: × 2
2
9. a. Student accurately creates In and Out table to represent the data in the table: In Out $75 15 $60 12 $90 18 b. Student gives correct answer: $5 per pie c. Student gives an accurate explanation. Wording may vary. Sample explanation: The selling price of the pies Trish sells represents the rule of the pattern found in her weekly sales. Unless she changes the price of her pies, you could take her total profit and divide it by 5 to find the total number pies she sold to make that money. Total
1
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Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
1. Patterns on an Addition Table, and a Hundreds Chart
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
MP.1, MP.2, MP.3, MP.6, MP.7
2. Patterns on a Multiplication Table
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
MP.1, MP.2, MP.6, MP.7
3. Finding Patterns Using In and Out Tables, Finding Patterns to Solve Word Problems
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
MP.1, MP.2, MP.4, MP.6, MP.7
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.
Copyright © Swun Math Grade 3 Unit 8 Constructed Response Rubric, Page 1
Grade 3 Unit 8 Constructed Response Identifying Patterns Scoring Rubric Question 1. a. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: When two even numbers are added together you get an even number. The reason this happens is because the ones digit in the sum can be shared equally. For example, when you add 4 plus 8 you get an even sum of 12. Another example would be when you add 2 plus 6 you get an even sum of 8. b. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: When an even number and an odd number are added together you get an odd number. The reason this happens is because the ones digit in the sum cannot be shared equally. For example, when you add 7 plus 4 you get an odd sum of 11. Another example would be when you add 9 and 6 you get an odd sum of 15. 2. a. Student gives correct answers: 47, 51, 55, 59 b. Student gives an accurate explanation. Wording may vary. Sample explanation: The pattern present in the number set I completed is that each number is four more than the previous number in the set. So to each number I had to add four. I observed that each number in the pattern is an odd number which is a result of adding the even number four to each odd number in the pattern. 3. a. Student gives correct answers: 55, 40, 22, 1 b. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: The rule present in the pattern I completed is each number is subtracted by a multiple of 3. So each number is subtracted by 3, 6, 9, 12, and so on. For example, the first number in the pattern, 85, is subtracted by three to get the second number 82. And then 82 is subtracted by 6 to get the next number in the pattern 76. 4. a. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: When two odd numbers are multiplied together you get an odd number. The reason this happens is because the ones digit in the product cannot be shared equally. For example, when you multiply 9 by 3 you get an odd product of 27. Another example would be when you multiply 3 by 5 you get an odd product of 15. b. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: When an even number and an odd number Copyright © Swun Math Grade 3 Unit 8 Constructed Response Rubric, Page 2
Points 2
2
1 2
1 2
2
2
Total
Grade 3 Unit 8 Constructed Response Identifying Patterns are multiplied together you get an even number. The reason this happens is because the ones digit in the product can be shared equally. For example, when you multiply 6 by 9 you get an even product of 54. Another example would be when you multiply 3 and 8 you get an even product of 24.
5. a. Student gives correct answers: 18, 21 and 27, 30 b. Student gives an accurate explanation. Wording may vary. Sample explanation: The multiplication table helped me find the missing numbers in the pattern because once I identified the rule that represented the problem, I used the table to identify the next factors in the pattern. In this case I noticed 3 was added to each number in the pattern, so I knew these numbers were multiples of three. With this information I was able to go to the table to find what the next numbers would be. In this case the missing numbers I was looking for were the products of 6 × 3, and 7 × 3 for the first missing numbers and then the products of 9 × 3, and 10 × 3 for the second missing numbers in the pattern.
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6. a. Student gives correct answer: 18 b. Student gives correct answer and accurate explanation. Wording may vary. Sample explanation: The rule that best represents the pattern in this scenario is the numbers are increased by 3, so +3. I know this is the rule because I am told Brad makes 3 goals the first week, 6 goals the second week, and 9 goals the third week. As can be seen, each number increases by three, so if he continues this pattern each week he will make three more goals than the previous week.
1 2
7. a. Student gives an accurate explanation. Wording may vary. Sample explanation: The rule that best represents the pattern in the table is the numbers are increased by 12, so +12. I know this is the rule because I am given an In value of 8 and an Out value of 20 in the table, and the difference between the two is twelve. The same happens with the In value of 24 and the Out value of 36; the difference between the two is 12. So the rule is 12 is added to each In value to get the Out value. b. Student gives correct answer and shows work: 16 and 44
2
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Grade 3 Unit 8 Constructed Response Identifying Patterns 8. a. Student gives an accurate explanation. Wording may vary. Sample explanation: The problem is asking me to find the number of pages she will read after four weeks, and the number of pages she should read per week, if she doubles the amount of pages she reads per week. I am told she reads 16 pages the first week and she wants to double the amount of pages she reads every week. So this means in the second week she needs to read twice as much as the first week, the third week she needs to read twice as much as the second week and finally the fourth week she needs to read twice as much as the third. Each value represents how much she needs to read each week. Then to find how many pages she has read total I need to add up all these weekly pages. Student gives correct answers: 240 pages, Week 1= 16, Week 2= 32, Week 3= 64, Week 4= 128; Rule: × 2
2
9. a. Student accurately creates In and Out table to represent the data in the table: In Out $75 15 $60 12 $90 18 b. Student gives correct answer: $5 per pie c. Student gives an accurate explanation. Wording may vary. Sample explanation: The selling price of the pies Trish sells represents the rule of the pattern found in her weekly sales. Unless she changes the price of her pies, you could take her total profit and divide it by 5 to find the total number pies she sold to make that money. Total
1
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