G6 U1 Constructed Response Rubric
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions Scoring Rubric Task
Common Core State Standard
Standards for Mathematical Practice
1. GCF, LCM, and Comparing/Ordering Decimals
6.NS.3: Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation. 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. 6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explain the meaning of 0 in each situation.
SMP.1, SMP.3, SMP.4, SMP.5, SMP.6, SMP.7 SMP.8
2. Add, Subtract, and Multiply Decimals
6.NS.3: Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.
SMP.1, SMP.2, SMP.3, SMP.4, SMP.6, SMP.8
3. Division of Whole numbers, Decimals, and Fractions
6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. 6.NS.2: Fluently divide multi-digit numbers using standard algorithm. 6.NS.3: Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.
SMP.1, SMP.3, SMP.4, SMP.5, SMP.6, SMP.8
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 6 Unit 1 Constructed Response Rubric, Page 1
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions Scoring Rubric Question: 1. a. Student gives explanation: After analyzing this problem, I determined that what the problem was asking me to find was the total number of baskets that could be made if all the baskets had the same amount of fruit inside. I’m given three different quantities of fruit that will be put equally into all the baskets. Since its asking for the greatest number of baskets that can be made, the best course to take is to find the greatest common factor of all three numbers. To do so I would need to make a GCF ladder to find the greatest common factor. This ladder would help me organize the process of finding the factors and later finding the product of these factors which will give me the greatest number of baskets that they can make. b. Student gives correct answer and shows work: 15 fruit baskets 2. a. Student gives correct answer and shows work: 36 tables and table covers b. Student gives explanation: The operations that were important in finding my answer were division and multiplication. In the LCM ladder I made I used division to divide out common prime numbers. And I later used multiplication to find the actual LCM by multiplying all the prime numbers along the side, or L of the LCM ladder. c. Student gives explanation: The process for finding my solutions in questions 1b and 2a were similar because I had to use a GCF and LCM ladder. This ladder model works the same for finding the LCM and GCF because it helps you extract all the common prime numbers. Where the processes were different was at the end when it was time to multiply the common prime factors. In the GCF ladders you only multiply the prime factors along the side of the ladder and in the LCM ladder you multiply all the prime factors along the “L” formed by the ladder. 3. a. Student gives correct answer: 9.10, 9.15, 9.17, 9.25 b. Student gives correct answers: In order for swimmer five to win the race, he would have to swim faster than 9.10 seconds. In order for him to qualify in fourth place he would have to swim faster than 9.25 seconds. c. Student gives explanation: If swimmer 2 had gotten a time of 9.45 seconds then Swimmer 3 would have come in third instead of fourth and swimmer 2 would have come in fourth place. 4. a. Student gives correct answer and shows work: $94.36 b. Student gives correct answer and shows work: $15.64 c. Student gives explanation: Combinations of items may vary. Ex. With Copyright © Swun Math Grade 6 Unit 1 Constructed Response Rubric, Page 2
Points 0.75
0.25 0.5 0.5
1
0.25 1
0.75
0.25 0.25 0.5
Total
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions
5.
6.
7.
8.
the money Fulton has left over he could buy a sunblock and hiking socks, hiking socks alone, sunblock alone, or another water bottle. a. Student gives correct answers: Corey: 83.42 feet; Sam: 83.17 feet b. Student gives correct answer and explanation: The brother who threw the discus the farthest was Corey. I know this because he threw the discus 83.42 feet and Sam threw it 83.17 feet. After comparing their distances I saw that his distance was longer only by the value of the 4 in the hundredths place. c. Student gives correct answer and shows work: 0.25 feet a. Student gives correct answer and shows work: $101.25 b. Student gives correct answer: $69.09 c. Student gives explanation: In order to find my solutions for each part I had to use both multiplication and addition. For part A I had to use multiplication to find the price for each group of tickets, and then I had to add them together to get the total amount. For part B I also use multiplication because I had to find the price for each group of food and drinks, and then I used addition to find the grand total. c. Student gives correct answer and explanation: During the trip to the zoo the family spent the most money on the entrance tickets to the zoo. Here they spent a total of $101.25, in comparison to their lunch purchase which was only $69.09. a. Student gives correct answer and work: 5.75 miles b. Student gives explanation: The mathematical operation that was important when solving this problem was division. I decided that this was the operation that I needed to use because there was certain information given to me in the problem that indicated that this was what I needed to do. The problem stated that both Neil and Christian could run a mile in an average of 7.3 min, and the problem is asking how many miles they can run in 42 minutes. So if I know the total time they are going to run and the time they can run one mile in, and I want to find out how many miles, or groups of 7 minutes, they can run in the 42 minutes, the most logical operation to use was division. a. Student gives correct answer and shows work: 3⁄4 yard b. Student gives correct answer and shows work: 6 bows c. Student creates model:
9. a. Student gives correct answer and shows work: 156 tubs of cookie dough Copyright © Swun Math Grade 6 Unit 1 Constructed Response Rubric, Page 3
0.5 1
0.5 0.25 0.25 1
0.5
0.25 0.75
0.5 0.5 1
0.25
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions b. Student gives correct answer and shows work: 12 tubs of cookie dough c. Student gives explanation: In order to prove that my answers are correct I would have to multiply my answers (quotients) for each part by the divisor from the problem. So for part A I would multiply 156 by 60 and for part B I would multiply 12 by 13. If the products are equal to the dividend from the problem then I know my answer is correct. d. Student shows process explained in question 9c. Test Total
Copyright © Swun Math Grade 6 Unit 1 Constructed Response Rubric, Page 4
0.25 1
0.5 15
Common Core State Standard
Standards for Mathematical Practice
1. GCF, LCM, and Comparing/Ordering Decimals
6.NS.3: Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation. 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. 6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explain the meaning of 0 in each situation.
SMP.1, SMP.3, SMP.4, SMP.5, SMP.6, SMP.7 SMP.8
2. Add, Subtract, and Multiply Decimals
6.NS.3: Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.
SMP.1, SMP.2, SMP.3, SMP.4, SMP.6, SMP.8
3. Division of Whole numbers, Decimals, and Fractions
6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. 6.NS.2: Fluently divide multi-digit numbers using standard algorithm. 6.NS.3: Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.
SMP.1, SMP.3, SMP.4, SMP.5, SMP.6, SMP.8
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 6 Unit 1 Constructed Response Rubric, Page 1
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions Scoring Rubric Question: 1. a. Student gives explanation: After analyzing this problem, I determined that what the problem was asking me to find was the total number of baskets that could be made if all the baskets had the same amount of fruit inside. I’m given three different quantities of fruit that will be put equally into all the baskets. Since its asking for the greatest number of baskets that can be made, the best course to take is to find the greatest common factor of all three numbers. To do so I would need to make a GCF ladder to find the greatest common factor. This ladder would help me organize the process of finding the factors and later finding the product of these factors which will give me the greatest number of baskets that they can make. b. Student gives correct answer and shows work: 15 fruit baskets 2. a. Student gives correct answer and shows work: 36 tables and table covers b. Student gives explanation: The operations that were important in finding my answer were division and multiplication. In the LCM ladder I made I used division to divide out common prime numbers. And I later used multiplication to find the actual LCM by multiplying all the prime numbers along the side, or L of the LCM ladder. c. Student gives explanation: The process for finding my solutions in questions 1b and 2a were similar because I had to use a GCF and LCM ladder. This ladder model works the same for finding the LCM and GCF because it helps you extract all the common prime numbers. Where the processes were different was at the end when it was time to multiply the common prime factors. In the GCF ladders you only multiply the prime factors along the side of the ladder and in the LCM ladder you multiply all the prime factors along the “L” formed by the ladder. 3. a. Student gives correct answer: 9.10, 9.15, 9.17, 9.25 b. Student gives correct answers: In order for swimmer five to win the race, he would have to swim faster than 9.10 seconds. In order for him to qualify in fourth place he would have to swim faster than 9.25 seconds. c. Student gives explanation: If swimmer 2 had gotten a time of 9.45 seconds then Swimmer 3 would have come in third instead of fourth and swimmer 2 would have come in fourth place. 4. a. Student gives correct answer and shows work: $94.36 b. Student gives correct answer and shows work: $15.64 c. Student gives explanation: Combinations of items may vary. Ex. With Copyright © Swun Math Grade 6 Unit 1 Constructed Response Rubric, Page 2
Points 0.75
0.25 0.5 0.5
1
0.25 1
0.75
0.25 0.25 0.5
Total
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions
5.
6.
7.
8.
the money Fulton has left over he could buy a sunblock and hiking socks, hiking socks alone, sunblock alone, or another water bottle. a. Student gives correct answers: Corey: 83.42 feet; Sam: 83.17 feet b. Student gives correct answer and explanation: The brother who threw the discus the farthest was Corey. I know this because he threw the discus 83.42 feet and Sam threw it 83.17 feet. After comparing their distances I saw that his distance was longer only by the value of the 4 in the hundredths place. c. Student gives correct answer and shows work: 0.25 feet a. Student gives correct answer and shows work: $101.25 b. Student gives correct answer: $69.09 c. Student gives explanation: In order to find my solutions for each part I had to use both multiplication and addition. For part A I had to use multiplication to find the price for each group of tickets, and then I had to add them together to get the total amount. For part B I also use multiplication because I had to find the price for each group of food and drinks, and then I used addition to find the grand total. c. Student gives correct answer and explanation: During the trip to the zoo the family spent the most money on the entrance tickets to the zoo. Here they spent a total of $101.25, in comparison to their lunch purchase which was only $69.09. a. Student gives correct answer and work: 5.75 miles b. Student gives explanation: The mathematical operation that was important when solving this problem was division. I decided that this was the operation that I needed to use because there was certain information given to me in the problem that indicated that this was what I needed to do. The problem stated that both Neil and Christian could run a mile in an average of 7.3 min, and the problem is asking how many miles they can run in 42 minutes. So if I know the total time they are going to run and the time they can run one mile in, and I want to find out how many miles, or groups of 7 minutes, they can run in the 42 minutes, the most logical operation to use was division. a. Student gives correct answer and shows work: 3⁄4 yard b. Student gives correct answer and shows work: 6 bows c. Student creates model:
9. a. Student gives correct answer and shows work: 156 tubs of cookie dough Copyright © Swun Math Grade 6 Unit 1 Constructed Response Rubric, Page 3
0.5 1
0.5 0.25 0.25 1
0.5
0.25 0.75
0.5 0.5 1
0.25
Grade 6 Unit 1 Constructed Response Operations With Decimals and Fractions b. Student gives correct answer and shows work: 12 tubs of cookie dough c. Student gives explanation: In order to prove that my answers are correct I would have to multiply my answers (quotients) for each part by the divisor from the problem. So for part A I would multiply 156 by 60 and for part B I would multiply 12 by 13. If the products are equal to the dividend from the problem then I know my answer is correct. d. Student shows process explained in question 9c. Test Total
Copyright © Swun Math Grade 6 Unit 1 Constructed Response Rubric, Page 4
0.25 1
0.5 15
