G5 U3 Constructed Response Rubric
Grade 5 Unit 3 Constructed Response Division Scoring Rubric Task
Common Core State Standard
Standards for Mathematical Practice
5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
1. Addition and Subtraction of Decimals
SMP.1, SMP.2, SMP.4, SMP.5, SMP.6
5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
2. Multiplication of Decimals
SMP.2, SMP.5, SMP.7, SMP.8
5.NBT.7: Add, subtract, multiply, and divide 3. Division of Decimals
decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
SMP.1, SMP.2, SMP.4, SMP.6, SMP.7, 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 5 Unit 3 Constructed Response Rubric, Page 1
Grade 5 Unit 3 Constructed Response Division Scoring Rubric Question 1. a. Student completes table: To solve this problem by using the number line strategy I need to first determine a range for the number line by finding an estimate of the possible. Once I have this estimate and I have drawn the number line, I can start adding. First, I need to plot the position of the decimals values, starting with the smallest value. From that point I need to add the whole numbers on the number line. The number that I stop at after adding is the answer to the problem. b. Student gives correct answer and shows work: $8.80; check students work for accuracy in using the number line strategy. 2. a. Student gives correct answer: 4.35 – 2.23 = 2.12 b. Student gives explanation: In order to write the subtraction sentence I first
Points 0.5
0.5 0.5 1.5
looked at the quantities of wholes, tenths blocks, and hundredths blocks on the place value mat. Looking at each column I saw that there was a total of 4 wholes, 3 tenths, and 5 hundredths. This meant that the minuend in my sentence was going to be 4.35. Next, I looked at the number of wholes, tenths, and hundredths that were being crossed off. Looking at each column I found this to be 2 wholes, 2 tenths, and 3 hundredths. This implied that the subtrahend of the sentence was going to be 2.23. The last part of my sentence was the answer. To find this I counted the un-crossed wholes, tenths, and hundredths. Looking at each column I saw that there was a total of 2 wholes, 1 tenth, and 2 hundredths. This meant that the answer in my sentence was going to be 2.12.
3. a. Student gives correct answer: 17.1 = 2.25 + 3.45 + 5.05 + x b. Student gives correct answer and shows work: 6.35 inches c. Student gives explanation: In order to find the solution to this problem I first
0.5 0.5 1
had to gather all the information I was given. I knew that the tree’s growth was measured over four months and the total growth was found to be 17.1 inches. I was told the measurements of growth for the first three months but not the fourth. Since all the measurement recorded were part of the total inches grown, I knew that I would have to add all these measurement up. So I set up my equation as 17.1 = 2.25 + 3.45 + 5.05 + x. To find the missing measurement I added up all the measurements I did have on the right of the equation together which equaled 10.75. I then subtracted this number from the total number of inches, 17.1, and I got an answer of 6.35 inches.
4. a. Student gives correct answer and shows work: 25.36; check students’ work for accuracy. b. Student gives explanation: The area model relates to the model for whole numbers because they both require you to break down the numbers Copyright © Swun Math Grade 5 Unit 3 Constructed Response Rubric, Page 2
1 1
Total
Grade 5 Unit 3 Constructed Response Division being multiplied. They become different when it comes down to the organization of the data in the model. When working with decimals, the numbers are broken down into how many wholes numbers and are represented by a one on the model. The values of the decimals are represented by either 0.1 for tenths or 0.01 for hundredths, and repeat in the table depending on the numerical value of the digit. On the area model of a whole number the numbers are broken down along the width of the rectangle and are multiplied by the number along the length. The information that goes inside the model is the product of this multiplication. 5. Student completes table: correct answer, shows work and gives explanation: 78.4; 1.) First I had to decompose both numbers in the expression.
2
2.) Decompose the decimal number one step further. 3.) Multiply the first number of 14 decomposed, which is 4, by each of the numbers from the decomposed 5.6. 4.) Multiply 10 by each of the numbers from the decomposed 5.6. 5.) Combine all the results into one expression and reorganize the order to make it easier to combine. 8.) Distribute each of the numbers. 7.) Line up all the decimals and add all the numbers together.
6. A. Student gives correct answer and shows work: $81.25 b. Student gives explanation: Answers may vary between student’s choice to solve this problem using the area model or the distributive property. 7. a. Student gives correct answer: 2.85 ÷ 0.15 b. Student gives correct answer and shows work: 12 sculptures; Student should have 2 grids completely filled to represent the 2 pounds of sugar and have the third grid filled to 0.85. Groups of 0.15 should be outlined within shaded region until there are 12 groups. 8. a. Student gives correct answer : 1.68 ÷ 6 = p (variable used may vary) b. Student gives correct answer: First one hundredths base ten block should be filled, and 0.68 of the second hundredths base ten block should be filled. c. Student gives correct answer and shows work: 0.28 pounds of blueberries
1 1
0.5
0.5 0.5 0.5
1
Each of the six hundredths base ten blocks should have 28 boxes filled to represent 0.28
9. a. Student gives explanation: The correct answer to the question Oscar answered is 1.02. Oscar may have made his error when he divided 0.14 by 7. He probably thought that the 2 in decimal was 2 tenths and not 2 hundredths. Test Total Copyright © Swun Math Grade 5 Unit 3 Constructed Response Rubric, Page 3
1 1 15
Common Core State Standard
Standards for Mathematical Practice
5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
1. Addition and Subtraction of Decimals
SMP.1, SMP.2, SMP.4, SMP.5, SMP.6
5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
2. Multiplication of Decimals
SMP.2, SMP.5, SMP.7, SMP.8
5.NBT.7: Add, subtract, multiply, and divide 3. Division of Decimals
decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
SMP.1, SMP.2, SMP.4, SMP.6, SMP.7, 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 5 Unit 3 Constructed Response Rubric, Page 1
Grade 5 Unit 3 Constructed Response Division Scoring Rubric Question 1. a. Student completes table: To solve this problem by using the number line strategy I need to first determine a range for the number line by finding an estimate of the possible. Once I have this estimate and I have drawn the number line, I can start adding. First, I need to plot the position of the decimals values, starting with the smallest value. From that point I need to add the whole numbers on the number line. The number that I stop at after adding is the answer to the problem. b. Student gives correct answer and shows work: $8.80; check students work for accuracy in using the number line strategy. 2. a. Student gives correct answer: 4.35 – 2.23 = 2.12 b. Student gives explanation: In order to write the subtraction sentence I first
Points 0.5
0.5 0.5 1.5
looked at the quantities of wholes, tenths blocks, and hundredths blocks on the place value mat. Looking at each column I saw that there was a total of 4 wholes, 3 tenths, and 5 hundredths. This meant that the minuend in my sentence was going to be 4.35. Next, I looked at the number of wholes, tenths, and hundredths that were being crossed off. Looking at each column I found this to be 2 wholes, 2 tenths, and 3 hundredths. This implied that the subtrahend of the sentence was going to be 2.23. The last part of my sentence was the answer. To find this I counted the un-crossed wholes, tenths, and hundredths. Looking at each column I saw that there was a total of 2 wholes, 1 tenth, and 2 hundredths. This meant that the answer in my sentence was going to be 2.12.
3. a. Student gives correct answer: 17.1 = 2.25 + 3.45 + 5.05 + x b. Student gives correct answer and shows work: 6.35 inches c. Student gives explanation: In order to find the solution to this problem I first
0.5 0.5 1
had to gather all the information I was given. I knew that the tree’s growth was measured over four months and the total growth was found to be 17.1 inches. I was told the measurements of growth for the first three months but not the fourth. Since all the measurement recorded were part of the total inches grown, I knew that I would have to add all these measurement up. So I set up my equation as 17.1 = 2.25 + 3.45 + 5.05 + x. To find the missing measurement I added up all the measurements I did have on the right of the equation together which equaled 10.75. I then subtracted this number from the total number of inches, 17.1, and I got an answer of 6.35 inches.
4. a. Student gives correct answer and shows work: 25.36; check students’ work for accuracy. b. Student gives explanation: The area model relates to the model for whole numbers because they both require you to break down the numbers Copyright © Swun Math Grade 5 Unit 3 Constructed Response Rubric, Page 2
1 1
Total
Grade 5 Unit 3 Constructed Response Division being multiplied. They become different when it comes down to the organization of the data in the model. When working with decimals, the numbers are broken down into how many wholes numbers and are represented by a one on the model. The values of the decimals are represented by either 0.1 for tenths or 0.01 for hundredths, and repeat in the table depending on the numerical value of the digit. On the area model of a whole number the numbers are broken down along the width of the rectangle and are multiplied by the number along the length. The information that goes inside the model is the product of this multiplication. 5. Student completes table: correct answer, shows work and gives explanation: 78.4; 1.) First I had to decompose both numbers in the expression.
2
2.) Decompose the decimal number one step further. 3.) Multiply the first number of 14 decomposed, which is 4, by each of the numbers from the decomposed 5.6. 4.) Multiply 10 by each of the numbers from the decomposed 5.6. 5.) Combine all the results into one expression and reorganize the order to make it easier to combine. 8.) Distribute each of the numbers. 7.) Line up all the decimals and add all the numbers together.
6. A. Student gives correct answer and shows work: $81.25 b. Student gives explanation: Answers may vary between student’s choice to solve this problem using the area model or the distributive property. 7. a. Student gives correct answer: 2.85 ÷ 0.15 b. Student gives correct answer and shows work: 12 sculptures; Student should have 2 grids completely filled to represent the 2 pounds of sugar and have the third grid filled to 0.85. Groups of 0.15 should be outlined within shaded region until there are 12 groups. 8. a. Student gives correct answer : 1.68 ÷ 6 = p (variable used may vary) b. Student gives correct answer: First one hundredths base ten block should be filled, and 0.68 of the second hundredths base ten block should be filled. c. Student gives correct answer and shows work: 0.28 pounds of blueberries
1 1
0.5
0.5 0.5 0.5
1
Each of the six hundredths base ten blocks should have 28 boxes filled to represent 0.28
9. a. Student gives explanation: The correct answer to the question Oscar answered is 1.02. Oscar may have made his error when he divided 0.14 by 7. He probably thought that the 2 in decimal was 2 tenths and not 2 hundredths. Test Total Copyright © Swun Math Grade 5 Unit 3 Constructed Response Rubric, Page 3
1 1 15
