G4 U2 Constructed Response Rubric
Grade 4 Unit 2 Constructed Response Multiplication Scoring Rubric Task
1. Multiplication Strategies
2. Multiplication Patterns
Common Core State Standard 4.OA.1: Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one digit number. Determine whether a given whole number in the range 1-100 is prime or composite. 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation itself by using equations, rectangular arrays, and/or area models. 4.OA.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation itself by using equations, rectangular arrays, and/or area models.
Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 1
Standards for Mathematical Practice
SMP.1, SMP.2, SMP.4, SMP.6, SMP.8
SMP.1, SMP.4, SMP.7, SMP.8
Grade 4 Unit 2 Constructed Response Multiplication
3. Comparison and Multi-step Word Problems
4.OA.2: Multiply or divide to solve word problems involving multiplicative comparison. 4.OA.3: Solve multistep word problems posed with whole numbers and having whole number answers using the four operations including problems in which remainders must be interpreted. Represent those problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
SMP.1, SMP.2, SMP.4, SMP.6
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 4 Unit 2 Constructed Response Rubric, Page 2
Grade 4 Unit 2 Constructed Response Multiplication Scoring Rubric Question 1. a. Student gives explanation: After analyzing the statement, I was able to extract information that will allow me to write a multiplication statement. I know that the quantities being compared are 72 and the product of 12 times 6. In the statement, I noticed the word “is” which means equal and “times” which means to multiply. So the statement is essentially saying that seventy-two is equal to twelve times six. b. Student gives correct answer : 72 = 12 x 6 c. Student gives explanation: This multiplication equation/sentence is true and I know this because I multiplied the right side of the equation and I got a product of 72, which is equal to the left side of the equation. d. Student creates illustration:
Points 0.5
0.25 0.5
0.5
12 x 6 = 72 d. Student gives correct answers: Possible answers: 18 x 4 = 72, 9 x 8 = 72 2. a. Student gives correct answers: 14 x 48 = ? b. Student gives correct answers: 1.) 14 x (10 + 10 + 10 + 10 + 8) 2.) 14X (40 + 8) c. Student gives correct answer and shows work: 672 d. Student gives explanation: To solve this problem, first I had to read through the scenario given and extract any information that could help me set up an expression to solve it. By doing this I found that Hallie was using 6 yellow flowers, 3 pink flowers, and 5 purple flowers per centerpiece, and she needs to make a total of 48 centerpieces. Since the question was asking me how many total flowers she needs to make all the centerpieces. I knew that she needs to make all the centerpieces. I knew that the best operation for me to use was multiplication. I could use multiplication to multiply the numbers of flowers per centerpiece times the total number of centerpieces. Each centerpiece has different flower colors, but the problem is asking me for the total number of flowers. So I added all the different flowers per bouquet, which was 14, and multiplied it by 48. To make this multiplication process easier I used the distributive property to decompose this multiplication expression into two different expressions.
Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 3
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Grade 4 Unit 2 Constructed Response Multiplication 3. a. Student gives explanation: A strategy I could use to solve this expression is using an area model. Multiplication using the area model involves drawing a large rectangle divided into sections for each place value of the larger multi-digit numbers. On the vertical left side of this rectangle goes the single digit number. The expanded notation of the multi-digit number goes on the horizontal side of the area model. A number sentence is written each place value section where the vertical number is multiplied by each part of the expanded notation. After all the products are found, the sum of each section is added together. b. Student gives correct answer and shows work: 4,975 c. Student gives explanation: The area model relates to concepts I have learned about finding the area of a rectangle. The area of a rectangle is found by multiplying the length or vertical side by the width or horizontal side of the rectangle. In the area model we are doing the same thing; only that in this model the rectangle is divided up into sections for each part of the expanded form of the multi-digit number. Each horizontal section is multiplied by the digit along the vertical side. 4. a. Student gives explanation: A good starting point for me to have in order to find the solution of the problem is to look for information on the starting point of the pattern, the rule to follow, and the number of terms being asked for in the sequence. Once I have gathered this information I can produce to creating the pattern being described. b. Student gives correct answer: 8 21 47 89 283 571 1st
2nd
3rd
4th
5th
1
0.5 0.5
0.5 0.25
6th
c. Student gives explanation: After creating the pattern I observed that all the numbers are even and they are multiples of the number 2 and number 4. 5. a. Student provides explanation: A math tool that can be used to represent this information is a function table. In this type of display you can show the input values being used and the output values resulting from the inputs being plugged into the rule. When a function table is complete you can easily visualize the pattern created by the rule. b. Student gives explanation: Input r 2 4 6 8 10 12 Output s 7 15 23 31 39 47 c. Student gives explanation: After completing the function table and output creating the pattern, I noticed that all the numbers in the sequence are odd, and that while the input increases by two, the output values Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 4
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Grade 4 Unit 2 Constructed Response Multiplication increases by eight. 6. a. Student creates function table: Input K 3 5 7 9 Output J 18 30 42 54 b. Student gives correct answer: J = 6 x K c. Student gives correct answers and shows work: 11 kites = $66; 13 kites = $78 d. Student gives explanation: The function helped me understand this problem because it organized the data into input values an output values. In doing this it was easier for me to visualize the relationship between the input and the output, which helped me to determine the rule that represented the prices per kite. With this information I could also determine the profit he could make if he sold additional kites. 7. a. Student gives correct answer: 3 x ? =150 b. Student gives correct answer: 50 ft c. Student creates illustration:
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150ft (blue boat)
50ft (red boat)
50ft
50ft
d. Student gives explanation: My illustration helps to prove that my answer is correct because it shows that there are 3 groups of 50 ft. in the total 150 ft. that the blue boat sailed. Since the red boat sailed 3 times less than the blue, its distance is represented by only one of the three sections. 8. a. Student gives complete answer and shows work: Yes, Nina will have money left over after her purchase at the toy store. The total she will have left over is $20. b. Student gives explanation: When finding the solution, the mathematical operations that were important to this process were multiplication, addition, and subtraction. Multiplication was important when I had to find the total cost for each item she wanted to buy. Addition was important because I had to add up the total prices of all the items together and finally I had to use subtraction to find how much money she had left over from her purchase. c. Student gives explanation: Since Nina has $20 left over she could either buy 2 books for $16 or she could buy a movie for $15 with the money. 9. Student creates word problem: Answers may vary; see question 8 for Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 5
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0.5
1
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Grade 4 Unit 2 Constructed Response Multiplication example of multistep problem. Test Total
Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 6
15
1. Multiplication Strategies
2. Multiplication Patterns
Common Core State Standard 4.OA.1: Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one digit number. Determine whether a given whole number in the range 1-100 is prime or composite. 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation itself by using equations, rectangular arrays, and/or area models. 4.OA.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation itself by using equations, rectangular arrays, and/or area models.
Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 1
Standards for Mathematical Practice
SMP.1, SMP.2, SMP.4, SMP.6, SMP.8
SMP.1, SMP.4, SMP.7, SMP.8
Grade 4 Unit 2 Constructed Response Multiplication
3. Comparison and Multi-step Word Problems
4.OA.2: Multiply or divide to solve word problems involving multiplicative comparison. 4.OA.3: Solve multistep word problems posed with whole numbers and having whole number answers using the four operations including problems in which remainders must be interpreted. Represent those problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
SMP.1, SMP.2, SMP.4, SMP.6
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 4 Unit 2 Constructed Response Rubric, Page 2
Grade 4 Unit 2 Constructed Response Multiplication Scoring Rubric Question 1. a. Student gives explanation: After analyzing the statement, I was able to extract information that will allow me to write a multiplication statement. I know that the quantities being compared are 72 and the product of 12 times 6. In the statement, I noticed the word “is” which means equal and “times” which means to multiply. So the statement is essentially saying that seventy-two is equal to twelve times six. b. Student gives correct answer : 72 = 12 x 6 c. Student gives explanation: This multiplication equation/sentence is true and I know this because I multiplied the right side of the equation and I got a product of 72, which is equal to the left side of the equation. d. Student creates illustration:
Points 0.5
0.25 0.5
0.5
12 x 6 = 72 d. Student gives correct answers: Possible answers: 18 x 4 = 72, 9 x 8 = 72 2. a. Student gives correct answers: 14 x 48 = ? b. Student gives correct answers: 1.) 14 x (10 + 10 + 10 + 10 + 8) 2.) 14X (40 + 8) c. Student gives correct answer and shows work: 672 d. Student gives explanation: To solve this problem, first I had to read through the scenario given and extract any information that could help me set up an expression to solve it. By doing this I found that Hallie was using 6 yellow flowers, 3 pink flowers, and 5 purple flowers per centerpiece, and she needs to make a total of 48 centerpieces. Since the question was asking me how many total flowers she needs to make all the centerpieces. I knew that she needs to make all the centerpieces. I knew that the best operation for me to use was multiplication. I could use multiplication to multiply the numbers of flowers per centerpiece times the total number of centerpieces. Each centerpiece has different flower colors, but the problem is asking me for the total number of flowers. So I added all the different flowers per bouquet, which was 14, and multiplied it by 48. To make this multiplication process easier I used the distributive property to decompose this multiplication expression into two different expressions.
Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 3
0.25 0.25 0.5
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Grade 4 Unit 2 Constructed Response Multiplication 3. a. Student gives explanation: A strategy I could use to solve this expression is using an area model. Multiplication using the area model involves drawing a large rectangle divided into sections for each place value of the larger multi-digit numbers. On the vertical left side of this rectangle goes the single digit number. The expanded notation of the multi-digit number goes on the horizontal side of the area model. A number sentence is written each place value section where the vertical number is multiplied by each part of the expanded notation. After all the products are found, the sum of each section is added together. b. Student gives correct answer and shows work: 4,975 c. Student gives explanation: The area model relates to concepts I have learned about finding the area of a rectangle. The area of a rectangle is found by multiplying the length or vertical side by the width or horizontal side of the rectangle. In the area model we are doing the same thing; only that in this model the rectangle is divided up into sections for each part of the expanded form of the multi-digit number. Each horizontal section is multiplied by the digit along the vertical side. 4. a. Student gives explanation: A good starting point for me to have in order to find the solution of the problem is to look for information on the starting point of the pattern, the rule to follow, and the number of terms being asked for in the sequence. Once I have gathered this information I can produce to creating the pattern being described. b. Student gives correct answer: 8 21 47 89 283 571 1st
2nd
3rd
4th
5th
1
0.5 0.5
0.5 0.25
6th
c. Student gives explanation: After creating the pattern I observed that all the numbers are even and they are multiples of the number 2 and number 4. 5. a. Student provides explanation: A math tool that can be used to represent this information is a function table. In this type of display you can show the input values being used and the output values resulting from the inputs being plugged into the rule. When a function table is complete you can easily visualize the pattern created by the rule. b. Student gives explanation: Input r 2 4 6 8 10 12 Output s 7 15 23 31 39 47 c. Student gives explanation: After completing the function table and output creating the pattern, I noticed that all the numbers in the sequence are odd, and that while the input increases by two, the output values Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 4
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Grade 4 Unit 2 Constructed Response Multiplication increases by eight. 6. a. Student creates function table: Input K 3 5 7 9 Output J 18 30 42 54 b. Student gives correct answer: J = 6 x K c. Student gives correct answers and shows work: 11 kites = $66; 13 kites = $78 d. Student gives explanation: The function helped me understand this problem because it organized the data into input values an output values. In doing this it was easier for me to visualize the relationship between the input and the output, which helped me to determine the rule that represented the prices per kite. With this information I could also determine the profit he could make if he sold additional kites. 7. a. Student gives correct answer: 3 x ? =150 b. Student gives correct answer: 50 ft c. Student creates illustration:
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150ft (blue boat)
50ft (red boat)
50ft
50ft
d. Student gives explanation: My illustration helps to prove that my answer is correct because it shows that there are 3 groups of 50 ft. in the total 150 ft. that the blue boat sailed. Since the red boat sailed 3 times less than the blue, its distance is represented by only one of the three sections. 8. a. Student gives complete answer and shows work: Yes, Nina will have money left over after her purchase at the toy store. The total she will have left over is $20. b. Student gives explanation: When finding the solution, the mathematical operations that were important to this process were multiplication, addition, and subtraction. Multiplication was important when I had to find the total cost for each item she wanted to buy. Addition was important because I had to add up the total prices of all the items together and finally I had to use subtraction to find how much money she had left over from her purchase. c. Student gives explanation: Since Nina has $20 left over she could either buy 2 books for $16 or she could buy a movie for $15 with the money. 9. Student creates word problem: Answers may vary; see question 8 for Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 5
0.5
0.5
1
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Grade 4 Unit 2 Constructed Response Multiplication example of multistep problem. Test Total
Copyright © Swun Math Grade 4 Unit 2 Constructed Response Rubric, Page 6
15
