G7 U4 Constructed Response Rubric
Grade 7 Unit 4 Constructed Response Multiplying Fractions Scoring Rubric Task
Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
7.NS.3: Solve real-world and mathematical
problems involving the four operations
1. Adding, Subtracting, with rational numbers. (Computations Multiplying, and Dividing Fractions and with rational numbers extend the rules for manipulating fractions to complex Mixed Numbers
MP.1, MP.2, MP.4, MP.6, MP.7
fractions.)
2. Simplifying Complex Fractions, and Terminating and Repeating Decimals
3. Approximating Square Roots
7.NS.4: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 7.NS.5: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.
MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.7,
MP.1, MP.2, MP.3, MP.4, MP.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 7 Unit 4 Constructed Response Rubric, Page 1
Grade 7 Unit 4 Constructed Response Multiplying Fractions Scoring Rubric Question 1
1. a. Student gives correct answers: 18 2 ÷ 3 b. Student gives correct answer and shows work by creating an accurate model: Models will vary. Sample model:
Points 1 2
1
Answer: 6 6 miles per day 1
5
1
5
2. a. Student gives two correct expressions: 1 − 4 − 8 ; 1 − (4 + 8) b. Student gives correct answer and shows work using an accurate number line or area model: Models will vary. Sample model: X X
X X
X X
1 1
X
1
Answer: 8 c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to write an expression to find the solution I used several pieces of important information given to me in the problem. I am told Christie bought a 1-pound bag of candy from a store, so I know anything I subtract will be from 1. I am also told Christie has friends over 1 and they eat 4 of the bag. I also know she later takes the bag to share at
2
5
work and 8 of the bag is eaten. Since candy is eaten from the bag I know I am subtracting both quantities from the 1 pound. So to write my equations 1 5 1 5 I know I need to subtract 4 and 8 from 1, or subtract the sum of 4 and 8 from one. Either equation helped me arrive at my solution. 3. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to solve this problem I had to use several important pieces of information. I am first told they raise a total of $600, so I know Copyright © Swun Math Grade 7 Unit 4 Constructed Response Rubric, Page 2
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Total
Grade 7 Unit 4 Constructed Response Multiplying Fractions they are combining the total amount of money they make to pay for their camping trip. I am then told the number of boxes of cookies each girl sold. Since I know they are combining all their sales, to find the denominator of the fraction for each girl I need to add up each quantity of cookies sold. With this number, I then need to create the fraction for each girl by placing the number of cookies they sold over the total sold. To find the amount of money they each raised, I need to multiply the fraction of the cookies each girl sold by their total profit of $600. b. Student gives correct answers and shows work: Stella Mary Sheryl 75 60 65 Fraction 200 200 200 $ Raised $225 $180 $195 4. a. Student gives correct answer and an accurate explanation. Wording may vary. Sample explanation: After analyzing Blaine’s work, I was able to determine his work and his answer are both incorrect. I know he is incorrect because he did not multiply the first fraction by the reciprocal of the second fraction. He was correct in changing both mixed numbers into improper fractions, however what he should have done next was multiply 22 8 22 5 by the reciprocal of 5. So the expression should have been 5 × 8. 5 3
b. Student gives correct answer and shows work: 2 4 1
1
5. a. Student gives correct answers: 16 2 ÷ 5 4 ;
1 16 2 1 5 4
b. Student gives correct answer and shows work: 3 baskets, there will be 3 of a pound of oranges left. 4 6. a. Student gives correct answer and shows work using prime factors: (Check student’s work for accuracy in using the strategy); terminate b. Student gives correct answer and shows work using long division: (Check student’s work for accuracy in using the strategy); 0.5625 c. Student gives an accurate explanation: Wording may vary. Sample explanation: I can conclude my answers make sense because when looking at the prime factors for the denominator, 16, there are only factors of 2. 9 Since powers of ten have prime factors of 2 and 5, I know 16 written as a decimal will terminate. After using long division to divide the numerator by the denominator, I was able to verify the decimal terminates because there was a finite number of digits after the decimal point. Copyright © Swun Math Grade 7 Unit 4 Constructed Response Rubric, Page 3
3
2
1 1 1 1 1 1
Grade 7 Unit 4 Constructed Response Multiplying Fractions 7. a. Student gives approximate answer and shows work using a number line: Sample number line: 8 √64
8.5 8.6
9
√72.5 √74
√81
Answer: 8.6 c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to check the reasonableness of my answer I could find the square of 8.6 (multiply 8.6 by 8.6). If the product is close to 74 then I know 8.6 is a reasonable answer for √74. d. Student accurately shows process described in question 7c. 8.62 = 73.96 8. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to place the measurements from least to greatest I first need to analyze the numbers I am given. I know automatically √150 is larger than √141. And since 13 squared is equal to 169, this measurement is going to be larger than both √141 and √150. So at this point I would know √141 < √150 < 13, however I still have one more value to look at and it is 12.5. This is less than 13 so I know the greater value will be 13. The three numbers I would need to compare are √141, √150 and 12.5. I can square 12.5 and compare that value to √141 and √150 to determine in which order these values go from least to greatest. b. Student gives correct answer and shows work: √141 𝑓𝑒𝑒𝑡, √150 𝑓𝑒𝑒𝑡, 12.5 𝑓𝑒𝑒𝑡, 13 𝑓𝑒𝑒𝑡 9. a. Student gives correct answer: 15 < √250 < 16 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the inequality, I first had to determine which two perfect squares √250 is between. I knew they were 15 and 16 because 152 = √225 and 162 = √256. Since √250 is between √225 and √256, the inequality is 15 < √250 < 16. c. Student gives correct answer and shows work: √250 = 15.81 Total
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Grade 7 Unit 4 Constructed Response Multiplying Fractions
Copyright © Swun Math Grade 7 Unit 4 Constructed Response Rubric, Page 5
Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
7.NS.3: Solve real-world and mathematical
problems involving the four operations
1. Adding, Subtracting, with rational numbers. (Computations Multiplying, and Dividing Fractions and with rational numbers extend the rules for manipulating fractions to complex Mixed Numbers
MP.1, MP.2, MP.4, MP.6, MP.7
fractions.)
2. Simplifying Complex Fractions, and Terminating and Repeating Decimals
3. Approximating Square Roots
7.NS.4: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 7.NS.5: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.
MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.7,
MP.1, MP.2, MP.3, MP.4, MP.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 7 Unit 4 Constructed Response Rubric, Page 1
Grade 7 Unit 4 Constructed Response Multiplying Fractions Scoring Rubric Question 1
1. a. Student gives correct answers: 18 2 ÷ 3 b. Student gives correct answer and shows work by creating an accurate model: Models will vary. Sample model:
Points 1 2
1
Answer: 6 6 miles per day 1
5
1
5
2. a. Student gives two correct expressions: 1 − 4 − 8 ; 1 − (4 + 8) b. Student gives correct answer and shows work using an accurate number line or area model: Models will vary. Sample model: X X
X X
X X
1 1
X
1
Answer: 8 c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to write an expression to find the solution I used several pieces of important information given to me in the problem. I am told Christie bought a 1-pound bag of candy from a store, so I know anything I subtract will be from 1. I am also told Christie has friends over 1 and they eat 4 of the bag. I also know she later takes the bag to share at
2
5
work and 8 of the bag is eaten. Since candy is eaten from the bag I know I am subtracting both quantities from the 1 pound. So to write my equations 1 5 1 5 I know I need to subtract 4 and 8 from 1, or subtract the sum of 4 and 8 from one. Either equation helped me arrive at my solution. 3. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to solve this problem I had to use several important pieces of information. I am first told they raise a total of $600, so I know Copyright © Swun Math Grade 7 Unit 4 Constructed Response Rubric, Page 2
2
Total
Grade 7 Unit 4 Constructed Response Multiplying Fractions they are combining the total amount of money they make to pay for their camping trip. I am then told the number of boxes of cookies each girl sold. Since I know they are combining all their sales, to find the denominator of the fraction for each girl I need to add up each quantity of cookies sold. With this number, I then need to create the fraction for each girl by placing the number of cookies they sold over the total sold. To find the amount of money they each raised, I need to multiply the fraction of the cookies each girl sold by their total profit of $600. b. Student gives correct answers and shows work: Stella Mary Sheryl 75 60 65 Fraction 200 200 200 $ Raised $225 $180 $195 4. a. Student gives correct answer and an accurate explanation. Wording may vary. Sample explanation: After analyzing Blaine’s work, I was able to determine his work and his answer are both incorrect. I know he is incorrect because he did not multiply the first fraction by the reciprocal of the second fraction. He was correct in changing both mixed numbers into improper fractions, however what he should have done next was multiply 22 8 22 5 by the reciprocal of 5. So the expression should have been 5 × 8. 5 3
b. Student gives correct answer and shows work: 2 4 1
1
5. a. Student gives correct answers: 16 2 ÷ 5 4 ;
1 16 2 1 5 4
b. Student gives correct answer and shows work: 3 baskets, there will be 3 of a pound of oranges left. 4 6. a. Student gives correct answer and shows work using prime factors: (Check student’s work for accuracy in using the strategy); terminate b. Student gives correct answer and shows work using long division: (Check student’s work for accuracy in using the strategy); 0.5625 c. Student gives an accurate explanation: Wording may vary. Sample explanation: I can conclude my answers make sense because when looking at the prime factors for the denominator, 16, there are only factors of 2. 9 Since powers of ten have prime factors of 2 and 5, I know 16 written as a decimal will terminate. After using long division to divide the numerator by the denominator, I was able to verify the decimal terminates because there was a finite number of digits after the decimal point. Copyright © Swun Math Grade 7 Unit 4 Constructed Response Rubric, Page 3
3
2
1 1 1 1 1 1
Grade 7 Unit 4 Constructed Response Multiplying Fractions 7. a. Student gives approximate answer and shows work using a number line: Sample number line: 8 √64
8.5 8.6
9
√72.5 √74
√81
Answer: 8.6 c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to check the reasonableness of my answer I could find the square of 8.6 (multiply 8.6 by 8.6). If the product is close to 74 then I know 8.6 is a reasonable answer for √74. d. Student accurately shows process described in question 7c. 8.62 = 73.96 8. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to place the measurements from least to greatest I first need to analyze the numbers I am given. I know automatically √150 is larger than √141. And since 13 squared is equal to 169, this measurement is going to be larger than both √141 and √150. So at this point I would know √141 < √150 < 13, however I still have one more value to look at and it is 12.5. This is less than 13 so I know the greater value will be 13. The three numbers I would need to compare are √141, √150 and 12.5. I can square 12.5 and compare that value to √141 and √150 to determine in which order these values go from least to greatest. b. Student gives correct answer and shows work: √141 𝑓𝑒𝑒𝑡, √150 𝑓𝑒𝑒𝑡, 12.5 𝑓𝑒𝑒𝑡, 13 𝑓𝑒𝑒𝑡 9. a. Student gives correct answer: 15 < √250 < 16 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the inequality, I first had to determine which two perfect squares √250 is between. I knew they were 15 and 16 because 152 = √225 and 162 = √256. Since √250 is between √225 and √256, the inequality is 15 < √250 < 16. c. Student gives correct answer and shows work: √250 = 15.81 Total
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Grade 7 Unit 4 Constructed Response Multiplying Fractions
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