G6 U2 Constructed Response Rubric
Grade 6 Unit 2 Constructed Response Rational Numbers Scoring Rubric Task
Common Core State Standard
Standards for Mathematical Practice
1. Rational Numbers: Elevation, Credit and Debit, Electrical Charge
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.2, SMP.3, SMP.4, SMP.6, SMP.8
2. Understanding Rational Numbers and Number Lines
3. Absolute value of Integers and Comparing Numbers
6.NS.7a: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 6.NS.7c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. 6.NS.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts. 6.NS.7c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
SMP.1, SMP.2, SMP.3, SMP.4, SMP.6, SMP.8
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 2 Constructed Response Rubric, Page 1
Grade 6 Unit 2 Constructed Response Rational Numbers Scoring Rubric Question: 1. a. Student creates visual model: Student drawings may vary; however, they should have something representative of a number line, which shows the position of each number at, above, or below zero. b. Student gives explanation: My model represents the feet above and below sea level on their trip. When they were on the boat they were at sea level which is 0 feet in altitude. When they dove to 20 feet below sea level, the elevation became negative because they were moving below or away from sea level. 2. a. Student gives correct answer: ‒$30/ negative $30/ minus $30 b. Student gives explanation: Based on my answer from part A I was able to conclude that Jared’s account is overdrawn, meaning he used all the money he had saved. He now owes money. c. Student gives correct answer: Combination of items returned can vary from the one given here. To have money go back into his account he would need to return the clothes he purchased and the souvenirs. He spent $55 on the clothes and $35 on souvenirs, and together this cost $90. If I add this $90 to his negative balance of $30 it would put him at a balance of $60. d. Student creates model: Students can create a number line to show the account balance after each purchase. 3. a. Student gives correct answer: ‒3 charge. It is a negative atom. b. Student creates visual model:
Points 0.5
0.5
0.25 0.25
1
0.5 1 1
+10
c. Student gives explanation: In order for this atom to have the opposite charge of ‒3, it would need a grouping of 13 protons and 10 electrons. This grouping would give the atom a positive 3 charge. 4. a. Student gives correct answer and explanation: After analyzing Stewart’s answer, I determined that his reasoning was incorrect. The question is asking for the opposite of the number 5.9 which means that it is asking for a negative number. Stewart switched the numbers from 5.9 to -9.5, so he Copyright © Swun Math Grade 6 Unit 2 Constructed Response Rubric, Page 2
1 1
Total
Grade 6 Unit 2 Constructed Response Rational Numbers
5.
6.
7.
8.
was correct in having the negative. However, he should not have switched the placement of the digits in the number. The correct answer should have been ‒5.9. b. Student creates model: Student should create a number line showing the position of 5.9 and -5.9. Student gives completes statements: ‒ 3.5 0.5 b. Student gives correct answer: 2 < 2.25 c. Student gives correct answer and explanation: The child with the highest growth was Jesse with 2.5 inches. It is not possible for Jesse’s growth to be the opposite in value in the next two months. The reason for this is because a person’s height can’t be negative. A person, especially a child, can grow or stay the same in height, but he or she can’t decrease in height. a. Student gives correct answers:|−5| = 5; The distance is 5 units from zero; |3| = 3; The distance is 3 units from zero. b. Student gives explanation: A visual model I could use to represent this model would be a vertical number line. The reason it would be a good model to use is because we are dealing with temperatures, and a vertical number line resembles a thermometer. This better helps you visualize which temperature is higher or lower. c. Student creates vertical number line: Number line should be vertical with -5°F labelled five units below zero, and 3°F labelled 3 units above zero. a. Student gives explanation: After analyzing the absolute values, I was able to develop a starting point for solving the problem. The first step I need to take is to find the absolute value for each number. My next step is to determine the units each number is from zero. Finally, I need to compare and order the numbers from least to greatest. A concept that I have learned before that would be helpful in this problem is place value and ordering decimals. b. Student gives correct answer: 1.3, 1.7, 2.5, 2.59, 4.5
9. Student gives correct answer and explanation: After analyzing Mark’s work I concluded that his answer was incorrect. I know this because when Copyright © Swun Math Grade 6 Unit 2 Constructed Response Rubric, Page 3
1 1 0.5 0.5 1
0.25 0.25
0.5 1
1 2
Grade 6 Unit 2 Constructed Response Rational Numbers comparing negative numbers, having a larger number does not mean it is higher in value than a negative number with a smaller value. When working with numbers, the higher the value of the negative number, the farther away it is from zero in the negative direction. Negative numbers that are lower in value are closer to zero. So in the case of temperature, the larger the negative number the farther away it is from zero, and the colder it is outside. Therefore, the correct answer to the problem should have been ‒ 16°F
Common Core State Standard
Standards for Mathematical Practice
1. Rational Numbers: Elevation, Credit and Debit, Electrical Charge
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.2, SMP.3, SMP.4, SMP.6, SMP.8
2. Understanding Rational Numbers and Number Lines
3. Absolute value of Integers and Comparing Numbers
6.NS.7a: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 6.NS.7c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. 6.NS.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts. 6.NS.7c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
SMP.1, SMP.2, SMP.3, SMP.4, SMP.6, SMP.8
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 2 Constructed Response Rubric, Page 1
Grade 6 Unit 2 Constructed Response Rational Numbers Scoring Rubric Question: 1. a. Student creates visual model: Student drawings may vary; however, they should have something representative of a number line, which shows the position of each number at, above, or below zero. b. Student gives explanation: My model represents the feet above and below sea level on their trip. When they were on the boat they were at sea level which is 0 feet in altitude. When they dove to 20 feet below sea level, the elevation became negative because they were moving below or away from sea level. 2. a. Student gives correct answer: ‒$30/ negative $30/ minus $30 b. Student gives explanation: Based on my answer from part A I was able to conclude that Jared’s account is overdrawn, meaning he used all the money he had saved. He now owes money. c. Student gives correct answer: Combination of items returned can vary from the one given here. To have money go back into his account he would need to return the clothes he purchased and the souvenirs. He spent $55 on the clothes and $35 on souvenirs, and together this cost $90. If I add this $90 to his negative balance of $30 it would put him at a balance of $60. d. Student creates model: Students can create a number line to show the account balance after each purchase. 3. a. Student gives correct answer: ‒3 charge. It is a negative atom. b. Student creates visual model:
Points 0.5
0.5
0.25 0.25
1
0.5 1 1
+10
c. Student gives explanation: In order for this atom to have the opposite charge of ‒3, it would need a grouping of 13 protons and 10 electrons. This grouping would give the atom a positive 3 charge. 4. a. Student gives correct answer and explanation: After analyzing Stewart’s answer, I determined that his reasoning was incorrect. The question is asking for the opposite of the number 5.9 which means that it is asking for a negative number. Stewart switched the numbers from 5.9 to -9.5, so he Copyright © Swun Math Grade 6 Unit 2 Constructed Response Rubric, Page 2
1 1
Total
Grade 6 Unit 2 Constructed Response Rational Numbers
5.
6.
7.
8.
was correct in having the negative. However, he should not have switched the placement of the digits in the number. The correct answer should have been ‒5.9. b. Student creates model: Student should create a number line showing the position of 5.9 and -5.9. Student gives completes statements: ‒ 3.5 0.5 b. Student gives correct answer: 2 < 2.25 c. Student gives correct answer and explanation: The child with the highest growth was Jesse with 2.5 inches. It is not possible for Jesse’s growth to be the opposite in value in the next two months. The reason for this is because a person’s height can’t be negative. A person, especially a child, can grow or stay the same in height, but he or she can’t decrease in height. a. Student gives correct answers:|−5| = 5; The distance is 5 units from zero; |3| = 3; The distance is 3 units from zero. b. Student gives explanation: A visual model I could use to represent this model would be a vertical number line. The reason it would be a good model to use is because we are dealing with temperatures, and a vertical number line resembles a thermometer. This better helps you visualize which temperature is higher or lower. c. Student creates vertical number line: Number line should be vertical with -5°F labelled five units below zero, and 3°F labelled 3 units above zero. a. Student gives explanation: After analyzing the absolute values, I was able to develop a starting point for solving the problem. The first step I need to take is to find the absolute value for each number. My next step is to determine the units each number is from zero. Finally, I need to compare and order the numbers from least to greatest. A concept that I have learned before that would be helpful in this problem is place value and ordering decimals. b. Student gives correct answer: 1.3, 1.7, 2.5, 2.59, 4.5
9. Student gives correct answer and explanation: After analyzing Mark’s work I concluded that his answer was incorrect. I know this because when Copyright © Swun Math Grade 6 Unit 2 Constructed Response Rubric, Page 3
1 1 0.5 0.5 1
0.25 0.25
0.5 1
1 2
Grade 6 Unit 2 Constructed Response Rational Numbers comparing negative numbers, having a larger number does not mean it is higher in value than a negative number with a smaller value. When working with numbers, the higher the value of the negative number, the farther away it is from zero in the negative direction. Negative numbers that are lower in value are closer to zero. So in the case of temperature, the larger the negative number the farther away it is from zero, and the colder it is outside. Therefore, the correct answer to the problem should have been ‒ 16°F
