G4 U1 Constructed Response Rubric
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction Scoring Rubric Common Core State Standard
Standards for Mathematical Practice
1. Read, Write and Compare MultiDigit Whole Numbers
4.NBT.2: Read and write multi-digit whole number using base ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, < symbols to record the results of comparisons.
SMP.1, SMP.2, SMP.5, SMP.7, SMP.8
2. Round, Add, and Subtract Multi-Digit Numbers
4.NBT.3: Use place value understanding to round multi-digit whole numbers to any place. 4.NBT.4: Fluently add and subtract multidigit whole numbers using the standard algorithm.
SMP.1, SMP.5, SMP.6, SMP.8
3. Generate Patterns That Follow A Rule
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.
SMP.1, SMP.4, SMP.7, SMP.8
Task
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 1 Constructed Response Rubric, Page 1
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction Scoring Rubric Question 1. a. Student gives explanation: A math tool I could use that would help me write this number in word form would be a place value chart. A place value chart has a column labelled for each place value, like ones, tens, hundreds, thousands, ten thousands. What ever each digit is placed is its place value. This makes it easy to know what place value to write for each of the digits in the number. b. Student gives correct answer and completes place value chart:
Points 0.5 0.5
eight hundred ninety five thousand, seven hundred sixty
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Hundreds
Thousands
8
9
5
7
6
0
2. a. Student gives correct answer and explanation: After analyzing the problem, I determined that Neil’s answer is incorrect. I know this because he made two major errors when he wrote the number in word form. His first error was that he wrote the digits in the number 930 as nine hundred thousand thirty. This way he wrote this means that the number was 900, 030. This part should have been written as nine-hundred thirty thousand. His second error was in the last three digits of the number. He wrote five hundred and two, which is incorrect. The correct way of writing this is five hundred two without the word “and.” b. Student gives correct answer: Seven million, nine hundred thirty thousand, five hundred two c. Student gives correct answer: 7,000,000 + 900,000+30,000+500+2 d. Student gives explanation: Word form and expanded form are similar to place value because, they both tell you the place value of the each digit either in words or by taking the number apart and showing its place value as seen in expanded form.
Copyright © Swun Math Grade 4 Unit 1 Constructed Response Rubric, Page 2
1
0.25 0.25 0.5
Total
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction 3. a. Student gives correct explanation: A strategy I could use to compare these numbers is to write all of them in standard form first. My next step would be to compare the place value of each digit in the three numbers. After comparing the numbers and figuring out their order, I need to use the greater than or less than symbols to compare their order. b. Student gives correct answer: 750, 110 > 705,205 > 700,050 or seven hundred fifty thousand, > 700,000 +5000+200+5 > 700,050 one hundred ten 4. a. Student gives correct answer: 452,000 butterflies b. Student gives explanation: In order to prove that my answer is correct I can use a number line. The number line below shows how my answer is correct:
1
1
0.5 0.5
451,789
451,000
452,000
5. a. Student gives correct answer and shows work: 817, 551 butterflies b. Student gives explanation: Estimations can be used to show that my answer is correct because when estimating you are rounding numbers to their closest high or low value. When you add these numbers together to find the estimated sum, you can compare it to your answer. If your answer is close to the estimation you made then the answer is correct and makes sense. c. Student shows estimation process: 384,251 +433,300 817,551
0.5
400,000 +400,000 800,000
6. a. Student provides explanation:
−
0.5 1
0.5
6
8,
3
2
7
3
9,
2
5
4
2
9,
0
7
3
b. Student gives explanation: In order to prove that my answer makes the number sentences true I would need to add the complete answer from the subtraction sentence to the 2nd subtrahend in the sentence. If the sum is Copyright © Swun Math Grade 4 Unit 1 Constructed Response Rubric, Page 3
1
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction equal to the larger 1st subtrahend then I know that the digits I placed in the number sentence are correct. The operation that is important in this process is addition. c. Student shows process:
0.5
39,254 +29,073 68,327
7. a. Student completes sequence:
1st
2nd
3rd
0.5
4th
5th
6th
b. Student gives explanation: After completing the sequence, I was able to determine that the sequence is a growing pattern. The reason I know this is because the sequence changes every time it repeats. This is best explained by the rule for the pattern. The rule that best represents this pattern is that 3 dots are added to each term of the sequence. So each term of the sequence increased by three, making it a growing pattern. 8. a. Student gives explanation: After analyzing the problem I am able to identify certain pieces of information that will help me generate the pattern. First, I am given a starting point of 8, which is my first term. Next, I am given my rule for the pattern. In this case it is increasing each number by 5. So starting from 8, I need to add 5 to each term of the sentence. My end point for the pattern is the seventh term of the sequence. b. Student gives correct answer: 8, 13, 18, 23, 28, 33, 38 c. Student gives explanation: Some prominent features I observed in the pattern are that the digit in the ones place for each number alternates between 8 and 3, and each number alternates between an even and odd number. 9. a. Student completes table with missing values: Month 2= 5, Month 4= 12, Month 6= 23, Month 8= 38 b. Student gives correct answer and explanation: The rule that best describes the pattern is that starting from 3, I increased the flowers planted every month by one. For example from 3, I added 2, then 3, then 4 and so on until I reached 8 months. The numbers I added to the previous sum Copyright © Swun Math Grade 4 Unit 1 Constructed Response Rubric, Page 4
0.5
1 1
1 0.5
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction always increased by one. c. Student gives explanation: After completing the pattern, I observed that the number I added to the previous sum always increased by one. I also observed that every two numbers alternated between even and odd numbers. Test Total
Copyright © Swun Math Grade 4 Unit 1 Constructed Response Rubric, Page 5
0.5
15
Standards for Mathematical Practice
1. Read, Write and Compare MultiDigit Whole Numbers
4.NBT.2: Read and write multi-digit whole number using base ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, < symbols to record the results of comparisons.
SMP.1, SMP.2, SMP.5, SMP.7, SMP.8
2. Round, Add, and Subtract Multi-Digit Numbers
4.NBT.3: Use place value understanding to round multi-digit whole numbers to any place. 4.NBT.4: Fluently add and subtract multidigit whole numbers using the standard algorithm.
SMP.1, SMP.5, SMP.6, SMP.8
3. Generate Patterns That Follow A Rule
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.
SMP.1, SMP.4, SMP.7, SMP.8
Task
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 1 Constructed Response Rubric, Page 1
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction Scoring Rubric Question 1. a. Student gives explanation: A math tool I could use that would help me write this number in word form would be a place value chart. A place value chart has a column labelled for each place value, like ones, tens, hundreds, thousands, ten thousands. What ever each digit is placed is its place value. This makes it easy to know what place value to write for each of the digits in the number. b. Student gives correct answer and completes place value chart:
Points 0.5 0.5
eight hundred ninety five thousand, seven hundred sixty
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Hundreds
Thousands
8
9
5
7
6
0
2. a. Student gives correct answer and explanation: After analyzing the problem, I determined that Neil’s answer is incorrect. I know this because he made two major errors when he wrote the number in word form. His first error was that he wrote the digits in the number 930 as nine hundred thousand thirty. This way he wrote this means that the number was 900, 030. This part should have been written as nine-hundred thirty thousand. His second error was in the last three digits of the number. He wrote five hundred and two, which is incorrect. The correct way of writing this is five hundred two without the word “and.” b. Student gives correct answer: Seven million, nine hundred thirty thousand, five hundred two c. Student gives correct answer: 7,000,000 + 900,000+30,000+500+2 d. Student gives explanation: Word form and expanded form are similar to place value because, they both tell you the place value of the each digit either in words or by taking the number apart and showing its place value as seen in expanded form.
Copyright © Swun Math Grade 4 Unit 1 Constructed Response Rubric, Page 2
1
0.25 0.25 0.5
Total
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction 3. a. Student gives correct explanation: A strategy I could use to compare these numbers is to write all of them in standard form first. My next step would be to compare the place value of each digit in the three numbers. After comparing the numbers and figuring out their order, I need to use the greater than or less than symbols to compare their order. b. Student gives correct answer: 750, 110 > 705,205 > 700,050 or seven hundred fifty thousand, > 700,000 +5000+200+5 > 700,050 one hundred ten 4. a. Student gives correct answer: 452,000 butterflies b. Student gives explanation: In order to prove that my answer is correct I can use a number line. The number line below shows how my answer is correct:
1
1
0.5 0.5
451,789
451,000
452,000
5. a. Student gives correct answer and shows work: 817, 551 butterflies b. Student gives explanation: Estimations can be used to show that my answer is correct because when estimating you are rounding numbers to their closest high or low value. When you add these numbers together to find the estimated sum, you can compare it to your answer. If your answer is close to the estimation you made then the answer is correct and makes sense. c. Student shows estimation process: 384,251 +433,300 817,551
0.5
400,000 +400,000 800,000
6. a. Student provides explanation:
−
0.5 1
0.5
6
8,
3
2
7
3
9,
2
5
4
2
9,
0
7
3
b. Student gives explanation: In order to prove that my answer makes the number sentences true I would need to add the complete answer from the subtraction sentence to the 2nd subtrahend in the sentence. If the sum is Copyright © Swun Math Grade 4 Unit 1 Constructed Response Rubric, Page 3
1
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction equal to the larger 1st subtrahend then I know that the digits I placed in the number sentence are correct. The operation that is important in this process is addition. c. Student shows process:
0.5
39,254 +29,073 68,327
7. a. Student completes sequence:
1st
2nd
3rd
0.5
4th
5th
6th
b. Student gives explanation: After completing the sequence, I was able to determine that the sequence is a growing pattern. The reason I know this is because the sequence changes every time it repeats. This is best explained by the rule for the pattern. The rule that best represents this pattern is that 3 dots are added to each term of the sequence. So each term of the sequence increased by three, making it a growing pattern. 8. a. Student gives explanation: After analyzing the problem I am able to identify certain pieces of information that will help me generate the pattern. First, I am given a starting point of 8, which is my first term. Next, I am given my rule for the pattern. In this case it is increasing each number by 5. So starting from 8, I need to add 5 to each term of the sentence. My end point for the pattern is the seventh term of the sequence. b. Student gives correct answer: 8, 13, 18, 23, 28, 33, 38 c. Student gives explanation: Some prominent features I observed in the pattern are that the digit in the ones place for each number alternates between 8 and 3, and each number alternates between an even and odd number. 9. a. Student completes table with missing values: Month 2= 5, Month 4= 12, Month 6= 23, Month 8= 38 b. Student gives correct answer and explanation: The rule that best describes the pattern is that starting from 3, I increased the flowers planted every month by one. For example from 3, I added 2, then 3, then 4 and so on until I reached 8 months. The numbers I added to the previous sum Copyright © Swun Math Grade 4 Unit 1 Constructed Response Rubric, Page 4
0.5
1 1
1 0.5
Grade 4 Unit 1 Constructed Response Multi-Digit Whole Numbers and Addition/Subtraction always increased by one. c. Student gives explanation: After completing the pattern, I observed that the number I added to the previous sum always increased by one. I also observed that every two numbers alternated between even and odd numbers. Test Total
Copyright © Swun Math Grade 4 Unit 1 Constructed Response Rubric, Page 5
0.5
15
