Formative Instructional and Assessment Tasks
Value of a Digit5.NBT.1 - Task 1
Domain / Number and Operations in Base Ten
Cluster / Understand the place value system.
Standard(s) / 5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Materials / Paper and pencil
Task / Part 1. Wallace and Logan were arguing about the size of 2 numbers. Wallace thought eight-tenths was ten times larger than eight-hundredths. Logan thought eight-hundredths was ten times larger than eight-tenths. Who is correct?
Part 2. Imagine you are the boys’ teacher. Draw a picture to help explain this concept to Wallace and Logan. Make sure you refer to place value in your explanation.
Part 3. Choose another pair of numbers that you could give to Wallace and Logan to assess whether they understand this concept. Which one is larger? How much larger?
Rubric
Level I / Level II / Level III
Limited Performance
· Student does not identify that Wallace is correct, or determines he is correct based on unsound reasoning.
· Student is unable to generate a picture to explain the concept.
· Student does not refer to place value in their explanation.
· Student does not generate another pair of numbers that fit with the concept. / Not Yet Proficient
· Student identifies that Wallace is correct.
· Student’s explanation and picture show good reasoning but are unclear or lack details.
· Student refers to place value in their explanation but does not clearly connect it to the task.
· Student generates another pair of numbers but the numbers don’t clearly highlight the concept being explained to Wallace and Logan. / Proficient in Performance
· Student identifies that Wallace is correct: eight-tenths is ten times larger than eight-hundredths.
· Student draws a picture and clearly explains why .8 is ten times larger than .08.
· Student includes references to place value in their explanation.
· Student generates another pair of numbers with the same digit in a different place. Student identifies that the digit in the place to the left is 10 times the value of the same digit in the other number.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
Value of a Digit
Part 1. Wallace and Logan were arguing about the size of 2 numbers. Wallace thought eight-tenths was ten times larger than eight-hundredths. Logan thought eight-hundredths was ten times larger than eight-tenths. Who is correct?
Part 2. Imagine you are the boys’ teacher. Draw a picture to help explain this concept to Wallace and Logan. Make sure you refer to place value in your explanation.
Part 3. Choose another pair of numbers that you could give to Wallace and Logan to assess whether they understand this concept. Which one is larger? How much larger?
Danny & Delilah5.NBT.1-Task 2
Domain / Number and Operations in Base Ten
Cluster / Understand the place value system.
Standard(s) / 5.NBT.1 Recognize that in a multi-digit number, a digit in ones place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Materials / Paper and pencil
Task / Danny and Delilah were playing a game where they drew digits and placed them on a game board. Danny built the number 247. Delilah built the number 724.
How much bigger is the 2 in Danny’s number than the 2 in Delilah’s number?
How much smaller is the 4 in Delilah’s number than the 4 in Danny’s number?
Write a sentence explaining how the size of the 7 in Danny’s number compares to the size of the 7 in Delilah’s number.
Rubric
Level I / Level II / Level III
Limited Performance
· Student does not have a clear enough understanding of place value to complete the task without assistance. / Not Yet Proficient
· Student understands that the values of the digits depend on their place in the number.
· Student is able to explain which digits are greater and which digits are less.
· Student does not use powers of 10 (10, 100, 1/10, 1/100) to compare the size of the numbers. / Proficient in Performance
· Student identifies that the 2 in Danny’s number is 10 times bigger than the 2 in Delilah’s number.
· Student identifies that the 4 in Delilah’s number is 1/10 the size of the 4 in Danny’s number.
· Student compares the size of the 7s in each number. Either of these sentences is correct: The 7 in Danny’s number is 1/100 the size of the 7 in Delilah’s number. The 7 in Delilah’s number is 100 times the size of the 7 in Danny’s number.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
Danny and Delilah
Danny and Delilah were playing a game where they drew digits and placed them on a game board. Danny built the number 247. Delilah built the number 724.
How much bigger is the 2 in Danny’s number than the 2 in Delilah’s number?
How much smaller is the 4 in Delilah’s number than the 4 in Danny’s number?
Write a sentence explaining how the size of the 7 in Danny’s number compares to the size of the 7 in Delilah’s number.
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Value of a Digit5.NBT.1 - Task 3
Domain / Number and Operations in Base Ten
Cluster / Understand the place value system.
Standard(s) / 5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Materials / Paper and pencil, Activity sheet
Task / Value of a Digit
Part 1. Sally and Tyrone were arguing about the size of 2 numbers. Sally thought six-tenths was one-tenth as large as six-hundredths. Tyrone thought six hundredths was one-tenth as large as six tenths. Who is correct?
Part 2. Imagine you are the students’ teacher. Draw a picture and use numbers to help explain this concept to Sally and Tyrone. Make sure you refer to place value in your explanation.
Part 3. Choose another pair of numbers that you could give to Sally and Tyrone to assess whether they understand this concept. Which one is larger? How much larger?
Rubric
Level I / Level II / Level III
Limited Performance
· Student does not identify that Tyrone is correct, or determines he is correct based on unsound reasoning.
· Student is unable to generate a picture to explain the concept.
· Student does not refer to place value in their explanation.
· Student does not generate another pair of numbers that fit with the concept. / Not Yet Proficient
· Student identifies that Tyrone is correct.
· Student’s explanation and picture show good reasoning but are unclear or lack details.
· Student refers to place value in their explanation but does not clearly connect it to the task.
· Student generates another pair of numbers but the numbers don’t clearly highlight the concept being explained to Wallace and Logan. / Proficient in Performance
· Student identifies that Tyrone is correct: six hundredths is one-tenth as large as six tenths.
· Student draws a picture and clearly explains why .06 is one-tenth as large as 0.6.
· Student includes references to place value in their explanation.
· Student generates another pair of numbers with the same digit in a different place. Student identifies that the digit in the place to the right is one-tenth times the value of the same digit in the other number.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
Value of a Digit
Part 1. Sally and Tyrone were arguing about the size of 2 numbers. Sally thought six-tenths was one-tenth as large as six-hundredths. Tyrone thought six hundredths was one-tenth as large as six tenths. Who is correct?
Part 2. Imagine you are the students’ teacher. Draw a picture and use numbers to help explain this concept to Sally and Tyrone. Make sure you refer to place value in your explanation.
Part 3. Choose another pair of numbers that you could give to Sally and Tyrone to assess whether they understand this concept. Which one is larger? How much larger?
Comparing Digits5.NBT.1-Task 4
Domain / Number and Operations in Base Ten
Cluster / Understand the place value system.
Standard(s) / 5.NBT.1 Recognize that in a multi-digit number, a digit in ones place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Materials / Paper and pencil, Activity sheet, Base ten blocks (optional)
Task / Comparing Digits
Tammy and Timmy were talking about the numbers 1,253 and 2,135.
Part 1:
With base ten blocks show or draw a picture of both numbers.
Part 2:
What is the value of the 1 in both of the numbers? How does the value of the 1 in the first number compare to the 1 in the second number?
Part 3:
What is the value of the 3 in both of the numbers? How does the value of the 3 in the first number compared to the value of the 3 in the second number?
Rubric
Level I / Level II / Level III
Limited Performance
· Student does not have a clear enough understanding of place value to complete the task without assistance. / Not Yet Proficient
· Student is unable to get / Proficient in Performance
· Part 1: The base ten blocks or picture of base ten blocks is correct.
· Part 2: Student identifies that the 1 in first number is 10 times bigger than the 1 in the second number.
· Part 3: Student identifies that the 3 in the first number is 1/10 the size of the 3 in the second number.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
Comparing Digits
Tammy and Timmy were talking about the numbers 1,253 and 2,135.
Part 1:
With base ten blocks show or draw a picture of both numbers.
Part 2:
What is the value of the 1 in both of the numbers? How does the value of the 1 in the first number compare to the 1 in the second number?
Part 3:
What is the value of the 3 in both of the numbers? How does the value of the 3 in the first number compared to the value of the 3 in the second number?
Veronica’s Statement5.NBT.2 - Task 1
Domain / Number and Operations in Base Ten
Cluster / Understand the place value system.
Standard(s) / 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Materials / Paper and pencil
Task / · In class Veronica told her teacher that when you multiply a number by 10, you just always add 0 to the end of the number. Think about her statement (conjecture), then answer the following questions.
· When does Veronica’s statement (conjecture) work?
· When doesn’t Veronica’s statement (conjecture) work?
· Is the opposite true? When you divide a number by 10, can you just remove a 0 from the end of the number? When does that work? When doesn’t that work?
· Rewrite Veronica’s statement (conjecture) so that it is true for ALL numbers. Write a statement (conjecture) about what happens when you divide a number by 10.
· Rewrite your statement (conjecture) again so that it applies to other powers of 10.
· Explain how these statements (conjectures) are related to place value. (HINT: Think about the decimal point!)
Rubric
Level I / Level II / Level III
Limited Performance
· Student is unable to explain why Veronica’s conjecture is incorrect.
· Student is unable to generate a conjecture that is correct for all numbers, or adjust the conjecture so that it applies to division and other powers of 10.
· Student is unable to explain how the task relates to place value. / Not Yet Proficient
· Student explains that Veronica’s conjecture is not always correct and gives some examples of when it will and won’t work.
· Student rewrites Veronica’s conjecture but it may not be true of all numbers.
· Student has difficulty generating conjectures for dividing by 10 and for working with other powers of 10. Student exhibits some sound and some faulty reasoning.
· Student makes some connection to place value, but explanation does not refer to the movement of the decimal point. / Proficient in Performance
· Student explains that Veronica’s conjecture is only true for whole numbers and will not work for decimals.
· Student explains that the opposite (dividing by 10 and removing a 0) will only work for whole numbers that end in 0.
· Student generates a conjecture about multiplying by 10 that is true for all numbers.
· Student adjusts their conjecture so that it applies to other powers of 10.
· Student’s explanation includes a description of how the decimal point moves when you multiply or divide by a power of 10.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
Veronica’s Statement