Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 56825
Multiplying By Ten Three Times
Students consider why a number multiplied by 10 to the third power will have three zeros in the product.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, place value, zero, base ten, exponent
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_Multiplying By Ten Three Times_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
1. The teacher asks the student, “What is ?”
2. Next, the teacher asks, “Can you explain how you determined your answer”
3. The teacher then asks, “What do you notice about the number of digits that are zero in the product and the value of the exponent?”
4. If the student correctly responds to the question in step 3, the teacher asks, “Can you explain why the number of digits that are zero in the product is the same as the
value of the exponent?”
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to correctly calculate
.
Examples of Student Work at this Level
The student:
page 1 of 3 Calculates
as 10 x 3 = 30 or 10 + 10 + 10 = 30. Then the student multiplies 15 by 30 to complete the calculation.
Incorrectly multiplies 15 by 1000.
Questions Eliciting Thinking
What does
mean?
This expression could be read 15 times three factors of 10. How can that help you determine the product?
Can you explain how you multiplied 15 by 1000?
Instructional Implications
Provide direct instruction on the meaning of exponents. Encourage the student to initially write exponential expressions in expanded form. Guide the student to rewrite
as 15 x (10 x 10 x 10), calculate the value of (10 x 10 x 10), and then multiply 15 by this product.
If needed, provide the student with examples of multiplying a number by 10, 100, and then 1,000. Encourage the student to describe patterns in the products.
Consider using the MFAS task Using Whole Number Exponents (5.NBT.1.2) to assess a student's understanding of using whole number exponents to denote powers of 10.
Moving Forward
Misconception/Error
The student does not understand the relationship between number of digits that are zero in the product and the value of the exponent.
Examples of Student Work at this Level
The student correctly calculates the value of
but does not observe the relationship between the number of digits that are zero in the product and the value of the
exponent.
Questions Eliciting Thinking
How many zeros are in the product of 15 and
? Did you notice that this is the same as the value of the exponent? Do you think that this is just a coincidence or will this
always be the case?
Instructional Implications
Ask the student to expand and calculate
Assist the student in observing that the number of digits that are zero in each expansion corresponds
to the value of the exponent. Next ask the student to calculate products of numbers and powers of 10 such as
. Again, assist the student in observing
that that the number of digits that are zero in each expansion corresponds to the value of the exponent. Finally, provide additional expressions involving powers of 10 and
ask the student to predict the numbers of digits that are zero in the product.
Almost There
Misconception/Error
The student can identify the relationship between the number of digits that are zero in the product of
but cannot explain it.
Examples of Student Work at this Level
The student correctly calculates
and explains that there are three digits of zero in the product since the exponent is three. However, the student is unable to
offer any explanation for why this is the case.
Questions Eliciting Thinking
When you multiply other numbers by powers of 10, will the exponent always correspond to the numbers of zeros in the product? Why do you suppose this is? Can you
think of a mathematical reason for this?
Instructional Implications
Provide additional examples of products of numbers and powers of 10. Help the student to observe and explain the pattern in the zeros based on place value
understandings. For example, the student might explain that multiplying a whole number by 10 makes the number 10 times larger which means that the ones digit of the
product will be zero. Multiplying 10 (or a multiple of 10) by 10 results in a number with two zeros in its representation, one in the tens place (since the original number
contained a zero in its ones place) and one in the ones place (since multiplying this number by 10 makes it 10 times larger).
Expose the student to model explanations given by classmates.
page 2 of 3 Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly calculates
and explains that there are three digits of zero in the product since the exponent is three.The student explains that when
multiplying by three factors of 10, you are actually multiplying by 1000. Multiplying 15 by 1000 makes 15 a thousand times larger which is written 15,000.
Questions Eliciting Thinking
How many digits of zero are in the product of 20 and
? Can you explain why it is not the same as five, the exponent?
Instructional Implications
Encourage the student to consider multiplying decimal numbers by powers of 10. For example, ask the student to multiply 3.8 by
. Then challenge the student to
explain how to determine the number of digits that are zero in the product.
Consider using the MFAS task, The Error (5.NBT.1.2), to help the student understand how to multiply a decimal number by 10.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Multiplying By Ten Three Times worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.5.NBT.1.2:
Description
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 wholenumber exponents to denote powers of 10.
page 3 of 3