Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 56845
Using Whole Number Exponents
Students are asked to explain what 10 to the third power means and to rewrite 1,000,000 and a product of 10 using exponents.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, whole number exponents, powers of ten
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_UsingWholeNumberExponents_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 provides the student with the Using Whole Number Exponents worksheet and reads the directions with the student to ensure understanding.
2. After each of the problems, the teacher should ask the student, "Can you tell me how you got your answer? Can you explain your thinking?"
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the meaning of exponents and holds any of several misconceptions about using exponents.
Examples of Student Work at this Level
The student says, “
is 10 + 10 + 10 = 30.”
The student says, “
is 10 x 3 = 30.”
The student says, “
is 10 x 10 x 10 = 300.”
The student doesn’t understand how to write the number using exponents.
page 1 of 3 Questions Eliciting Thinking
What does this three mean as an exponent?
What part of the number is the base?
Have you heard the term “power” before?
What about squared or cubed? What do those terms means?
How many times are we multiplying 10? How can we show that with a base and an exponent?
Instructional Implications
Provide clear instruction on the meaning of exponents. Explicitly describe the exponent as indicating the number of factors of the base. To reinforce the meaning of the
exponent, initially encourage the student to write exponential expressions in expanded form before calculating (e.g.,
= 10 x
10 x 10 =1000).
Provide the student with sets of matching cards. One set of cards should contain numbers in standard notation. The other set contains the corresponding numbers written
in using exponents. Mix the cards up and have the student match a standard notation card to the correct exponential notation card.
Provide opportunities for the student to observe that the number of zeros in a power of 10, written in standard notation, is equal to the exponent when written in
exponential notation (e.g., 10,000 has four zeros, so the power of 10 is four which is 104 in exponential form). Consider using the MFAS task How Many Zeros (5.NBT.1.2).
Making Progress
Misconception/Error
The student has some understanding of the use of exponents but holds misconceptions about the process for writing numbers in exponential notation or his or her
explanation is inadequate.
Examples of Student Work at this Level
The student writes
The student writes
instead of
when asked to write 10 x 10 x 10 x 10 x 10 with exponents.
or
when asked to write 1,000,000 as a
power of 10 using exponents.
The student writes 1,000,000 x 1,000,000 x 1,000,000 x 1,000,000 x 1,000,000 x 1,000,000 x 1,000,000 x 1,000,000 x 1,000,000 x 1,000,000 when asked to write
1,000,000 as a power of 10 using exponents.
The student is able to correctly complete the task but is unable to explain the pattern in powers of 10 and exponents.
The student writes 10 (as opposed to one) and then adds zeros to convert to standard form. When writing 1,000,000 as an exponent, the student cuts off one of the
zeros as seen in the video below.
Questions Eliciting Thinking
What does the exponent tell you?
What number are you multiplying by?
How would you write 100 using exponents? How many tens would you multiply to get 100?
How many tens would you multiply to get 1,000? 10,000? 100,000? Is there a pattern that you notice?
Instructional Implications
Provide opportunities for the student to observe that the number of zeros in the expansion of 10 is equal to n. After the student understands this relationship, encourage
him or her to explain it using place value. e.g., When determining 10 the student might say, “You shift every digit three places to the left and replace with zeros because
multiplying by one 10 moves the digits one place to the left so multiplying by three tens moves the digits three times to the left.” Model for the student how to write a number as a power of 10 using exponents. Then provide opportunities for the student to work with a partner writing numbers as
powers of 10 using exponents and checking their work with one another.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
page 2 of 3 Examples of Student Work at this Level
The student explains that when multiplying by three factors of 10 the answer is 1,000 and that is 10 x 10 x 10.
The student writes 10 x 10 x 10 x 10 x 10 as
.
The student writes 1,000,000 as
.
The student is able to use patterns to find and explain answers.
Questions Eliciting Thinking
What does
What does
mean?
mean?
Instructional Implications
Consider using the MFAS task Multiplying By Ten Three Times (5.NBT.1.2) to help the student understand how to multiply a number by powers of 10.
Provide opportunities for the student to practice writing numbers in standard notation given the numbers written in exponential notation with a base other than 10.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Using Whole Number Exponents 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.
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