Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 59155
Paul’s Pennies
Students are asked to write and evaluate a numerical expression using exponents.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, numerical expression, exponent, base, power
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_PaulsPennies_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher ask the student to complete the problem on the Paul’s Pennies worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand what it means to write a numerical expression.
Examples of Student Work at this Level
The student:
Attempts to calculate the number of pennies Paul will receive on the eighth day.
page 1 of 3 Attempts to write an equation related to the problem context.
Questions Eliciting Thinking
What were you asked to do in this problem?
Do you know what a numerical expression is? Can you write an example of a numerical expression?
Do you know what an exponent is? Can you write an example of an exponential expression?
Can you explain the equation you wrote and how it relates to the number of pennies Paul will receive on the eighth day?
Instructional Implications
Define the terms numerical expression, algebraic expression, and equation. Provide numerous examples of each and ask the student to classify each example as one of these
three algebraic entities. Review vocabulary associated with various mathematical operations. Have the student make a chart or table that includes vocabulary that suggests
operations and examples of each. Provide the student with opportunities to practice writing numerical expressions from verbal descriptions.
Review the meaning of exponents. Define the terms base and exponent and explicitly describe the exponent as indicating the number of factors of the base. Ask the
student to write each quantity of pennies mentioned in the table from the worksheet for this task as factors of two (e.g., 8 = 2 x 2 x 2). Guide the student to extend the
table to the fourth through eighth days and write those entries as factors of two. Then ask the student to rewrite each quantity using exponents.
Provide additional opportunities to write numerical expressions involving exponents from verbal descriptions that arise in the context of problems.
Consider implementing MFAS task Cube House (6.EE1.1) for additional practice with exponents in context.
Moving Forward
Misconception/Error
The student writes an expression with exponents that is incomplete or incorrect.
Examples of Student Work at this Level
The student writes:
An expression that represents the number of pennies on the fourth day.
Exponential expressions for the first three entries in the table, some of which contain errors.
Questions Eliciting Thinking
How did you determine the exponent in your expression? What does the exponent mean?
Does the expression that you wrote represent the number of pennies Paul will receive on the eighth day?
Can you extend the pattern in the table to the fourth, fifth, and sixth days?
What relationship(s) do you see between each day and the number of pennies Paul received that day?
How many pennies is Paul's dad adding each day? Is there a pattern?
Instructional Implications
Review the meaning of exponents. Define the terms base and exponent and explicitly describe the exponent as indicating the number of factors of the base. Ask the
student to write each quantity of pennies mentioned in the table from the worksheet for this task as factors of two (e.g., 8 = 2 x 2 x 2). Guide the student to extend the
table to the fourth through eighth days and write those entries as factors of two. Then ask the student to rewrite each quantity using exponents.
Provide additional opportunities to write numerical expressions involving exponents from verbal descriptions that arise in the context of problems.
Consider implementing MFAS task Cube House (6.EE.1.1) for additional practice with exponents in context.
Almost There
Misconception/Error
The student writes the expression in terms of repeated factors but does not use exponents.
page 2 of 3 Examples of Student Work at this Level
The student represents the number of pennies Paul will receive on the eighth day as 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.
Questions Eliciting Thinking
Can you use exponents to write your answer in an equivalent form?
Instructional Implications
Review the meaning of exponents. Define the terms base and exponent and explicitly describe the exponent as indicating the number of factors of the base. Guide the
student to rewrite 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 using exponents. Provide additional opportunities to write numerical expressions involving exponents from verbal descriptions
that arise in the context of problems.
Consider implementing MFAS task Cube House (6.EE.1.1) for additional practice with exponents in context.
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 represents the number of pennies Paul will receive on the eighth day as
and correctly evaluates this expression as 256.
Questions Eliciting Thinking
Can you write a numerical expression involving exponents that represents the number of pennies Paul will receive on the 25th day?
Instructional Implications
Challenge the student with the following problem: What is the tens digit in the expansion of
? Allow the student to use a calculator to explore patterns in the smaller
powers of six.
Ask the student to create a word problem involving quantities that can be described using exponents to share with his or her classmates.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Paul’s Pennies 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.6.EE.1.1:
Description
Write and evaluate numerical expressions involving whole-number exponents.
page 3 of 3