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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
- Assessment Limits :
s Exponents must be integers. Bases must be whole numbers. Variables may not be used. - Calculator :
No
- Context :
No context
- Test Item #: Sample Item 1
- Question:
Which expression is equivalent to
? - Difficulty: N/A
- Type: MC: Multiple Choice
- Test Item #: Sample Item 2
- Question:
Which expression is equivalent to
? - Difficulty: N/A
- Type: MC: Multiple Choice
- Test Item #: Sample Item 3
- Question:
An equation is shown.
What are possible values for m and n?
- Difficulty: N/A
- Type: EE: Equation Editor
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
This low-tech lesson will have students stand up holding different exponent cards. This will help them write and justify an equivalent expression and see the pattern for expressions with the same base and descending exponents. What happens as you change from 2 to the fourth power to 2 to the third power; 2 to the second power; and so forth? This is an introductory lesson to two of the properties of exponents:
and 
Type: Lesson Plan
Problem-Solving Tasks
Student Center Activity
Tutorials
Video/Audio/Animations
MFAS Formative Assessments
Students are given numerical expressions and asked to use properties of integer exponents to find equivalent expressions.
Students are asked to complete a table of powers of three and provide an explanation of zero powers.
Students are asked to apply the properties of integer exponents to generate equivalent numerical expressions.
Students are given expressions with negative exponents and are asked to identify those that are equivalent from given sets of expressions.
Student Resources
Problem-Solving Task
This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. It is good for students to learn the convention that negative time is simply any time before t=0.
Type: Problem-Solving Task
Student Center Activity
Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.
Type: Student Center Activity
Tutorials
This video discusses exponent properties involving products.
Type: Tutorial
This video models how to use the Quotient of Powers property.
Type: Tutorial
This tutorial shows students the rule for negative exponents. Students will see, using variables, the pattern for negative exponents.
Type: Tutorial
In this tutorial, students will learn about negative exponents. An emphasis is placed on multiplying by the reciprocal of a number.
Type: Tutorial
In this tutorial, you will apply what you know about multiplying negative numbers to determine how negative bases with exponents are affected and what patterns develop.
Type: Tutorial
This tutorial reviews the concept of exponents and powers and includes how to evaluate powers with negative signs.
Type: Tutorial
This tutorial demonstrates how to use the power of a power property with both numerals and variables.
Type: Tutorial
If a term raised to a power is enclosed in parentheses and then raised to another power, this expression can be simplified using the rules of multiplying exponents.
Type: Tutorial
Any expression consisting of multiplied and divide terms can be enclosed in parentheses and raised to a power. This can then be simplified using the rules for multiplying exponents.
Type: Tutorial
Video/Audio/Animations
Exponentiation can be understood in terms of repeated multiplication much like multiplication can be understood in terms of repeated addition. Properties of multiplication and division of exponential expressions with the same base are derived.
Type: Video/Audio/Animation
Integer exponents greater than one represent the number of copies of the base which are multiplied together. hat if the exponent is one, zero, or negative? Using the rules of adding and subtracting exponents, we can see what the meaning must be.
Type: Video/Audio/Animation
Exponential expressions with multiplied terms can be simplified using the rules for adding exponents.
Type: Video/Audio/Animation
Exponential expressions with divided terms can be simplified using the rules for subtracting exponents.
Type: Video/Audio/Animation
Exponential expressions with multiplied and divided terms can be simplified using the rules of adding and subtracting exponents.
Type: Video/Audio/Animation
Parent Resources
Problem-Solving Tasks
This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass. The solution below converts the mass of humans into grams; however, we could just as easily converted the mass of ants into kilograms. Students are unable to go directly to a calculator without taking into account all of the considerations mentioned above. Even after converting units and decimals to scientific notation, students should be encouraged to use the structure of scientific notation to regroup the products by extending the properties of operations and then use the properties of exponents to more fluently perform the calculations involved rather than rely heavily on a calculator.
Type: Problem-Solving Task
This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. It is good for students to learn the convention that negative time is simply any time before t=0.
Type: Problem-Solving Task
Tutorials
This tutorial reviews the concept of exponents and powers and includes how to evaluate powers with negative signs.
Type: Tutorial
This tutorial demonstrates how to use the power of a power property with both numerals and variables.
Type: Tutorial
