Properties of Integer Exponents

By (date), when given 5 mathematical expressions involving integer exponents, (name) will use the properties of integer exponents to generate an equivalent numerical... expressions and the final integer value correctly for (4 out of 5) expressions (e.g. "2^3 x 2^5 = 2^(3+5) = 2^8 = 256").
  • By (date), when given (5) mathematical expressions involving integer exponents and a color-coded glossary of the properties of integer exponents, (name) will use the properties of integer exponents to generate an equivalent numerical expressions and the final integer value correctly for (4 out of 5) expressions (e.g. "2^3 x 2^5 = 2^(3+5) = 2^8 = 256").
  • By (date), when given 5 mathematical expressions involving only positive whole-number integer exponents and bases and a color-coded glossary of the properties of integer exponents, (name) will use the properties of integer exponents to generate an equivalent numerical expressions and the final integer value correctly for (4 out of 5) expressions (e.g. "2^3 x 2^5 = 2^(3+5) = 2^8 = 256").
  • By (date), when given (5) expressions of integer exponents with a single term (e.g. "2^3"), (student) will select the equivalent expression in expanded form (e.g. "2 x 2 x 2") correctly for (4 out of 5) problems.

UDL Strategies About UDL

  • UDL I 3.2 Highlight patterns, critical features, big ideas, and relationships
    Teachers can color code the bases and exponents in different colors so that students can more easily distinguish between the two. Teachers can also color code similar bases so that students can clearly see which terms can be combined or simplified.
  • UDL II 4.1 Vary the methods for response and navigation
    Teachers can give students a variety of methods for responses to questions. Instead of having the student write the equivalent expression or final number, the student identify the correct final integer and intermediate equivalent expressions among fixed answer choices . Students can use a variety of methods to indicate which choice is correct such as verbal expression or using physical body motions such as tapping to indicate the correct answer.
  • Vary demands and resources to optimize challenge
    Teachers can scaffold the types of exponent expression they present to students. They can focus on only positive exponent relationships or only use positive integers up to 10. Teachers have the flexibility to teach the topic but increase the amount of arithmetic or number of simplification steps based on the abilities of the students.

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Common Core Standards

8.EE.1 Work with radicals and integer exponents
8.EE.1 Work with radicals and integer exponents
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/(33) = 1/27.

Standard Staircase

Evaluating Expressions Involving Whole Number Exponents

By (date), when given a problem involving a whole number exponent (e.g. with base that is a whole number, positive decimal, or positive fraction), (name) will use order of operations and the properties of exponents to write and evaluate the corresponding numerical expression for (4 out of 5) problems.

Equivalent Expressions

By (date), when given (5) problems involving writing or comparing equivalent linear expressions with rational coefficients, (name) will apply algebraic operations (e.g. collecting like terms, distributive property) to the linear expression to answer (4 out of 5) problems.

Properties of Integer Exponents Current Goal

By (date), when given 5 mathematical expressions involving integer exponents, (name) will use the properties of integer exponents to generate an equivalent numerical expressions and the final integer value correctly for (4 out of 5) expressions (e.g. "2^3 x 2^5 = 2^(3+5) = 2^8 = 256").

Referenced Strategies

  • Highlighting

    Highlighting could include highlighting key words/phrases, key points or arguments or text structures such as headings. This adaptation can ...

  • Multiple Choice

    Before students are comfortable generating a free-form response, they can demonstrate their knowledge by selecting the correct answer(s) fro...

  • Math Dictionary

    A math dictionary is a type of dictionary that contains mathematical terms, definitions and visual representations. The math dictionary may ...