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-Aligned Strategies About UDL

  • 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.
  • 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.
  • 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.

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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.

Write Repeated Addition Sentence

By (date), when given (2-4) groups that each contain the same number of tangible objects (e.g. jelly beans, erasers, small toys), (name) will write a repeated addition sentence to represent the total number of objects on a graphic organizer and solve, for (3 out of 3) repeated addition exercises.

Makes Visual Representations of Word Problems

By (date), given a (1)-sentence word problem involving multiplication (e.g., Sarah makes 10 bracelets in an hour, how many bracelets will she make in 3 hours?”), a multiplication chart, and graph paper, (student) will develop a visual representation of the problem (e.g., draw 3 boxes and 10 lines/bracelets in each box) correctly for (4) out of (5) math problems.

Recognize Equivalent Equations

By (date), after a review of the associative and commutative addition rules, when given an illustrated addition equation with (2) or more single-digit addends (e.g. 5 + 2 + 3 = 10), (name) will choose the equivalent illustrated equation from a bank of (3) options, for (3 out of 3) addition equations.

Writing Expressions for Problems with Percents

By (date), (name) will correctly write algebraic expressions for problems involving percents (e.g. new enrollment from percent increase in number of students, sale price due to percent decrease in original price) for (4 out of 5) problems.

Recognize Equivalent Equations

By (date), after a review of the associative and commutative addition rules, when given an illustrated addition equation with (2) or more single-digit addends (e.g. 5 + 2 + 3 = 10), (name) will choose the equivalent illustrated equation from a bank of (3) options, for (3 out of 3) addition equations.

Write Repeated Addition Sentence

By (date), when given (2-4) groups that each contain the same number of tangible objects (e.g. jelly beans, erasers, small toys), (name) will write a repeated addition sentence to represent the total number of objects on a graphic organizer and solve, for (3 out of 3) repeated addition exercises.

Makes Visual Representations of Word Problems

By (date), given a (1)-sentence word problem involving multiplication (e.g., Sarah makes 10 bracelets in an hour, how many bracelets will she make in 3 hours?”), a multiplication chart, and graph paper, (student) will develop a visual representation of the problem (e.g., draw 3 boxes and 10 lines/bracelets in each box) correctly for (4) out of (5) math problems.

Finding the Area and Circumference of a Circle

By (date), when given (5) problems on finding the area or circumference of a circle with a geometric component (e.g. radius, length of side of inscribed square) labeled, (name) will find the area or circumference of a circle by using the correct formula (e.g. A = π*r^2, C = 2*π*r) for (4 out of 5) problems.

Properties of Integer Exponents

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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").

Write Repeated Addition Sentence

By (date), when given (2-4) groups that each contain the same number of tangible objects (e.g. jelly beans, erasers, small toys), (name) will write a repeated addition sentence to represent the total number of objects on a graphic organizer and solve, for (3 out of 3) repeated addition exercises.

Makes Visual Representations of Word Problems

By (date), given a (1)-sentence word problem involving multiplication (e.g., Sarah makes 10 bracelets in an hour, how many bracelets will she make in 3 hours?”), a multiplication chart, and graph paper, (student) will develop a visual representation of the problem (e.g., draw 3 boxes and 10 lines/bracelets in each box) correctly for (4) out of (5) math problems.

Recognize Equivalent Equations

By (date), after a review of the associative and commutative addition rules, when given an illustrated addition equation with (2) or more single-digit addends (e.g. 5 + 2 + 3 = 10), (name) will choose the equivalent illustrated equation from a bank of (3) options, for (3 out of 3) addition equations.

Proving Polynomial Identities

By (date), when given a polynomial identity (e.g. x^2 - y^2 = (x + y)(x - y)), (name) will substitute given values (e.g. x = 6 and y = 2) and check if both sides of the identity are equal; for cases where equality is shown using numerical values, (name) will use algebraic operations (e.g. distributive property, collecting like terms) to prove that the polynomials are equivalent expressions for (4 out of 5) problems.

Equivalent Exponential Expressions

By (date), when given an exponential function for a real-world problem (e.g. population of bacteria P(t) = 1000e^(.25*t), t in hours; amount after compounding interest A(t) = 500*(1.05)^t, t in years), (name) will use the properties of exponents (e.g. power rule x^(m*n) = (x^m)^n) and a calculator to write an equivalent expression and determine the required rate of growth or decay for (4 out of 5) problems.

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 ...