Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Purpose and Instructional Strategies
In grade 8, students generated equivalent algebraic expressions using the Laws of Exponents
with integer exponents. In Algebra I, students expand this work to include rational-number
exponents. In later courses, students extend the Laws of Exponents to algebraic expressions with
- Instruction includes using the terms Laws of Exponents and properties of exponents
- Instruction includes student discovery of the patterns and the connection to mathematical
- Students should be able to fluently apply the Laws of Exponents in both directions.
- For example, students should recognize that 6 is the quantity (3)2; this may
helpful when students are factoring a difference of squares.
- When generating equivalent expressions, students should be encouraged to approach
from different entry points and discuss how they are different but equivalent strategies
- The expectation for this benchmark does not include the conversion of an algebraic
expression from exponential form to radical form and from radical form to exponential
Common Misconceptions or Errors
- Students may not understand the difference between an expression and an equation.
- Students may not have fully mastered the Laws of Exponents and understand the
mathematical connections between the bases and the exponents.
- Student may believe that with the introduction of variables, the properties of exponents
differ from numerical expressions.
Strategies to Support Tiered Instruction
- Instruction includes the opportunity to distinguish between an expression and an
equation. These should be captured in a math journal.
- For example, when generating equivalent expressions, place an equal sign in
between the expressions and label each expression and the equation.
- Instruction provides opportunities to write each term in expanded form first and then use
Laws of Exponents to combine like factors. It may also be helpful to chunk each step.
- For example, to rewrite the expression (83)2 with one exponent, write out
(8)()()()(8)()()() and then use the commutative property to write
(8)(8)()()()()()() = 646.
- Teacher provides instruction for problems that require multiple applications of the Laws
of Exponents by chunking the steps so that students are applying one property at each
time and explaining the property applied. Each time ask students to identify the property
of exponents that they applied.
- Teacher provides students side-by-side problems, one with variable bases and the other
choosing a value for the variable. As students work through the problems, ask them about
the similarities in the problem-solving process.
- For example, teacher can model generating equivalent expressions like the ones
Teacher provides a review of the relationship between the base and the exponent by
modeling an example of operations using a base and exponent.
- For example, determine the numerical value of 63.
- 63 which is equivalent to 6 ⋅ 6 ⋅ 6 which is equivalent to 216.
- Given the function () = 100.2 , what is the rate of growth or decay?
- Instructional Task 2 (MTR.3.1, MTR.4.1)
- Part A. Write the algebraic expression as an equivalent expression where each variable only appears once.
- Part B. Compare your method of simplifying with a partner.
- Given the algebraic expression 2.32−1, create an equivalent expression.
- Use the properties of exponents to create an equivalent expression for the given expression
shown below with no variables in the denominator.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.