Standard #: MA.912.NSO.1.3

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.912.AR.5.2
• MA.912.AR.5.4
• MA.912.AR.5.6
• MA.912.AR.5.7 
• MA.912.AR.7.1 
• MA.912.F.1.2
• MA.912.F.1.6

 

Terms from the K-12 Glossary

• Base 
• Exponent 
• Expression 
• Rational Number

 

Vertical Alignment

Previous Benchmarks

• MA.8.AR.1.1

Next Benchmarks

 

Purpose and Instructional Strategies

In Algebra I, students generated equivalent algebraic expressions with rational-number exponents and performed operations with numerical expressions involving square or cube roots. In Math for College Algebra, students extend the Laws of Exponents to algebraic expressions involving radicals. 

• Instruction includes using the terms Laws of Exponents and properties of exponents interchangeably. 
• Instruction includes student discovery of the patterns and the connection to mathematical operations (MTR.5.1). 
• Students should be able to fluently apply the Laws of Exponents in both directions. 
  • For example, students should recognize that $a$⁶ is the quantity ($a$³)², this may be 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 (MTR.2.1). 
• It is important to reinforce and activate the prior knowledge of simple calculations with radicals within this benchmark.

 

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. 
• Students may not know how to do simple calculations with radicals; therefore, they may not take the square root of the perfect square factor, or they may suggest using a factor pair within a radical that does not contain a perfect square as a factor. 
• Students may confuse radicands and coefficients and perform the operations on the wrong part of the expression. 
  • For example, express (2$p$)^{$\frac{\text{1}}{\text{5}}$} in radical form. The correct answer is $\sqrt[\mathrm{<i>5</i>}]{\mathrm{2p}}$ instead of 2$\sqrt[5]{\mathrm{p}}$.

 

Instructional Tasks

Instructional Task 1 (MTR.2.1, MTR.3.1, MTR.5.1) 

• Evaluate the expression √($\sqrt[3]{64}$). Compare your strategy with a partner.

Instructional Task 2 (MTR.2.1, MTR.3.1, MTR.5.1) 

 

• Part A. Without the use of technology, graph $f$($x$) = $\sqrt[3]{\mathrm{x}}$ over the domain −1 ≤ $x$ ≤ 1.
• Part B. Without the use of technology, graph $f$($x$)= $x$^{$\frac{\text{2}}{\text{3}}$} over the domain −1 ≤ $x$ ≤1.
• Part C. Compare the graphs from Part A and Part B.

• Express the following as a radical (36$x$⁴)^0.5.

Instructional Item 2 

• Expression 5$\sqrt[3]{\mathrm{abc}}$ as an expression with exponents.

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.