MA.8.AR.1.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.8.NSO.1.3
• MA.8.NSO.1.7

Terms from the K-12 Glossary

• Coefficient
• Linear Expression
• Rational

Vertical Alignment

Previous Benchmarks

• MA.7.NSO.1.1
• MA.7.NSO.2.2
• MA.7.AR.1.1
• MA.7.AR.1.2

Next Benchmarks

• MA.912.AR.1.3
• MA.912.AR.1.4
• MA.912.AR.1.7

Purpose and Instructional Strategies

• Instruction includes working with multiplying two linear expressions and connecting the distributive property.
• Instruction includes modeling this benchmark concretely. One way to do this is to model with algebra tiles to generate equivalent expressions.
  • For example, 2($x$ + 3) can be modeled using the algebra tiles to showcase the equivalent expression of 2$x$ + 6.
    
    
    
• Instruction moves from concrete models of examples with integer coefficients to rational coefficients.
• Instruction includes providing and discussing tasks that involve students analyzing errors which helps students with the ability to self-correct misconceptions within their own work.

Common Misconceptions or Errors

• Students may incorrectly apply the distributive property by multiplying the monomial to only one of the terms in the parentheses. To address this misconception, emphasize that it is the distributive property of multiplication over addition to help support student understanding.
• Students may incorrectly apply the rules of integers as they distribute when working with the operations of negative numbers and applying the distributive property of multiplication over addition.
• Students may incorrectly change the degree of the variable in order to simplify terms.

Strategies to Support Tiered Instruction

• Teacher models examples using the area model for multiplication, showing that the monomial should be multiplied by each term of the polynomial.
  • For example, the area model can be used to determine the product between 45 and 5 is 225. Once students understand how distribution works, teachers reintroduce variables and solve problems the same way.

• For example, the area model can be used to determine the product between $x$ −3 and 4 is 4$x$ −12.     

• For example, the area model can be used to determine the product between 3$y$ and $y$ + 2$y$² is 3$y$² + 6$y$³.
  
  
  
• If teachers did not utilize algebra tiles in whole group instruction, algebra tiles could be used when solving problems using the distributive property. This will help students who incorrectly distribute the monomial to only one term of the polynomial.
• Teachers may color code each step of the problem so students can see the progression of distribution.
  • For example, the expression 3($x$ + 7) is equivalent to 3$x$ +21.
    
    
    
• Instruction includes emphasizing that it is the distributive property of multiplication over addition to help support student understanding.

Instructional Tasks

A rectangle is given below. Note: The figure is not drawn to scale.

• Part A. Find the area in terms of $x$.
• Part B. If the value of $x$ is 4 cm, what is the area of the rectangle in square centimeters?

 

Instructional Items

Instructional Item 1
An expression is given below.
−$\frac{\text{7}}{\text{8}}$$x$ ($\frac{\text{3}}{\text{4}}$$x$ − $\frac{\text{5}}{\text{6}}$)
What is the product of the expression?

Instructional Item 2
Find the product of 0.25$x$(0.55$x$ − 0.3).

 

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

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