### Examples

The product of (1.1+x) and (-2.3x) can be expressed as -2.53x-2.3x² or -2.3x²-2.53x.### Clarifications

*Clarification 1:*Problems are limited to products where at least one of the factors is a monomial.

*Clarification 2:* Refer to Properties of Operations, Equality and Inequality (Appendix D).

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**8

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Coefficient
- Linear Expression
- Rational

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 7, students applied properties of operations to add and subtract linear expressions with rational coefficients. Additionally, students determined if two linear expressions were equivalent. In grade 8, students apply properties of operations to multiply two linear expressions with rational coefficients. In Algebra 1, students will add, subtract, multiply and divide polynomial expressions.- 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.

- 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.

- 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

*Instructional Task 1*

**(MTR.4.1)**- Part A. Is Kevin’s answer correct?
- Part B. If no, explain his misconception and how he can correct his mistake. If yes, explain why he is correct and the steps he could have used.

*Instructional Task 2*

**(MTR.7.1)**- 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.*

## Related Courses

## Related Access Points

## Related Resources

## Lesson Plan

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## Student Resources

## Problem-Solving Tasks

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Type: Problem-Solving Task

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. This exercise turns the focus away from the familiar "finding the solution" problem to thinking about what it really means for a number to be a solution of an equation.

Type: Problem-Solving Task

## Parent Resources

## Problem-Solving Tasks

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Type: Problem-Solving Task

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. This exercise turns the focus away from the familiar "finding the solution" problem to thinking about what it really means for a number to be a solution of an equation.

Type: Problem-Solving Task