## chapter 6 outline

**Section 6.1:**In this section, you will learn additional strategies for comparing expressions. The strategies will involve maintaining equivalence and determining relationships between expressions. You will also solve inequalities and represent their solutions on a number line.

**Section 6.2:**In this section, you will use algebra tiles to explore what you can learn when expressions are equal. Solving equations will also provide you an opportunity to develop efficient simplification strategies and to learn how to know that your solution is correct.

## Big Ideas

Simplify and compare two algebraic expressions.

Write and solve algebraic inequalities.

Solve for a variable when two expressions are equal.

Write and solve an equation to solve a word problem.

Write and solve algebraic inequalities.

Solve for a variable when two expressions are equal.

Write and solve an equation to solve a word problem.

## Guiding Questions

What is the relationship?

Are they equivalent?

How can I represent it?

How can I solve it?

Are they equivalent?

How can I represent it?

How can I solve it?

## vocabulary

5-D Process

boundary point

coefficient

constant term

Distributive Property

equation

Equation Mat

evaluate

expression

Expression Comparison Mat

factor

factoring

inequality

inequality symbols

proportional relationship

ratio

solution

simplify

term

variable

boundary point

coefficient

constant term

Distributive Property

equation

Equation Mat

evaluate

expression

Expression Comparison Mat

factor

factoring

inequality

inequality symbols

proportional relationship

ratio

solution

simplify

term

variable

## CCSS Standards in Unit

. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.__7.EE.3__*For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.*Solve word problems leading to equations of the form__7.EE.4a.__*px*+*q*=*r*and*p*(*x*+*q*) =*r*, where*p*,*q*, and*r*are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.*For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?*Solve word problems leading to inequalities of the form__7.EE.4b.__*px*+*q*>*r*or*px*+*q*<*r*, where*p*,*q*, and*r*are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.*For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make,**and describe the solutions.*