# Chapter 1: Using Algebra

## Introduction

Here you will get a preview of a variety of algebra topics. First, you will learn how to interpret data and represent data with bar graphs and histograms. Next, you will learn all about algebraic expressions, and how variables can help you to represent real-world problems with expressions. You will also be introduced to the idea of solving an equation, and the difference between an expression and an equation. You will see formulas as examples of equations that can be used to solve problems. Finally, you will learn how to make a problem solving plan.

## Chapter Outline

- 1.1. Interpret Given Bar Graphs
- 1.2. Understanding and Interpreting Frequency Tables and Histograms
- 1.3. Represent Real-World Data Using Bar Graphs, Frequency Tables and Histograms
- 1.4. Evaluate Numerical and Variable Expressions Using the Order of Operations
- 1.5. Connect Variable Expressions and the Order of Operations with Real-World Problems
- 1.6. Evaluate Numerical and Variable Expressions Involving Powers
- 1.7. Use the Order of Operations to Evaluate Powers
- 1.8. Evaluate Variable Expressions with Given Values
- 1.9. Translate Verbal Phrases into Variable Expressions
- 1.10. Write and Evaluate Variable Expressions for Given Situations
- 1.11. Solve and Check Single-Variable Equations Using Mental Math and Substitution
- 1.12. Solve Real-World Problems by Writing and Solving Single-Variable Equations
- 1.13. Find Perimeter and Area of Squares and Rectangles Using Formulas
- 1.14. Use the Formula for Distance to Find Distances, Rates and Times
- 1.15. Understand the Problem-Solving Plan
- 1.16. Solve Real-World Problems by Using Strategies and a Plan

### Chapter Summary

## Summary

You started by thinking about different kinds of data, and learned how to represent this data in either a bar graph or a histogram. You also learned how to interpret data that was represented by a graph.

Next, you learned about expressions. You learned to evaluate expressions by replacing a variable with a number and then used the order of operations to find your answer. You also learned how to write expressions to represent different situations.

Then you focused on equations, and learned that the difference between an expression and an equation is an equals sign. You learned to solve basic equations mentally by asking yourself what number the variable would have to be in order to make the equation true. You learned that you can write equations to represent real-world situations. Formulas are a good example of equations, and you used formulas to calculate perimeter, area, and distance/rate/time.

Finally, you started to think about problem solving. In math, you will often be presented with a problem that you don't know how to solve right away. It's important to have some problem solving strategies ready so that you don't just give up when presented with a difficult problem. Problem solving with a plan also helps you to communicate to other people what you are trying to do, the strategies you have tried, and why.