The key components of pre-algebra include integers (positive and negative numbers), exponents and square roots. A lot of students have problems with pre-algebra because it is too abstract and does not seem to be related to real life. Use these real-world examples to bring the subject to life and to show how shoppers, travelers and construction workers use math every day.

## Master Positive and Negative Numbers by Shopping

Pretend to go shopping; buy whatever you like, but make sure you "accidentally" spend more money than you have. For example, you have $100 in your checking account. Buy a PlayStation game for $39 with your debit card. That leaves you $61. Buy lunch for $7, and you will have $54 in your account. Now purchase a pair of shoes for $56, and watch your account show a deficit of $2. The bank charges an overdraft fee of $35. Since you're now at -$37, you deposit $60 to bring your balance to $23.

In algebra, the shopping experience would be expressed this way:

100 - 39 = 61

61 - 7 = 54

54 - 56 = -2

-2 + (-35) = -37

-37 + 60 = 23

## Use Temperature to Understand Positive and Negative Numbers

Say you travel from Minneapolis, where it is -16 degrees, then to Tallahassee, where it is 75 degrees warmer than Minneapolis. What is the temperature in Tallahassee?

(Put in mathematical terms: -16 + 75 = 59.) Now you fly to Phoenix, where the temperature is 23 degrees warmer than Tallahassee. What is the temperature in Phoenix? (59 + 23 = 82.) If you fly straight back to Minneapolis, you will notice a temperature drop of 100 degrees. How cold is it in Minneapolis? (82 - 100 = -18)

## Make a Math Notebook of Exponents

Exponents are used in many types of algebraic problems, such as monomials and polynomials. Have students decorate the cover of a spiral notebook or three-ring math binder with an exponent design. Their work of art will serve as a reminder of how exponents work all through the school year. (Note: The numbers in parentheses should be written as exponents.) Use a different color marker when you write the exponents to make them stand out:.

```
2 = 2(1) = 2
2 x 2 = 2(2) = 4
2 x 2 x 2 = 2(3) = 8
2 x 2 x 2 x 2 = 2(4) = 16
2 x 2 x 2 x 2 x 2 = 2(5) = 32
```

2 x 2 x 2 x 2 x 2 x 2 = 2(6) = 64

## Angles and the Pythagorean Theorem

Every right triangle is composed of two legs and a diagonal, which is named the hypotenuse. The first leg is called "a," and the second leg is called "b"; "c" is the hypotenuse.The Pythagorean theorem is a-squared + b-squared = c-squared.

For example, say there is a triangle where the "a" leg is 3 inches and the "b" leg is 4 inches. How long is the hypotenuse? 3-squared + 4-squared = c-squared. So, 9 + 16 = c-squared = 25. The square root of 25 is 5, so the hypotenuse is 5. The Pythagorean theorem, which uses exponents, is employed all the time in the real world. Home improvement projects are full of corners and right triangles to measure. Pretend you are building a deck and need to add a diagonal support to keep it from falling down. Measure the height (leg "a") and length (leg "b") of the deck. Use the Pythagorean theorem to determine the length of the diagonal support beam ("c," the hypotenuse) that you will need to cut and install.