## Teacher Guide

### Creating Equations

#### Getting Started

A fun way to introduce equations is with a math game called "Magic Squares."

In Magic Squares, the player is presented with an empty 3 × 3 grid and has to write the numbers 1-9, one number per cell, such that the sums of each row and each column are all the same.

Start your class with a magic square that has the numbers 2, 9, 4 in the top row, 5 in the very middle space, and 6 in the lower left space. The first row tells the player that the required sum for each row and column is 15. Using the middle column, a player can calculate the number in the middle of the bottom row, using the equation 9 + 5 + X = 15. Using proper algebraic procedures, place a -9 and -5 on both sides of the equation to isolate X. It's important that your students understand how to add and subtract integers when calculating the answer.

Let your class go from there. Students can then use the same method to solve for the remaining squares.

#### Opening Discussion

Equations are a useful tool when solving for an unknown variable. They can be useful when completing everyday activities such as going to the bank or renting a car.

Equations always include:

- one or more variables
- one or more constants
- one or more coefficients
- an 'equals' sign

Write an equation on the board and highlight the specific parts listed above. Construct an equation with your class that represents an activity that your students can relate to, for example, going to the state fair:

*Johnny goes to the state fair and spends $8 to enter the fairgrounds. To go on the rides, Johnny must buy coupons that cost $2 per ticket. If Johnny spends $32 at the fair, how many coupons did he buy?*

*The equation would be written as: 8 + 2x = 32**Isolate x by subtracting 8 from both sides: -8 +8 +2x = 32 - 8 or 2x = 24**Remove the coefficient (2) by dividing both sides of the equation by that number: 2x / 2 = 24 / 2 or x = 12**The unknown number, x, is therefore 12*

**Extra Practice**

- 4x + 6 = 26 (5)
- 2x - 9 = 31 (20)
- x/4 + 2 = 6 (16)
- 2x/3 + 6 = 10 (6)
- 5x + 8 - 18 = 0 (2)
- 5(x + 3) - 10 = 20 (3)

### Activities:

- Make a Graphic Novel, Storyboard, or ...
##### Equations in Everyday Life

View Activity - Make a Storyboard
##### Equations in Science

View Activity - Extension / Modification
##### Challenge

*(Extension / Modification)*Solve questions with x and y variables (functions) where the y variable can be substituted with an equation containing x, e.g. 2x + 3y = 12 where y = 2x +3.

- Extension / Modification
##### Explore

*(Extension / Modification)*Have students create their own algebra "color by number" activity sheet.

### Concluding Discussion

Understanding equations is an essential skill. Explore a variety of science equations by manipulating the equation so that every variable has been solved for. Examples of scientific equations include:

- Ohm’s Law
- concentration
- molarity
- velocity
- speed
- pressure
- kinetic energy