## Writing and Solving One-Step Linear Equations In One Variable

Now that students have reviewed how to solve one-step linear equations in one variable, it is time they learn how to write these equations from written word problems. Learning how to solve word problems is why mathematics is so important in real life.

Materials: the poster with the three important ideas for solving equations; another poster of the four-step problem solving process

Preparation: Make a poster of the four-step problem solving process found on page 33 of the students' text.

Write the following problem on the board: Three soccer players want to buy their coach a present for \$19.50. The cost will be divided equally among the 3 players. How much is each player's share?

• Say: To help us understand this problem, we need to ask ourselves some questions. What is this problem asking us to find?
Students will say they are being asked to find what each player's share of the cost of the present will be.

• Say: Our variable will represent each player's share of the cost of the present. Let's label the variable s to represent a share.

• Ask: What information do we know that can help us solve this problem?
Students should say that there are 3 soccer players and a cost of \$19.50 for a present.

• Ask: A method that is often used to solve problems in mathematics is to write an equation and then solve the equation. Is there an equation we could write that would help us solve this problem?
Students should suggest the equation 3 s = \$19.50.

• Ask: Who would like to volunteer to come to the board and solve the equation using our three important ideas from yesterday.

• Have a student come to the board and solve the equation emphasizing getting the variable onto one side by itself, undoing the multiplication by dividing, and dividing both sides of the equation by 3 to keep the equation in balance. Make sure the student properly labels the answer.

• Say: Let's check the answer in the original equation. Does 3 times \$6.50 equal \$19.50? (Yes)

• Say: Let's look back at our answer, does it make sense? Does the answer of \$6.50 seem reasonable for the original problem?
Students should say that it does make sense because 3 times \$6 equals \$18, 3 times \$7 equals \$21, and \$19.50 is between \$18 and \$21.

• Say: Let's solve another word problem.
Write the following problem on the board: Randy bought a sweatshirt and a T-shirt for \$32.85. If the sweatshirt cost \$23.95, how much did he pay for the T-shirt?

• Ask: What are we trying to find in this problem?
Students will say they are trying to find the cost of the T-shirt.

• Ask: What do we know that will help us solve the problem?
Students should say they know that Randy bought a sweatshirt and a T-shirt and paid a total of \$32.85. They should also say they know that the sweatshirt cost \$23.95.

• Say: That's right. Could someone tell us an equation we could use to solve the problem?
Students may suggest a couple of equations. One would be \$23.95 + x = \$32.85. They may also suggest \$23.95 + x = \$32.85 or \$32.85 – \$23.95 = x.

• Ask: Who would like to come to the board and solve the equation?
Have a student come to the board and solve one of the equations. Be sure to stress the three important ideas to help solve linear equations shown on the poster. Also be sure students label the answer appropriately.

• Ask: What would I do to check to see if the answer of \$8.90 is correct?
Students should suggest substituting \$8.90 into the equation.