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.
- Ask: Does the answer make sense?
Students should say that it does, since adding $10.00 to $23.95 would give a value of $33.95, which is close to the actual sum.
Wrap-Up and Assessment Hints
There is a big difference between knowing "how to do" something and understanding "why you do" the things you do. For example, knowing that you must divide both sides of the equation 3 n = 15 by 3 in order to solve it, is different from understanding that when you divide the left side of the equation by 3, it makes the quantity equal to 1/3 of its original value. So, to have an equation that is a true statement, we need to do the same action on the right side of the equation to the number 15. Then the quantities remaining on both sides of the equation will be equal. When assessing students, ask them why they do the things they do, not just what they do. Ask questions which ensure an understanding of the three important ideas for solving linear equations. This will make the students' knowledge much richer and will extend to solving more difficult equations.