Lesson Plan 2.3: Applications of Linear Equations[edit]

Objectives:[edit]

Students should be able to translate verbal statements into mathematical statements and vice versa.
Students should be able to set up and solve simple word problems related to interest, distance, currency, and mixing applications.

MWF: You have three days. The first day, get through at least Problem 4. The second day, lecture on distance and mixing problems. The third day, lecture on interest and currency problems.
MW/TR: You have two days. The first day, get through Problem 4 and lecture on distance problems. The second day, lecture on mixing, interest, and currency problems.

For this entire section, stress to students to declare their variables. Make an example while lecturing by doing the same yourself.
This is a long section. The story problems will take students a long time. For time purposes, it's not a bad idea to use workbook problems as class examples.

Provide many examples of changing from verbal to mathematical and vice versa, such as:
- "The sum of 5 and r" translates to: 5+r
- "Three-fourths of the difference of 13 and x" translates to (3/4)*(13-x)
- (7y-z)/2 translates to "half the difference of 7 times y and z"
Take the opportunity to point out where parentheses are important, and key words such as "of" and the ordering of terms after "difference."
Have students work on problems 1-3.
Work through the following problem on the board (or some other short problem that does not fit into the below categories). Emphasize the transition between the statement of the question and the mathematical statement that you can construct from it.
- If three more than half the number of kittens your friend Teri owns is 10, how many kittens does Teri own?
Explain to students that when problems are similar, we can come up with formulas so we don't have to start from scratch every time to motivate talking about “Distance,” “Mixing,” “Interest/Percent,” and “Currency” problems.

Start problem 4 together on the board, then have students finish it in their groups. It should *theoretically* walk them through the process of solving everything.
Let the students work on problem 4 for a while before reminding them of the distance formula, d=rt. Be sure to remind them what all these variables represent.
For all the problems of this type, encourage students to draw pictures with arrows labeled with the information they are given.
Work one of these problems from the workbook with the class, then have them work on the remainder in their groups. Remember to stress declaring variables.

Work problem 8 as a class and have students do the other in groups.
You'll need to take special care to point out that in problem 9, water is 0% sulfuric acid.
Students often have a lot of trouble with these types of problems. One way to try to alleviate this is to teach them using pictures. For example, for problem 8, you might set up the problem like this on the board:

It might also be helpful to set up a table with the following information:

Have students talk about problem 10 in groups and perhaps initiate a group discussion on this idea.

Remind students that we have previously used interest in this course both as principal earned on things like bank accounts and as taxes or tips on purchases or services.
Work through problem 4 on the reading guide as a class. Again, make a big deal about declaring your variables.
Have students work on problems 11-12.

Remind your students that (monetary units of the same kind) * (worth or denomination) = (total monetary value).
Do a quick, simple example, then let students try problem 13 on their own.

Although the formula speed = distance/time might be a more intuitive way of thinking about distance problems, it might be more helpful to first show students the formula distance=speed*time. (Starting with this formula makes solving for time more straightforward for students.)

Question 10: Students often give up on these types of "why" questions, but encourage them to talk it out in their groups.