Application Lesson Plan
Objective: Given and real-life problem, the student determines how, if at all, the solutions to that
problem is facilitated by developing and graphing an equation (application).
Stage 1: Initial Problem Confrontation and Analysis
After having talked about how to graph equations, students are given the following two
problems to see which one we can find all solutions to by graphing.
1) Ashley and Josh won a contest for the 2010 World Cup final match in South Africa. With the
contest come tickets to the game, boarding, food, and transportation while they’re in South
Africa. All Ashley and Josh need to worry about is getting there. Josh, being the chivalrous one,
decides to pay for everything. His budget for the trip is $5200. Also, Josh is planning on buying a
ring while he’s there to propose to Ashley at the games half time show. Josh needs to find out
how best to use his budget to cover the airline tickets but still have enough left over to get a yes
out of Ashley. Give three possible solutions to how much josh could spend on each plane ticket
and the ring by graphing all possible solutions and picking what you think are the best three
options.
2) Ashley and Josh won a contest for the 2010 World Cup final match in South Africa. With the
contest come tickets to the game, boarding, food, and transportation while they’re in South
Africa. All Ashley and Josh need to worry about is getting there. Josh, being the chivalrous one,
decides to pay for everything. His budget for the trip is $5200. Ashley can’t “bear” the trip
without her lifelong stuffed animal Bruno, which is a 5-foot teddy bear. The cost of bringing the
bear is $75 each way. What is the most Josh can spend on airline tickets and stay within his
budget?
After being introduced to the problems, I lead the students in a discussion on how to solve the
problems and then explain why the objective’s content was used in the first problem but not the other.
Stage 2: Subsequent Problem Confrontation and Analysis
The students work in groups to solve the following problems:
1) Josh is going to buy a 30 GB iPod. He also needs to buy a car adapter and buy songs on i-tunes to
download to his iPod. A 30 GB i-Pod is $200, and each song on i-tunes is $1.29. Graph a line that
shows all possible ways Josh can spend his money if he has $350. If Josh wants to have at least
20 songs on his i-pod, and the better adaptors are generally more than $50, what are your 3
suggestions?
2) Josh is going to buy a 30 GB iPod. He also needs to buy songs on i-tunes to download to his iPod.
A 30 GB i-Pod is $200, and each song on i-tunes is $1.29. If Josh has $250, how many songs can
he buy?
The groups work together to solve the problems in a similar manner as in stage 1. After each group
has reached a conclusion, they share their results and discuss similarities and differences in the
problems.
Stage 3: Rule articulation
The students will work with their groups to develop rules for when the content of our objective
applies and when it does not. Each group will share their findings and we will have a class discussion on
similar and different findings from the groups. Students are expected to find that we use our objective
when there are 2 objectives. This allows us to put it in the form of y= ax + b and graph all solutions,
rather than just solving for one.
Stage 4: Extension into Subsequent Lessons
This lesson leads us right into solving systems of equations graphically.