Math Teacher Notes

MA.A.3.3.2
MA.D.1.3.1
MA.E.1.3.1
MA.E.1.3.3
MA.E.3.3.1

Conceptual Knowledge
Linear Equations
Graphing Calculators
Interpret Data

Procedural Knowledge
y = mx + b
Graphing Linear Equations
Graphing Calculator Commands
Make Predictions

Problem Solving
Reasoning
Communication
Connections
Representation

It is Saturday and the new water theme park has just opened. You
and your friends are making plans to attend. You check the plans
at the ticket counter, and since you have a limited amount of
money, you want the best buy.

Students work individually or in pairs

Graphing Calculator

Study the two plans below and then decide which plan you will
recommend to your friends.

Plan A	Plan B
$ 5.00 admission	$ 10.00 admission
$ 1.00 per ride	$ .50 per ride

Which plan will you recommend? ___________
Why? (be specific and write complete sentences)
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________

Calculate the total cost under both plans for riding 0, 1, 2, 3, 4, 5,
and 6 rides. Do this without a calculator.

Plan A		Plan B
Rides	Total Cost	Rides	Total Cost
1		1
2		2
3		3
4		4
5		5
6		6

Describe how to find the total cost of going under Plan A and riding any number of rides .

The total cost will equal _____ plus _____ times the number of rides.

Describe how to find the cost using symbols only !
Use Y to equal the total cost and X to equal the number of rides.
Y = _____ + _____X

Describe how to find the total cost of going under Plan B and riding any number of rides.

The total cost will equal _____ plus _____ times the number of rides.

Describe how to find the cost using symbols only!
Use Y to equal the total cost and X to equal the number of rides.
Y = _____ + _____X

Now use the graphing calculator to see the graphs of the equations that you have written .
Press [Y=] and type in your equation for Plan A next to Y1 =.
Press [ENTER] and type in your Plan B equation next to Y2 =.
Press [ZOOM] 6 to see the graphs of the equations.
Press [ZOOM] 8 [ENTER] to see the equations in an integer window.

Now press [TRACE] and use the arrow keys to trace along the
equations. The left and right arrow keys trace along a graph and
the up and down arrow keys change the graph that is being traced.
If you do not see and equation at the top left corner of the screen,
press [2nd] [ZOOM], highlight ExprOn, and press [ENTER].
Press [GRAPH] to see the lines. The equation tells you which
graph you are currently tracing, Plan A is Y1 and Plan B is Y2.

Trace along the appropriate line and answer the following questions using your graphs.

1. If I ride 9 rides under Plan A, it will cost _____ .
2. If I ride 9 rides under Plan B, it will cost _____ .
3. If I ride 30 rides under Plan A, it will cost _____ .
4. If I ride 30 rides under Plan B, it will cost _____ .
5. If I spent $15 under plan A, how many rides did I ride_____ ?
6. If I spent $20 under plan B, how many rides did I ride_____ ?
7. When would it cost the same under both plans?
______________________________________________________
8. Explain what you see on the graph that shows you this.
______________________________________________________
9. When would it cost more under Plan A?
______________________________________________________
10. Explain what you see on the graph that helps you to
determine this.
______________________________________________________
11. When would it cost less under Plan A?
______________________________________________________
12. Explain what you see on the graph that helps you to
determine this.
______________________________________________________
13. Comparing the graphs of Plan A and B, which of the lines is
steeper and what does this mean as it relates to the total cost?
______________________________________________________
14. Predict what the line would look like if you graphed the
following situations:
a. a plan that has no admission price and each ride is $3.00
______________________________________________________
b. a plan that has $25 admission price and no charge for the rides
______________________________________________________
c. a plan that has $5 admission price for 3 free rides, then $1 for each additional ride
______________________________________________________

As a result of this activity, students will learn how a system of
equations can be used to find the best use of information to make
decisions in real world situations.