# 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

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.

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