domino effectdomino effect packets/chapter 7 domino barbie.… · a medium, 3-topping pizza really...

Created by Lance Mangham, 6th grade math, Carroll ISD

Activity A-1: Domino Effect Name:

Adapted from Mathalicious.com

DOMINO EFFECTDOMINO EFFECTDOMINO EFFECTDOMINO EFFECT

Show all work and write all answers (other than the graphs) on a piece of notebook paper. Make

your work and answers easy to find and easy to understand. Problems with a W require

computation work to be shown.

Domino’s pizza is delicious. The company’s success is proof that people enjoy their pizzas. You can order online and they even have a pizza tracker so you can keep tabs on your delivery.

Domino’s does not tell you how much the component pieces cost; they only tell you an item’s final price after you build it. In this lesson we will use linear equations to find the base price and cost per additional topping.

PART 1

Below are prices for a medium 2-topping pizza and a medium 4-topping pizza from Domino’s in Washington, DC.

Medium (12”) Hand Tossed Pizza

Pepperoni, Green Peppers Price: $13.97

Medium (12”) Hand Tossed Pizza

Pepperoni, Italian Sausage, Onions, Green Peppers Price: $16.95

1. Plot the two points representing the pizzas on the included graph. Then use a ruler to draw a line connecting the two points and extending across the entire graph. (W)

2. Based on the information in the picture above how much does it appear Domino’s is charging for each topping?

3. A medium, 3-topping pizza really costs $15.46 at this Dominos. Does that match what you would expect? So far we have assumed each number topping costs the same amount. What would it mean if Dominos charged you a price different than $15.46 for a 3-topping pizza?

4. For the 2-topping pizza, how much in total are you spending on toppings? (W)

5. For the 4-topping pizza, how much in total are you spending on toppings? (W)

6. If you wanted to order a medium cheese pizza (no toppings), how much would you expect to spend? Explain. (W)



Often times linear equations are written in the format: y mx b= +

y is the dependent variable. x is the independent variable. m is the slope of the line. b is the y-intercept of the line.

This is called slope-intercept form.

7. In our pizza problem, which variable is the independent variable and which is the dependent variable?

8. Now write an equation in slope-intercept form for the price of a medium pizza.

9. Explain what each component of your equation above means.

10. Determine the cost of a 6 topping and a 12 topping pizza. Does a pizza with 12 toppings cost twice as much as a pizza with 6 toppings? Why or why not? (W)

11. Is your graph linear? How do you know?

12. Does your graph represent a proportional or non-proportional relationship? How do you know?

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Domino Effect



PART 2 Below are prices for two small pizzas and two large pizzas from Domino’s in Washington, DC.

Small (10”) Hand Tossed Pizza

Pepperoni Price: $9.99

Large (14”) Hand Tossed Pizza

Pepperoni, Italian Sausage, Onions, Green Peppers Price: $19.75

Small (10”) Hand Tossed Pizza

Pepperoni, Mushrooms, Green Peppers Price: $11.99

Large (14”) Hand Tossed Pizza

Pepperoni Price: $14.68

1. Plot the small and large pizzas on the same graph as the medium pizza, draw the lines with a ruler, and then use the information to answer the following questions.

2. How much does Domino’s appear to be charging for each topping on a small pizza?

3. How much does Domino’s appear to be charging for each topping on a large pizza? (W)

4. How much would a small pizza with no toppings cost?

5. How much would a large pizza with no toppings cost? (W)

6. Now write an equation in slope-intercept form for the price of a small pizza.

7. Now write an equation in slope-intercept form for the price of a large pizza.

8. Explain what each component of your equations above mean.



9. Which line/lines – small, medium, or large – is/are the steepest? Why?

10. Which line/lines – small, medium, or large – has/have the lowest starting value? Why?

11. Look at the graphs (next page) of how much Domino’s really charges for pizza in Washington, DC. How is the actual situation different than what you expected?

Use your original information to answer the questions below.

12. What is the y-intercept of the small pizza graph?

13. What is the y-intercept of the medium pizza graph?

14. What is the y-intercept of the large pizza graph?

15. What does the y-intercept represent in each of the equations above?

The slope of a straight line shows how steep the straight line is. The slope is calculated by the following:

2 1

2 1

slope rate of changey yy

x x x

−∆= = =

∆ −

16. What is the slope of the small pizza graph?

17. What is the slope of the medium pizza graph?

18. What is the slope of the large pizza graph?

19. What does the slope represent in each of the equations above?



20.

According to the graph everything looks normal until the fourth topping. At this point Domino’s appears to stop charging for additional toppings. What is the slope of the line between topping 4 and topping 10?

21. Not many people order more than 4 toppings. If you are someone who loves toppings and you order 9, how much are you saving with the pricing above compared to what you thought it was going to be?

22. Dominos has 15 different toppings. What is one reason why it appears that Domino’s does not allow you to order more than 10 toppings no matter how much you are willing to pay?

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Domino Effect



EXTENSION – You may use a calculator for this page.

Pizza chains like Domino’s charge different prices for toppings depending on the size of the pizza: a topping for a small pizza costs less than a topping for a medium pizza, which costs less than a topping for a large pizza. This makes sense: the larger the pizza, the more topping you get. How do the differences in topping prices compare to the differences in topping amounts? If pepperoni costs $1 on a small pizza and $1.49 on a medium are you really getting $0.49 more worth of pepperoni?

The large pizza has a 14 inch diameter including a 1 inch crust all around. The medium pizza has a 12 inch diameter including a 1 inch crust all around. The small pizza has a 10 inch diameter including a 1 inch crust all around.

1. Using the formula for the area of a circle, 2

A rπ= , determine the interior area (area available for toppings) of a large pizza. Round to the nearest whole number.

2. Determine the interior area of a medium pizza. Round to the nearest whole number.

3. Determine the interior area of a small pizza. Round to the nearest whole number.

4. Complete the table below. Round percentages to the nearest percent.

5. Based on your results do you think the cost of an additional topping is fair compared to the amount of topping you get in each case? Why or why not?

Percent Change (Increases)

Percent more area

Percent change in price of one topping

Small to Medium 58%

Medium to Large

Small to Large



EXTENSION 2 Pizza Hut pizzas come in three sizes: large; medium; and personal. Find out how much a cheese pan pizza costs in each size where you live. How much are you paying for each slice and is the pizza with the cheapest slice the best deal? A large pizza is 14 inches in diameter (8 slices). A medium is 12 inches in diameter (8 slices) and a personal is 6 inches in diameter (4 slices). For each size, how much pizza (in square inches) are you getting with each slice? Based on your answers above, which pizza would you say is the best deal and why? No matter the size, Pizza Hut crust is always the same width: 1‐inch. For each pizza, calculate the area of the pizza that’s inside (i.e. the cheesy part), and the area of the pizza that’s crust. Plot the “inside percent” and “crust percent” for each size: large, medium & personal. Then, pick two more diameters and plot their percents. What do you notice and how does this influence which size you think is the best deal?

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BARBIE BUNGEE GROUPS


Activity B-1: Barbie Bungee Challenge Name:

Adapted from www.mathlab.com and Laying The Foundation.

Barbie Bungee Challenge Think about the cord length in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and splat! We are going model a bungee jump using a Barbie® doll and rubber bands. You will find the relationship between the number of rubber bands and the distance that Barbie falls. You will be creating a bungee jump for a Barbie® doll. Your objective is to give Barbie the greatest thrill while still ensuring that she is safe (and alive after the activity is complete). This means that she should come as close as possible to the ground without hitting. You will conduct an experiment, collect data, and then use the data to predict the maximum number of rubber bands that should be used to give Barbie a safe jump from the top of the high school bleachers (15 feet). Formulate a conjecture (that means make a reasonable guess): I believe that _____ is the maximum number of rubber bands that will allow Barbie to safely jump

from the top of the high school bleachers.

Now, conduct the experiment to test your conjecture. Complete each step below. Materials needed: Barbie, rubber bands, yardsticks, recording page Assign roles to each group member: 1 Rubber band expert 1 Barbie dropper 1 or 2 Data recorders Create a double-loop to wrap around Barbie’s feet. A double-loop is made by securing one rubber band to another with a slip knot. Then, wrap the open end of the double-loop tightly around Barbie’s feet. Next, attach a second rubber band to the first one, again using a slip knot.



How far would Barbie fall with zero rubber bands attached to her feet (if you just held her feet and dropped her)? Record your number in the y column below. Note that it is NOT zero. We will measure Barbie’s jump using a yardstick. Hold the yardstick near a wall with zero being the highest number. With two rubber bands now attached, hold the end of the rubber bands at the jump line (top of yardstick) with one hand, and drop Barbie from the line with the other hand. Have the other two group member determine the lowest point (not the final position) that Barbie reaches on this jump. Perform the experiment 3 times with the 2 rubber bands attached and record the values in the data table. Then find the average distance of the three jumps to ensure accuracy. Repeatedly attach two additional rubber bands for each new jump, measure the jump distance, and record the results in the data table.

Accuracy is important—Barbie’s life could depend on it!

x Jump #1 Jump #2 Jump #3 y

Number of Rubber Bands

Distance Bungeed (in inches)



Average of 3 Jumps (in inches)

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Rewrite your x and y-values below from the data. Then plot the points (x, y) on the graph below

x y

Plot the points on the axes on the next page.

Sketch a line that best fits your data.

To do this, pick TWO points. One should be your y-intercept and the other should create a straight line such that some points are above the line and some

are below the line. Extend your line across the entire graph.



1. Do you think the length of the cord and the size of the person matters when bungee jumping? Why?

2. Would it be smart to lie about your height or weight? Why or Why not?

3. Why is an accurate estimate of height and weight important to conduct a safe bungee jump?

4.

Choose two points, one near the left side of the graph and one near the right side of the graph that best represent the data that you have collected. Use the SAME TWO points you used to draw your line on the graph! The two points are ( ___, ___ ) and ( ___, ___ ).

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5.

Using these two points, find the slope of the line through them. Simplify your answer to the nearest tenth.

Recall: 2 1

2 1

change in rise

change in run

y y ym

x x x

−= = =

−

6. What does the slope represent in this context?

7. Based on your line of best fit what is the y-intercept of the line?

8. What does the y-intercept represent in this context?

9.

Write an equation in the form of bmxy += for your Barbie bungee jumps.

______________ += xy

(slope) (y-intercept)

10. Number of rubber bands and the height of Barbie’s fall: Which is the independent variable and which is the dependent variable in this experiment?

11.

Based on your data, what would you predict is the maximum number of rubber bands so that Barbie could still safely jump from the top of the high school bleachers (15 feet)?

FINAL PREDICTION: __________

12. What is the minimum height from which Barbie should jump if 25 rubber bands are used? (You should use the line of best fit to determine an answer.)

13. Use your equation to determine what distance Barbie would fall using 50 rubber bands.

14. Use your equation to determine how many rubber bands you would need to use to have Barbie plunge to a distance of 150 inches.

15. Barbie wants to bungee off the Eiffel Tower. It is 986 feet tall. How many rubber bands will you need so Barbie just brushes her hair (hopefully not her head) on the ground?

We are now at the moment of truth. Which team has best predicted the maximum number of rubber bands required to give Barbie the bungee jump of a lifetime?

Let the Official Barbie Bungee jumps begin!!!

Our team’s minimum Barbie distance from the ground: _____________________


Team Members

1st attempt 2nd attempt 3rd attempt

Rubber bands Distance Rubber bands Distance Rubber bands Distance

domino effectdomino effect packets/chapter 7 domino barbie.… · a medium, 3-topping pizza really...

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