Variables and Patterns - Brockton Public Schools



Variables and Patterns

CMP II ACE Investigation 1 p. 20 #10

CMP I ACE Investigation 2 p. 28 #3

10. Make a table and a graph of (time, temperature) data that fit the following information about a day on the road: [Hint: There is no one right answer. Time and Temperature may not be exact numbers in this problem, so you will need to use the clues to make reasonable estimations.]

• We started riding at 8 A.M. The day was quite warm, with dark clouds in the sky.

• About midmorning the temperature dropped quickly to 63°F, and there was a thunderstorm for about an hour.

• After the storm, the sky cleared and there was a warm breeze.

• As the day went on, the sun steadily warmed the air. When we reached our campground at 4 P.M. it was 89° F.

| | | |10am | | | | |

|Time (x) |8am |9am |(Mid-morni|11am |12pm |1pm |2pm |

| | | |ng) | | | | |

|Total cost |$30 |35 |40 |45 |50 |55 |60 |

[Hint: Sketch a graph for Source Video]

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5 10 15 20 25 30

Supreme Video does not have a membership package. Dezi made the graph below to show how the cost at Supreme Video is related to the number of DVDs rented.

[Hint: Make a table for Supreme Video]

|Number of videos rented |0 |5 |10 |15 |20 |25 |30 |

|Total cost |$0 | | | | | | |

a. If both video stores have a good selection of movies, and Dezi’s family plans to watch about two movies a month, which video store should they choose for the whole year?

b. Write a paragraph explaining to Dezi how he could decide which video store to use.

c. For each store, describe the pattern of change relating the number of videos rented to the cost.

Variables and Patterns

CMP II ACE Investigation 4 p. 67 #5

5. When the University of Maryland won the NCAA basketball tournament in 2002, the campus store ordered special shirts and caps to sell to fans. They did some market research and predicted these relations between price, p, (in dollars) and number sold, n. The campus store found that the maximum number of shirts that could be sold was 5000. They also determined that every time the price of the shirts was increased by $1.00, the number of sold would decrease by 150 shirts. Thus, the equation

Shirts: n = 5000 – 150p

Because camps are not worn by girls that much, the campus store determined that the maximum number of caps that could be sold was 3000. They also found that every time the price of a cap was increased by $1.00, the number of sold would decrease by 100 caps. Thus, the equation

Caps: n = 3000 – 100p

Use these equations to answer questions a–d. Calculator tables and graphs might help.

[Hint: How many shirts will be sold if the price is set at $10?

n = 5000 – 150p

n = 5000 – (150 x 10)

n = 5000 – 1500

n = 3500

3500 shirts will be sold if the price is set at $10.

What price per shirt will lead to the sale of 500 shirts?

n = 5000 – 150p

500 = 5000 – 150p

150p = 5000 – 500

150p = 4500

p = 4500 ( 150

p = 30

A $30 price per shirt will lead to the sale of 500 shirts

What price per shirt will lead to the sale of 2500 caps?

n = 3000 – 100p

2500 = 3000 – 100p

100p = 3000 – 2500

100p = 500

p = 5

A price per shirt of $5 will lead to the sale of 2500 caps

a. How many shirts will be sold if the price is set at $20?

b. What price per shirt (p) will lead to the sale of 3500 shirts (n)?

c. How many caps will be sold if the price is set at $17?

d. What price per cap (p) will lead to the sale of 1800 caps (n)?

Name__________________________________________________Date__________________

Adapted Variables and Patterns: Unit Test

1. The tour operators thought it would be a good idea to get a souvenir T-shirt for each customer who went on the Ocean Bike Tour. They found a company who would sell them shirts with their logo for $6.00.

a. Make a table and a graph that show number of shirts (x) and cost (C).

|Table |Graph |

|x C |[pic] |

b. Would it make sense to connect the points on your graph with a line? Why or why not?

c. Write an equation using symbols to determine the T-shirt cost (C) for any number of customers (x).

2. The drawings below show a series of dot figures.

Figure 1 Figure 2 Figure 3 Figure 4

a. Make a table showing the number of dots needed to make Figures 1–10.

|Figure (n) |1 |

|1 (January) | 10.0 |

|2 (February) | 10.2 |

|3 (March) | 11.7 |

|4 | 13.1 |

|5 | 14.3 |

|6 | 15.0 |

|7 | 14.5 |

|8 | 13.8 |

|9 | 12.5 |

|10 | 11.0 |

|11 | 10.5 |

|12 | 10.0 |

5. The number of hours of daylight in a day changes throughout the year. We say that the days are “shorter” in winter and “longer” in summer. Sketch a graph showing the hours of daylight over the course of a year (January through December). Explain your decisions as you made the sketch of the graph.

[pic]

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[pic]7CMP2e_VP2_ta12

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