T-SHIRTS

Enduring Understanding: Develop a better understanding of how to graph an equation. Develop a better understanding of how to make a conjecture and research information to validate the conjecture.

Essential Questions:

 What is an informative title for a graph?  What is an appropriate interval for the x- and y-axes?  How can a graph be used to make predictions?  What is the dependent variable?  What is the independent variable?  How do you know that these are linear functions?  How do you clearly define the variables?  What is meant by the term “domain”?  How can a conclusion be supported using mathematical information and calculations?

Lesson Overview:

 Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to fundraisers that they have been involved in. Who is involved in AAU Basketball, the band, the debate team, USVBA teams and other activities.  What is meant when two graphs intersect?  A good warm-up could be Payday or Ernie Elephant or Patience’s Patience.  How can you support a conclusion that you make? What evidence from graphs can be used to support/justify your conclusion?  How can a conclusion be supported using symbolic  Use resources from your building.

EALRs/GLEs:

1.4.6 1.5.2 2.2.1 2.2.2 3.1.1 3.2.2 5.1.1 5.1.2

Item Specifications: PS03; AS01; SR03; SR04; MC01 Assessment:  Use WASL format items that link to what is being covered by the classroom activity  Include multiple choice items T-Shirts

Adapted from Charles A. Dana Center at the University of Texas at Austin, ©2002

A school organization has found four different places from which they may place an order for t-shirts. Each equation below could represent the cost (c) of placing a t-shirt order as a function of the number of t-shirts (t) purchased. Each scenario represents a potential t-shirt company.

Scenario 1: c = 5t Scenario 2: c = 3.25t + 55 Scenario 3: c = 3t + 100 Scenario 4: c = 6t – 55

1. Write a scenario for each equation.

Scenario 1: ______

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Scenario 2: ______

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Scenario 3: ______

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Scenario 4: ______

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2. Do all four equations fit a t-shirt situation? ______

Explain your answer. ______

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______3. Make a table for each equation for each scenario with the anticipation that the club will sell at most 200 t-shirts.

4. Graph each equation on the same coordinate grid. Differentiate by labeling and using different colors for each graph. ______5. Describe the differences in the x-intercepts for each graph. Describe, in real world terms, how the x-intercepts pertain to this scenario. Are there any domain restrictions? If so, what are they?

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6. Describe the differences in the y-intercepts for each graph. Describe, in real world terms, how the y-intercepts pertain to this scenario. Given the domain, describe the realistic range values.

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7. From which t-shirt company should the group purchase the shirts if they are going to purchase 50 t-shirts? Support your answer using information from your graph and/or equations.

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______8. The club is anticipating that they will sell 200 t-shirts. Which scenario will provide the least amount of cost to the club? Support your answer using information from your graph and/or equations.

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9. In Scenario 1 the company decided to give you a $40 discount because the owner has a daughter at your school. How would that change the equation?

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10. Rewrite the equation to reflect the discount. ______11. Which equation represents the graph?

3 O A. y= - x + 3 7 3 O B. y= x + 3 7 7 O C. y= - x + 3 3 3 O D. y= - x + 7 7

12. Which line has the steepest positive slope? 13. Earnest Ernest’s Autorama claims that their car repair rates are the lowest in town. Earnest charges an initial fee of $50 plus $30 per hour. Earnest’s has always been known for telling the truth. Therefore, his claim is likely to be true.

Which of the graphs best describes the rates charged by Ernest’s competitors?

14. The speed of sound in water is 1.46 103 meters per second. The speed of sound in air is 3.31 102 meters per second.

Which represents how much faster sound travels in water than in air?

O A. 1.85 10-3 m/s O B. 1.129 102 m/s O C. 1.85 102 m/s O D. 1.129 103 m/s

15. Three-fourths of the 36 members of a club attended a meeting. Ten of those attending the meeting were female.

Which question can be answered with the information given?

O A. How many males are in the club? O B. How many females are in the club? O C. How many male members of the club attended the meeting? O D. How many female members of the club did not attend the meeting?