Algebra 1 Connection Patterns & Functions Connecting Patterns & Functions.2 Stacking Cups Algebra 1 Connection Patterns & Functions Algebra 1 by Southwest Washington Common Core is licensed under a Creative Commons Attribution 4.0 International License 2014-2015

When have you solved a problem with an equation or graph? Learning Target Connecting Patterns & Functions Target 3a I can write and graph equations and use them to solve problems. When have you solved a problem with an equation or graph?

Launch What would you need to answer the question, “How many nested cups will it take to be as tall as your teacher?“

Stacking Cups Challenge 1: How many nested cups will it take to be as tall as your teacher? Winner: The group that gets the closest without going over, and can support that answer. Prize: Bragging Rights Tools: 1 stack of Styrofoam cups for each group, rulers or tape measures. (convert inches to centimeters)

Stacking Cups Challenge 2 Choose the questions you want to answer. You must continue to work during work time. Measure the lip and base of each. Ask your teacher will give you a copy of this graphic. Which will be taller after three cups? Which will be taller after one hundred cups? How many cups does it take stack A to rise above stack B?

Stacking Cups Challenge 3 How many nested cups will it take to get as close to the ceiling as possible? Task 1: Send half of your team as ambassadors to another group (that had different cups). Ambassadors present their solution to another group. The non-ambassadors listen to the ambassadors presentation, and ask questions to help the ambassadors improve their work.

Function Notation How many nested cups will it take to get as close to the ceiling as possible? Task 2: Ambassadors go back to their team and revise their work as needed. Task 3: The team presents their solution in writing or with a multi-media presentation to their teacher.

Function Notation We can use function notation to describe the relationship between the height of the stack and the number of cups in that stack. In Mrs. Schneider’s class h(2) = 13 means a stack of 2 cups is 13 cm high. What do you think h(3) = 14.5 means? What do you think h(5) means? Find h(5) = ___.

Function Notation 3. What do you think h(n) = 22 means? Find the value of n such that h(n) = 22. Fill in the blanks: h(n) is the _______ (input or output) which counts _________. n is the _______ (input or output) which counts _________.

Function Notation The function for Dylan’s stack of cups is f(x) = 10 + 2x where x = number of cups, and f(x) = height of stack. 7. Find f(4).  What does f(4) mean? Find f(24). Solve for x when f(x) = 84 What does f(x) = 84 mean?

Function Notation The function for Dylan’s stack of cups is f(x) = 10 + 2x where x = number of cups, and f(x) = height of stack. 12. Solve for x when f(x) = 75 Is f(x) a function?  Describe all of the quantities that can be used for any input of the function. Describe all of the quantities that can be used for any output of the function. (It may be easier to find quantities that cannot be used.)