Stacking Cups

Algebra 1Connection Patterns & Functions

Connecting Patterns & Functions.2

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?

When have you solved a problem with an

equation or graph?

LaunchWhat 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 2Choose 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 3How 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 NotationHow 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? 4. 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.)

•