Lessons 1&2: Describing and Graphing Situations
Problem No. 1 Instructions:
- Gather in groups of 4.
- Individually, think about the first question.
- Share your thinking with your group.
A customer at a bagel shop is buying 13 bagels. The shopkeeper says, “That would be $16.25.”
Jada, Priya, and Han, who are in the shop, all think it is a mistake.
Explain how the shopkeeper, Jada, Priya, and Han could all be right.
Consider displaying a table to summarize the different possibilities for calculating the price of 13 bagels (or the prices for 6 or more bagels), as well as the table showing the best price for each number of bagels bought.
Class discussion
- “If we graph the relationship between ’number of bagels’ and ’price’...
- “If we graph the relationship between ’number of bagels’ and ’best price’...
- “’Number of bagels’ and ’price’ do not form a function, but ’number of bagels’ and ’best price’ do form a function. Why is this?
Problem No. 2
- Individually, think about the second problem.
- Share your thinking with your group.
Three days in a row, a dog owner tied his dog’s 5-foot-long leash to a post outside a store while he ran into the store to get a drink. Each time, the owner returned within minutes.
The dog’s movement each day is described here.
Your teacher will assign one of the days for you to analyze. Write the day in the space below. 
Sketch a graph that could represent the dog’s distance from the post, in feet, as a function of time, in seconds, since the owner left.
From the graph, is it possible to tell how many times the dog changed directions while walking around? Explain your reasoning.