IM 7.6.6 Lesson: Distinguishing between Two Types of Situations

Which equation doesn’t belong? Explain your reasoning.




Sort the cards into 2 categories of your choosing.

Explain the meaning of your categories.

Now, sort the cards into 2 categories in a different way.

Explain the meaning of your new categories.

AB

Story 1: Lin had 90 flyers to hang up around the school. She gave 12 flyers to each of three volunteers. Then she took the remaining flyers and divided them up equally between the three volunteers. Which diagram goes with this story? Explain your reasoning.

What part of the story does the variable in the diagram represent?

Write an equation corresponding to the story above. If you get stuck, use the diagram.

Find the value of the variable in the story.

AB

Story 2: Lin had 90 flyers to hang up around the school. After giving the same number of flyers to each of three volunteers, she had 12 left to hang up by herself. Which diagram goes with this story? Explain your reasoning.

What part of the story does the variable in the diagram represent?

Write an equation corresponding to the story above. If you get stuck, use the diagram.

Find the value of the variable in the story.

A tutor is starting a business. In the first year, they start with 5 clients and charge $10 per week for an hour of tutoring with each client. For each year following, they double the number of clients and the number of hours each week. Each new client will be charged 150% of the charges of the clients from the previous year.

Organize the weekly earnings for each year in a table.

Assuming a full-time week is 40 hours per week, how many years will it take to reach full time and how many new clients will be taken on that year?

After reaching full time, what is the tutor’s annual salary if they take 2 weeks of vacation?

Is there another business model you’d recommend for the tutor? Explain your reasoning.