# Distinguishing between Two Types of Situations

Warmup

Activity #1

`Sorting Equations into Categories.` • Sort the cards into 2 categories of your choosing.

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

Activity #2

` Application of Tape Diagrams to Solve Problems.` • Here below are two stories: Read them carefully and answer the questions that follow.

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.

(1.) Which diagram goes with this story? Explain your reasoning.

(2.) What part of the story does the variable in the diagram represent?

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

(4.) Find the value of the variable in the story.

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.

(1.) Which diagram goes with this story? Explain your reasoning.

(2.) What part of the story does the variable in the diagram represent?

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

(4.) Find the value of the variable in the story.

Activity #3

`Match a Story to an Equation.` • Match each story below to an equation.

(1.) Jada’s teacher fills a travel bag with 5 copies of a textbook. The weight of the bag and books is 17 pounds.

(2.) A piece of scenery for the school play is in the shape of a 5-foot-long rectangle. The designer decides to increase the length. There will be 3 identical rectangles with a total length of 17 feet.

(3.) Elena spends \$17 and buys a \$3 book and a bookmark for each of her 5 cousins.

(4.) Noah packs up bags at the food pantry to deliver to families. He packs 5 bags that weigh a total of 17 pounds. Each bag contains 3 pounds of groceries and a packet of papers with health-related information.

Elena walked 20 minutes more than Lin. Jada walked twice as long as Elena. Jada walked for 90 minutes. The equation  2(x +20) = 90.

Match the following statement to the mathematical expression it represents in the story.

Challenge #1

(1.) A school ordered 3 large boxes of board markers. After giving 15 markers to each of 3 teachers, there were 90 markers left. The diagram below represents the situation.

How many markers were originally in each box?

(2.) The diagram below can be represented by the equation 25 = 2 + 6 . Explain where you can see the 6 in the diagram.

Challenge #2

Elena walked 20 minutes more than Lin. Jada walked twice as long as Elena. Jada walked for 90 minutes. The equation  2(x + 20) = 90 describes this situation.

Match each expression with the statement in the story with the expression it represents.

Challenge #3

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.

(1.) 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?

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

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

Quiz Time