Using Negative Numbers to Make Sense of Contexts

Warmup

Activity #1

Practice Adding and Subtracting Positive and Negative Numbers using Money.

 The black money represents money you have. The red money represents money you owe.

• Put a mixture of money in the middle when adding. ​
• Add them up and tell how much you have or owe.​
• Take them away when subtracting. You can add or subtract positive (black) or negative (red) amounts. Black and red money can cancel out – a debt is paid by money you have.

Activity #2

Interpret Data From a Table.

The manager of the concession stand keeps records of all of the supplies she buys and all of the items she sells. The table shows some of her records for Tuesday.

• Study the table and answer the questions that follow.

(1.) Which items did she sell? Explain your reasoning.

(2.) How can we interpret -58 in this situation?

(3.) How can we interpret -10.35 in this situation?

(4.) On which item did she spend the most amount of money? Explain your reasoning.

Activity #3

Interpret Data on a Chart.

A vending machine in an office building sells bottled beverages. The machine keeps track of all changes in the number of bottles from sales and from machine refills and maintenance. This record shows the changes for every 5-minute period over one hour.

• Study the chart and answer the questions that follow.

(1.) What might a positive number mean in this context?

(2.) What about a negative number?

(3.) What would a “0” in the second column mean in this context?

(4.) Which numbers—positive or negative—result in fewer bottles in the machine?

(5.) At what time was there the greatest change to the number of bottles in the machine? 

(6.) How did that change affect the number of remaining bottles in the machine?

(7.) At which time period, 8:05–8:09 or 8:25–8:29, was there a greater change to the number of bottles in the machine? Explain your reasoning.

(8.) The machine must be emptied to be serviced. If there are 40 bottles in the machine when it is to be serviced, what number will go in the second column in the table?

Challenge #1

(1.) Make up a situation where a quantity is changing.

(2.) Explain what it means to have a negative change. Give an example.

(3.) Explain what it means to have a positive change. Give an example.

Challenge #2

On the number line, label the points that are 4 units away from 0.

(1.) If you fold the number line so that a vertical crease goes through 0, the points you label would match up. Explain why this happens.

(2.) On the number line, label the points that are units from 0. What is the distance between these points?