Your teacher will give you a set of number cards. Take turns with your partner placing a card from the set in order from least to greatest. 

1. For each placement that you make, explain your reasoning to your partner. 
2. For each placement that your partner makes, listen carefully to their explanation. If you disagree, discuss your thinking, and work to reach an agreement.
3. Pause after the first set so your teacher can review your ordering. 
4. Your teacher will give you a second set of cards to add in order with the first set.

The number line shows 4 points: , , , and .

Use each of the following phrases in a sentence describing or comparing the values of 2 of the points.

• greater than

• less than

• opposite of (or opposites)

• negative number

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 table shows the changes for every 1-hour period over one day.

1. What does a positive number in the second column mean in this context? What does a negative number mean in this context?

   time	number of bottles
   8:00–8:59	-1
   9:00–9:59	+12
   10:00–10:59	-4
   11:00–11:59	-1
   12:00–12:59	-5
   1:00–1:59	-12
   2:00–2:59	-2
   3:00–3:59	0
   4:00–4:59	0
   5:00–5:59	-6
   6:00–6:59	+24
   7:00–7:59	0
   service

2. What would a “0” in the second column mean in this situation?
3. Which numbers—positive or negative—result in fewer bottles in the machine?
4. At what time was there the greatest change in the number of bottles in the machine? How did that change affect the number of remaining bottles in the machine?
5. At which time period, 9:00–9:59 AM or 1:00–1:59 PM, was there a greater change to the number of bottles in the machine? Explain your reasoning.
6. 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?