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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: One day in January the temperature in Toronto was 9°C and in Reykjavik it was −9°C. Which one is to the left of 0 on the number line? The negative sign tells us: −9. How many units from 0 is 9? How many units from 0 is −9? Both are 9 units. So 9 and −9 are opposites — same distance from 0, opposite sides. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartSimplify 8x + 5 − 3x.

   1. A5x + 5
   2. B10x
   3. C5x
   4. D8x + 2

   How do you know?
3. 3

   Warm restartWhich pair are like terms?

   1. A4m and 9m
   2. B4m and 9
   3. C4m and 9m²
   4. D4m and 9n

   How do you know?
4. 4

   Warm restartSimplify 2a + 7b + 5a.

   1. A7a + 7b
   2. B14ab
   3. C12ab
   4. D7a + 5b

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhich integer represents a 3-yard loss when the line of scrimmage is 0?

   1. A-3
   2. B3
   3. C0
   4. D-30

   Why is that the answer?
2. 6

   Think it throughThe four plays are -10, 4, -3, and 21. What is the team's net result?

   1. A12 yards gained
   2. B18 yards gained
   3. C38 yards gained
   4. D12 yards lost

   How do you know? Give a second reason as well.
3. 7

   Think it throughWhat does 0 represent in this football situation?

   1. AThe line of scrimmage, the spot where the series started
   2. BA play in which nobody touched the ball
   3. CThe end zone at the edge of the field
   4. DThe number of yards still needed for a first down

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelHow did you decide what 0 meant in each situation, and how did that decide the sign of the integer?

Use the words

Fill each blank with a word from the bank.

• A counting number, its opposite, or 0 is an ___.
• A number the same distance from 0 but on the other side is the ___.
• A number less than 0, written with a − sign, is a ___.
• A number greater than 0 is a ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: The most common mistake in this lesson is thinking that the opposite of a negative integer is still negative — for example, saying the opposite of -7 is -7, or that the opposite of -12 is -24.
2. 10

   Say moreHow can you tell from the words in a situation whether the integer will be negative or positive?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The lowest elevation in North America is Badwater Basin in Death Valley. A sign there reads 86 meters below sea level. On the same sign, sea level itself is marked as 0.

   Show your work

Last check

These two come from Lesson 6.15. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which situation is best represented by the integer -15?

   1. AA diver 15 meters below the surface of the water
   2. BA hill 15 meters above sea level
   3. CA deposit of $15 into a bank account
   4. DA football play with a 15-yard gain

   Explain your choice.
2. 13

   From Lesson 6.15Explain your thinking — Simplify 6x + 3 + 2x + 5.

   1. A8x + 8
   2. B8x² + 8
   3. C62x + 35
   4. D16x

   How do you know?
3. 14

   From Lesson 6.15If each stage has 4 microphones (m = 4), how many cables in total?

   1. A74
   2. B60
   3. C64
   4. D29

   How do you know?

Be honest — this tells your teacher what to do next