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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: Now let's find |3|. Where is 3 on the number line? It is 3 steps to the right of zero. How far is it from zero? It is 3 units away. So |3| equals what? It equals 3. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhich number sits between 2 and 3 on a number line?

   1. A2.4
   2. B3.2
   3. C−2.5
   4. D1.9

   How do you know?
3. 3

   Warm restartWhat is the opposite of 3/4?

   1. A−3/4
   2. B4/3
   3. C3/4
   4. D0

   How do you know?
4. 4

   Warm restartBetween which two integers does −1/2 sit on a number line?

   1. A−1 and 0
   2. B0 and 1
   3. C−2 and −1
   4. D−1/2 is not on the number line

   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 throughWhat is |−150|?

   1. A150
   2. B−150
   3. C0
   4. D300

   Why is that the answer?
2. 6

   Think it throughWhich craft is FARTHER from sea level?

   1. AThe helicopter, because 200 > 150
   2. BThe submarine, because −150 < 200
   3. CThey are the same distance
   4. DYou cannot compare them

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

   Think it throughWhich craft is at the LOWER position?

   1. AThe submarine, because −150 < 200
   2. BThe helicopter, because 200 > 150
   3. CThey are equal
   4. DThe submarine, because 150 < 200

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

   Back to the modelHow does the number line help you see the difference between an integer and its absolute value?

Use the words

Fill each blank with a word from the bank.

• The distance of an integer from zero is its ___ ___.
• A whole number or its opposite, like −2, 0, or 5, is an ___.
• A number greater than zero is ___.
• A number less than zero is ___.

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: A common mistake in Integers and Absolute Value is judging size by the digits alone instead of position on the number line — students think -8 is 'more' than -3 because 8 > 3, when really -8 sits farther left (colder, deeper, or lower) and is actually the SMALLER integer.
2. 10

   Say moreA diver is at -30 feet and a hawk is at +30 feet. How can absolute value help you describe how far each is from sea level?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Claire is performing a science experiment with two liquids. The temperatures of the two liquids in Celsius are shown, and she needs to use the beaker with the temperature closer to 0°C.

   Show your work

Last check

These two come from Lesson 7.2. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which integer has an absolute value of 8 and is located to the LEFT of zero on the number line?

   1. A8
   2. B-8
   3. C0
   4. D-80

   Explain your choice.
2. 13

   From Lesson 7.2Explain your thinking — Which rational number is located between -2 and -3 on the number line?

   1. A-1.5
   2. B-2.75
   3. C-3.5
   4. D2.5

   How do you know?
3. 14

   From Lesson 7.2Why are rational numbers more useful here than integers alone?

   1. AThey let the scientist record part-of-a-foot changes like 0.75 and −1.25
   2. BThey are easier to add
   3. CIntegers cannot be negative
   4. DThey make the lake bigger

   How do you know?

Be honest — this tells your teacher what to do next