Start here

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.

   Let's try together: 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.

   My first step is ___ , because the problem asks for ___ .

   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
3. 3

   Warm restartWhat is the opposite of 3/4?

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

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?

   I chose ___ because ___ .
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?

   I chose ___ because ___ .
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.

   I chose ___ because ___ .
4. 8

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

   The integer ___ is located ___ units from zero, so its absolute value is ___. Even though ___ is negative, its distance from zero is still ___.

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?

   The diver is ___ feet from sea level because |-30| = ___.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   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 knowQuick check — you've got this: 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.

   I know it is ___ because ___ .
2. 13

   From Lesson 7.2Quick check — you've got this: 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
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

Be honest — this tells your teacher what to do next