Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Let's do one together:

   1. Find |3|, the absolute value of 3.
   2. Where is 3 on the number line? (3 units to the right of 0.)
   3. How far is 3 from 0? (3 units)
   4. So what is |3|? (|3| = 3)

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

   Show your work
2. 2

   Quick reviewWhich number sits between 2 and 3 on a number line? 🔊 Listen 💡 Hint

   1. A1.9
   2. B2.4
   3. C−2.5
   4. D3.2
3. 3

   Quick reviewWhat is the opposite of 3/4? 🔊 Listen 💡 Hint

   1. A0
   2. B−3/4
   3. C3/4
   4. D4/3
4. 4

   Quick reviewBetween which two integers does −1/2 sit on a number line? 🔊 Listen 💡 Hint

   1. A0 and 1
   2. B−1 and 0
   3. C−1/2 is not on the number line
   4. D−2 and −1

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughWhat is |−150|? 🔊 Listen 💡 Hint

   1. A0
   2. B150
   3. C−150
   4. D300

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughWhich craft is FARTHER from sea level? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   1. AThe helicopter, because 200 > 150
   2. BThey are equal
   3. CThe submarine, because 150 < 200
   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? 🔊 Listen 💡 Hint

   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.

• 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 ___.
• The distance of a number from zero, never negative (zero is allowed), is its ___.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   1. A-80
   2. B-8
   3. C0
   4. D8

   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? 🔊 Listen 💡 Hint

   1. A-3.5
   2. B-2.75
   3. C-1.5
   4. D2.5
3. 14

   From Lesson 7.2Why are rational numbers more useful here than integers alone? 🔊 Listen 💡 Hint

   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

Check your progress

Choose the box that best describes how you feel about each skill.