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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 plot 0.75. Which two whole numbers is it between? It is between 0 and 1. What does 0.75 mean? It is 3/4 of the way from 0 to 1. So we split 0 to 1 into 4 equal parts and place the dot at the 3rd mark. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhat is the opposite of −6?

   1. A6
   2. B−6
   3. C0
   4. D−12

   How do you know?
3. 3

   Warm restartOn a number line, which number is farther to the LEFT: −8 or −3?

   1. A−8
   2. B−3
   3. CThey are the same
   4. DNeither is on the line

   How do you know?
4. 4

   Warm restartWhich integer is the LEAST: −3, 5, −8, 2, 0?

   1. A−8
   2. B−3
   3. C0
   4. D5

   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 throughWhere does −1.25 fall on the number line?

   1. ABetween −1 and −2
   2. BBetween −1 and 0
   3. CBetween 1 and 2
   4. DExactly at −1

   Why is that the answer?
2. 6

   Think it throughWhich day had the water level closest to the painted mark?

   1. AWednesday at −0.5 ft
   2. BMonday at +0.75 ft
   3. CTuesday at −1.25 ft
   4. DThursday at +1.5 ft

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

   Think it throughWhy 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

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

   Back to the modelHow did you decide exactly where to place rational numbers that fall between whole numbers?

Use the words

Fill each blank with a word from the bank.

• A rational number always has one exact spot on the ___ ___.
• A number you can write as a fraction of two integers, with a bottom number that is not zero, is a ___.
• A number that shows part of a whole, like 3/5, is a ___.
• A number that uses a point to show parts of a whole 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: A common mistake in Rational Numbers on the Number Line is treating the numerator and denominator of a negative fraction as two separate whole numbers instead of one value between two integers — for example, plotting -3/4 by going to -3 and then counting 4 more units to the left, landing (incorrectly) at -7, instead of recognizing that -3/4 = -0.
2. 10

   Say moreWhere would you place -1 1/2 on the number line, and how do you decide between which two integers it falls?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Captain Vega zoomed in on a stretch of the treasure map between -3 and -2. One point sits about halfway between those two marks, and a second point sits a little to the right of -2.

   Show your work

Last check

These two come from Lesson 7.1. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain 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

   Explain your choice.
2. 13

   From Lesson 7.1Explain 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

   How do you know?
3. 14

   From Lesson 7.1What 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

   How do you know?

Be honest — this tells your teacher what to do next