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 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.

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

   Show your work
2. 2

   Warm restartWhat is the opposite of −6?

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

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

   1. A−8
   2. B−3
   3. C0
   4. D5

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?

   I chose ___ because ___ .
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?

   I chose ___ because ___ .
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.

   I chose ___ because ___ .
4. 8

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

   To plot ___, I found the whole numbers it falls between, which are ___ and ___. Then I estimated ___ of the way between them because ___.

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?

   -1 1/2 is between ___ and ___.
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 7.1. 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 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.

   I know it is ___ because ___ .
2. 13

   From Lesson 7.1Quick check — you've got this: 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
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

Be honest — this tells your teacher what to do next