Practice Set · Part 1
Compare and Order Integers and Rational Numbers
Pick up where we left off
Where we left off
Our goal: I can compare and order integers using a number line, explain how I can tell, and judge a case I have not seen before.
The big idea: Order rational numbers by their place on the number line, because a negative number with a greater absolute value is farther left and less.
Model to copy — Example · Order four rational numbers
- Order from least to greatest: −2, 1.5, −2.5, −0.5.
- Plot all four numbers on a number line: −2, 1.5, −2.5, −0.5
- Read the numbers from left to right: −2.5, −2, −0.5, 1.5
- Check the two closest negatives with absolute value: |−2.5| = 2.5 → |−2| = 2
- −2.5 < −2 < −0.5 < 1.5
Start here
You did these with your group. Now do them on your own — the model above is yours to copy.
- 1
Same stepsFinish what the group started. Use the model above, step for step.
Try it together — then prove it: Compare −2 and 3. Use < or >. Which number is to the left? Which is to the right? (−2 is left of 0. 3 is right of 0.) Write the comparison with a symbol. (−2 < 3) Is every negative number less than every positive number? Why? (Yes. Negative numbers are left of 0, and positive numbers are right of 0.)Show your work - 2
Warm restartWhat is the absolute value of -9?
- A-9
- B0
- C1
- D9
How do you know?
- 3
Warm restartWhich integer has the GREATEST absolute value: -3, 7, -5, 2?
- A-5
- B-3
- C2
- D7
How do you know?
- 4
Warm restartWhat is |0|?
- A1
- B-1
- C0
- DThere is no answer
How do you know?
Practice Set · Part 2
Compare and Order Integers and Rational Numbers
Keep going
You answered these out loud. Now write them.
Answer, then say how you know — the reason is the part that counts.
- 5
Think it throughWhich day was coldest?
- AThursday at −1°F
- BTuesday at 2°F
- CMonday at −4°F
- DWednesday at −7°F
Why is that the answer?
- 6
Think it throughWhich is colder, −4°F or −1°F?
- A−4°F, because it is farther left on the number line
- B−1°F, because 1 is smaller than 4
- CThey are the same
- D−1°F, because it is closer to zero
How do you know? Give a second reason as well.
- 7
Think it throughOrder the temperatures from coldest to warmest.
- A−1, −4, −7, 2, 5
- B2, 5, −1, −4, −7
- C5, 2, −1, −4, −7
- D−7, −4, −1, 2, 5
Explain your thinking. What would have to change for a different choice to be right?
- 8
Back to the modelHow does plotting on the number line help you compare and order integers?
Practice Set · Part 3
Compare and Order Integers and Rational Numbers
Words and reasoning
Word bank · Banco de palabras
Use the words
Fill each blank with a word from the bank.
- To plot integers in order, place them on a ___.
- To decide which number is larger or smaller is to ___ them.
- To arrange numbers from least to greatest or greatest to least is to ___ them.
- On a number line, a number farther to the right is ___ another number.
Explain the thinking
- 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 Compare and Order Integers is thinking that a negative number with a bigger digit is the bigger value — for example, believing -15 is greater than -8 because 15 is greater than 8. - 10
Say moreOrder these temperatures from coldest to warmest: -8, 3, -1, 5. How does the number line help you put them in order?
- 11
Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A dive team marks the depth of each treasure on a map, measured in feet relative to sea level. The gold coin is at -2 ft, the silver crown at -7 ft, the ruby ring at -5 ft, and a buoy floats at +3 ft.
Show your work
Practice Set · Part 4
Compare and Order Integers and Rational Numbers
Show what you know
Last check
These two come from Lesson 7.3. If they are shaky, that is the lesson to revisit — not this one.
- 12
Show what you knowExplain your thinking — Which list shows the integers in order from LEAST to GREATEST?
- A-5, -2, 0, 3, 7
- B-2, -5, 0, 3, 7
- C0, -2, -5, 3, 7
- D7, 3, 0, -2, -5
Explain your choice.
- 13
From Lesson 7.3Explain your thinking — Which integer has an absolute value of 8 and is located to the LEFT of zero on the number line?
- A-80
- B-8
- C0
- D8
How do you know?
- 14
From Lesson 7.3Which craft is at the LOWER position?
- AThe helicopter, because 200 > 150
- BThey are equal
- CThe submarine, because 150 < 200
- DThe submarine, because −150 < 200
How do you know?
Be honest — this tells your teacher what to do next
| I can… | Not yet | Getting there | Got it |
|---|---|---|---|
| I can compare and order integers using a number line, explain how I can tell, and judge a case I have not seen before. | |||
| I can explain why it works: Order rational numbers by their place on the number line… | |||
| I can justify my answer to a skeptic and connect it to a second strategy or representation. |
One question I want to ask my group next time