Learning Goal: Compare and order rational numbers and use absolute value to describe distance from zero.
Vocabulary
rational numberAny number that can be written as a fraction, including integers and decimals.
absolute valueThe distance a number is from zero, always zero or positive; written |x|.
inequalityA statement comparing values using < or >.
magnitudeHow big a value is, shown by its absolute value, ignoring its sign.
What You Need to Know
On a number line, numbers farther right are greater; farther left are smaller.
Every negative number is less than every positive number.
For negatives, the one closer to zero is larger; −2 > −5.
Absolute value is distance from zero, so |−8| = 8 and |8| = 8.
A statement like −3 < 1 means −3 is to the left of 1 on the number line.
In context, absolute value can show size without direction, like a $40 debt being 'larger' than a $25 debt.
Worked Example I Do — watch how it works
Order these temperatures from coldest to warmest: −3, −1.5, 0, 2, −7.
Step 1. Coldest means smallest, so start farthest left on the number line.
Step 2. The negatives in order are −7, then −3, then −1.5.
Step 3. Then come 0 and 2, giving −7, −3, −1.5, 0, 2.
Answer: −7, −3, −1.5, 0, 2
Guided Practice We Do — try it together
1. Use < or > to compare −2 and −5.
💡 Hint: On a number line, −2 is to the right of −5.
2. Find |−8| and |5|, then tell which is greater.
💡 Hint: Absolute value is distance from zero.
3. Order from least to greatest: −2.5, −2, −3.5, −1.
💡 Hint: Most negative is least.
Independent Practice You Do — show your work
1. Compare using < or >: −9 and −4.
2. Find |−12|.
3. Order from greatest to least: 1, −6, 0, −2.
4. Account A owes $40 and Account B owes $25. Which debt is larger?
5. Which is colder, −4°F or −1°F?
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.NS.C.7.
Item 1Selected Response6.NS.C.7
Which list orders the numbers from least to greatest?
Select the correct answer.
Item 2Selected Response6.NS.C.7
Maya owes $30 and Theo owes $18. Which statement is true?
Select the correct answer.
Item 3Constructed Response6.NS.C.7
Explain why −2 is greater than −5, even though 5 is greater than 2.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
−9 < −4
Independent 2
12
Independent 3
1, 0, −2, −6
Independent 4
Account A, because |−40| > |−25|
Independent 5
−4°F
Item 1 · 6.NS.C.7
C — From least to greatest the order is −3, −1, 0, 2, moving left to right on the number line.
Item 2 · 6.NS.C.7
B — Maya's debt is larger in size, so |−30| > |−18|, even though −30 < −18 as values.
Item 3 · 6.NS.C.7
−2 is closer to zero, so it is to the right of −5. — On the number line −2 is to the right of −5, so −2 > −5.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.NS.C.7