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Ordering and Absolute Value of Rational Numbers

Use the number line to verify ordering. For absolute value problems, state the distance from 0.

Grade 6·21 problems·~35 min·Common Core Math - Grade 6·standard·6-ns-c-7
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Which number is greater: −3 or −7?

2.

Which inequality correctly compares −5 and 2?

3.

How many units from 0 is the number −8 on the number line?

B

Fluency Practice

Number line from −8 to 4 with dots at −6, −1, and 3 showing their order from least to greatest
1.

Which correctly orders −1, −6, and 3 from least to greatest?

2.

Write an inequality using << or >> to compare −4-4 and −9-9. Which is greater?

3.

The temperature in Fairbanks, AK is −13°C-13\degree C. The temperature in Oslo, Norway is −10°C-10\degree C. Write an inequality comparing these temperatures and identify the colder city.

4.

What is ∣−12∣|-12|?

5.

Evaluate: ∣−34∣\left|-\frac{3}{4}\right|

C

Varied Practice

Number line from −10 to 2 with labeled dots at −8 and −3, and a rightward arrow labeled greater
1.

The statement −8<−3-8 < -3 means which of the following on the number line?

2.

Death Valley has an elevation of −86-86 m. The Dead Sea has an elevation of −430-430 m. Write an inequality: ___>___\_\_\_ > \_\_\_. In words, this means Death Valley is at a   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   elevation than the Dead Sea.

higher value (left of >):
lower value (right of >):
comparison word:
Number line showing −30 with a double-headed arrow from 0 to −30 labeled |−30| = 30, representing the magnitude of a $30 debt
3.

A bank account balance is −30-30 dollars. The statement ∣−30∣=30|-30| = 30 means:

4.

For the pair −50-50 and −30-30:
Which number is greater (further right on the number line)?   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  
Which number has greater absolute value (further from 0)?   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

greater number:
greater absolute value:
5.

For which pair of numbers do the ordering comparison (a<ba < b) and the absolute value comparison (∣a∣<∣b∣|a| < |b|) give the same result (both point the same direction)?

D

Word Problems

1.

Two cities recorded these overnight temperatures: City X: −17°F and City Y: −9°F.

Write an inequality comparing the temperatures. Which city is colder?

2.

A bank account has a balance of −$50. A second account has a balance of −$20.

1.

Which account has the lower balance?

2.

Which account has the greater debt (larger magnitude)?

3.

Priya's account balance is less than −$30. Her brother's account balance is −$10.

Whose account has the greater debt? Explain using both ordering and absolute value.

E

Error Analysis

1.

Jaylen was asked to order −2,−8,5-2, -8, 5 from least to greatest. He wrote: '−8,5,−2-8, 5, -2' because "8 is the biggest number and 5 comes next."

What error did Jaylen make?

2.

Rosa evaluated ∣−7∣|-7| and wrote: '∣−7∣=−7|-7| = -7 because there is a negative sign inside the absolute value bars, and absolute value doesn''t change the sign.'

What error did Rosa make?

F

Challenge / Extension

1.

If ∣x∣=5|x| = 5, list all possible values of xx.

2.

For negative numbers aa and bb, if a<ba < b, is it always true that ∣a∣>∣b∣|a| > |b|? Explain with an example.

0 of 21 answered