Integers · Absolute value · 3.3

Value vs distance.

Bigger absolute value does not mean bigger number. −8 is farther from 0 than 3 (|−8| > |3|), but −8 < 3 because it sits to the left.

01 / THE IDEA

See it work.

On the number line

Start at 0, hop right 0.

0 + 0 = 0

-1010

Watch the method

Value vs distance

−8 is farther from 0 than 3, yet −8 < 3.

1 / 1
−8  □  3-8 \;\square\; 3
1

Compare on the number line

Further right is greater. -8 is left 3.

−8  <  3-8 \;<\; 3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type <, =, or >.

streak 0
best 0
…
— / WHY IT WORKS

The idea underneath.

Two different questions

“Which is greater?” is about position (right wins). “Which is farther from 0?” is about absolute value.

Why it works

−8 °C is colder (less) but a bigger change from 0.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Compare: 12 ▢ -4

1

Compare on the number line

Further right is greater. 12 is right -4. 12 > -4

EX 2medium

Compare: 5 ▢ 7

1

Compare on the number line

Further right is greater. 5 is left 7. 5 < 7

EX 3hard

Compare: 1 ▢ 5

1

Compare on the number line

Further right is greater. 1 is left 5. 1 < 5

04 / COMMON TRAPS

Where students slip.

Trap

Saying −8 > 3 because 8 > 3.

Fix

Compare position: −8 is left of 3, so smaller.

Trap

Confusing “greater” with “farther from 0”.

Fix

They are different questions.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Compare: 12 ▢ -4

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
C2

Compare: 4 ▢ 7

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
C3

Compare: -5 ▢ -2

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
C4

Compare: 4 ▢ -8

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
Apply

Apply (4)

A1

Compare: 5 ▢ 7

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
A2

Compare: -1 ▢ -7

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
A3

Compare: -6 ▢ 8

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
A4

Compare: 12 ▢ -2

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
Extension

Extension (4)

E1

Compare: 1 ▢ 5

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
E2

Compare: 12 ▢ 12

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
E3

Compare: -2 ▢ 12

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.
E4

Compare: -7 ▢ 8

Need a hint?
  • Greater = further right.
  • Farther from 0 = bigger absolute value.