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Understand Absolute Value

Students learn that the absolute value of a number is its distance from zero on the number line and is always non-negative. They compute absolute values of integers and rational numbers and interpret absolute value in real-world contexts such as distance and magnitude.

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Understand Absolute Value

Grade 6 · Negative Numbers and the Number Line · question 1 of 3

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20 rungs. A star at the top.

Type the absolute value of −1.

How it is taught

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Absolute value is distance from 0 on the number line.

Distance is never negative.

−10−50510G

Read it: Which side of 0, how far

On a line with 0 in the middle, −6 is 6 steps left of 0 and −1 is 1 step left. So −6 < −1, though −6 is farther from 0.

  1. Find 0. A negative number sits to its left, a positive number to its right.
  2. Count the steps from 0 to the mark: that is its distance, its absolute value.
  3. To compare two numbers, read the line from left to right: the one farther left is less.

−6 and 6 are both 6 steps from 0, on opposite sides, so |−6| = |6| = 6.

A distance is never negative, so |−6| is 6, not −6.

Each step to the right adds 1, so −1 is greater than −6, and 0 is greater than both.

The sign says which side of 0 a number is on, the absolute value says how far, and farther left is less.

Calling −6 greater than −1, because 6 is greater than 1.

On the line −6 is farther left, so −6 < −1, even though |−6| > |−1|.

A mark sits at −9 on a line with 0 in the middle. How many units is it from 0? — 9. −9 is 9 units to the left of 0, and a distance is never negative.

|-4| and |3|

A submarine is four meters below the surface. A bird is three meters above. How far is each from the surface?

Let's use a number line. Zero is the surface — positive numbers go up, negative numbers go down.

Here's the submarine at negative four.

Absolute value asks one simple question: how far is this number from zero?

From negative four, we count one, two, three, four jumps to reach zero.

We write this with two straight bars: the absolute value of negative four.

The absolute value of negative four is four. Distance is never negative.

How far from the surface?🐦 bird: 3 m up〰️ surface = 0🚢 submarine: 4 m downDistance from zero-55-4-3-2-101234↑ zero-44 units| -4 |= 433 units| 3 | = 3Absolute value ≥ 0 always| -4 | = 4| 3 | = 3Distance from zero — never negative.KEY IDEA|x|= distance to 0
Grade 6 · Distance from zero on the number line

Now the bird at positive three.

From three, it's three jumps back to zero.

So the absolute value of three is just three.

Absolute value strips away the sign — it's always zero or positive.

Both the submarine and the bird have a magnitude — a distance from the surface. That's absolute value!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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