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Locate Rational Numbers on a Number Line

Students place positive and negative rational numbers (including fractions and decimals) on a horizontal and vertical number line. They understand that a rational number and its opposite are equidistant from zero on opposite sides.

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Locate Rational Numbers on a Number Line

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

0 of 20

20 rungs. A star at the top.

−2−1012FGH

−0.5 appears once. Choose that point.

Which lettered dot sits there?

How it is taught

0:00 of 2:55

A rational number is a point on the line, positive or negative.

Negatives sit to the left of 0.

−3−2−10123GHJ

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 is 6 steps of 0.1 to the left of 0. What number is it? — −0.6. 6 steps of 0.1 to the left of 0 is −0.6: the side gives the sign, and the steps give how far.

Plot −1.5 and its opposite

Today we'll find where negative one point five lives on the number line — and discover its opposite.

Here's a number line from negative two to two. Each big tick is a whole number.

Zero sits right in the middle. Positive numbers go right, negative numbers go left.

Negative one point five is halfway between negative one and negative two — right on this little tick.

We drop a dot there and label it negative one point five.

Every number has an opposite. Opposites are the same distance from zero, but on opposite sides.

Mirror across zero and we land on positive one point five. We plot it on the right.

Look — both points are exactly one point five steps from zero.

Where does −1.5 live on the number line?−22−101the middle← negativepositive →halfway−1.5Opposites mirror across 0+1.51.5 units1.5 unitsOPPOSITES±1.5same distance from 0
Grade 6 · Negatives and opposites on the number line

Negative one point five and positive one point five are opposites. Same distance, opposite sides. Nice work!

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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