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Compare and Order Rational Numbers

Students write inequality statements to compare rational numbers and order a set of rational numbers from least to greatest or greatest to least. They use the number line to justify comparisons and understand that farther to the left means less.

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Compare and Order Rational Numbers

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

0 of 20

20 rungs. A star at the top.

−303RABC

Of the dots from −3 to 3, which number is the greatest?

Compare the dots by position.

How it is taught

0:00 of 3:09

On a number line, greater means farther right.

With negatives, a bigger digit can be farther left.

−3−2−10123EFG

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|.

Which is smaller, −8 or −5? — −8. −8 sits farther left than −5 on a line with 0 in the middle: farther left is less, whatever the digits say.

Order -2, 1, and -0.5 from least to greatest

Let's order three numbers from least to greatest: negative two, one, and negative one-half.

Here's the trick: on a number line, the farther LEFT a number is, the smaller it is.

Let's draw a number line from negative three to three.

First, negative two. It sits two steps to the left of zero.

Next, negative one-half. That's halfway between negative one and zero.

Now positive one, one step to the right of zero.

Reading from left to right, we see: negative two, then negative one-half, then one.

Order from least to greatest:−2 1 −0.5Farther LEFT = smallerOrder: −2, 1, −0.5−3−2−10123−2−0.51least → greatest−2 < −0.5 < 1ORDERED−2 <−0.5 < 1least to greatest
Grade 6 · Using the number line to compare positives, negatives, and decimals

So from least to greatest, we write negative two is less than negative one-half is less than one.

And that's our order! Farther left means less. Great job comparing rational numbers!

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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