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Understand Positive and Negative Numbers

Students are introduced to negative numbers as quantities representing values below zero, such as temperatures, debt, and sea level. They identify negative integers and rational numbers on a number line and interpret their meaning in real-world contexts.

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Understand Positive and Negative Numbers

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

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20 rungs. A star at the top.

In football, a gain of 7 yards is written as 7. What integer stands for a loss of the same number of yards?

How it is taught

0:00 of 3:03

A negative number names a value below 0.

The same distance on the other side is its opposite.

−50−2502550FGHJ

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 5 steps to the left of 0. What number is it? — −5. 5 steps to the left of 0 is −5: the side gives the sign, and the steps give how far.

Morning +5°, Night −3°

Have you ever seen a thermometer drop below zero on a freezing day? Numbers can go below zero too!

Here's a number line. Zero sits right in the middle — it's our starting point.

Numbers to the right of zero are positive. They count up: one, two, three, and so on.

Say the morning temperature is five degrees above zero. We mark plus five to the right of zero.

Numbers to the left of zero are negative. They count down below zero.

By night, it drops to three degrees below zero. We write negative three, with a little minus sign in front.

Notice: negative three and positive three are the same distance from zero — just opposite directions.

What's colder than zero?❄️ Brrr! ❄️Some numbers live below zero.The Number Line−55−5−4−3−2−1012345zeroPositive →+5morning ☀️← Negative−3night 🌙+3Same distance from 0 — opposite sides.🌡 −10° cold💰 −$5 owed🌊 −20 ft deepREMEMBER+ vs −above & below 0Negative numbers extend the number line below zero.
Grade 6 · Numbers above and below zero

We use negative numbers everywhere: cold temperatures, money owed, or depths below sea level.

Positive numbers go up from zero, negative numbers go down. Together, they let us describe the whole world!

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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