Negative numbers: distance also extends left of zero

Where we are on the map

We extend the number line from natural numbers to integers.

Begin with a familiar image

A temperature three degrees below 0°C is −3°C. If it rises by seven degrees, we move seven steps to the right on the number line.

Precise meaning

A negative number represents a value below zero. A minus attached to a number is its sign; a minus between two numbers can mean subtraction.

The lesson’s support signal

meaning → model → calculation → check → explain in your own words

right → increase; left → decrease; opposite numbers are equally far from zero

Worked example

−3 + 7 = 4: seven steps right from −3 pass −2, −1, 0, 1, 2, 3, and end at 4.

Example with a fading prompt

Change the numbers in the example and repeat the solution without copying its steps. Estimate first, calculate exactly, and check against the original condition.

Recall without a prompt

1. Define the main idea in one sentence.
2. Rebuild the support signal from memory.
3. Solve the example with different numbers and explain why every step is valid.

Find and correct the mistake

Saying −5 is greater than −2 is wrong. −5 lies farther left on the number line, so −5 < −2.

Transfer to a new setting

Apply the same relationship to something you can measure yourself. Name the quantities, units, and the boundary within which the model is valid. Check the answer by a second representation or an inverse operation.

Exercise

Required. Show −6 + 9, 4 − 11, and −3 − 5 on a number line and describe the direction of every movement.

With your own data. Create one everyday example with the same structure and show it in words, a formula, and a check.

Optional. Seven days later, change the numbers and repeat without the support map.

Open perspective

Divisibility reveals how numbers are built from factors and prepares us to simplify fractions.

Course contents