Original independent learning guide. Not official KICD content.
Read a number line
On a horizontal number line, values increase to the right. Negative five is smaller than negative two because it lies farther to the left. The magnitude of a number describes its distance from zero; it does not tell you whether the number is positive or negative. Draw equal spaces between adjacent integers. Unequal spacing makes a diagram misleading and can produce a wrong estimate even when the labels look correct.
Worked example: a temperature increase
A temperature rises from minus 3 degrees to 5 degrees. It takes three steps to reach zero and another five to reach the final temperature, so the increase is 8 degrees. The final position is 5, but the change is 8. Write the calculation as 5 minus negative 3 equals 8. Check the meaning of the result: a rise should give a positive change.
Adding and subtracting a change
Starting at minus 4, adding 6 means move six steps right, arriving at 2. Starting at 3, adding negative 5 means move five steps left, arriving at minus 2. Subtracting a positive change reverses that change. Subtracting a negative change reverses a movement to the left, producing a movement to the right. Use a small drawing to justify the direction instead of remembering a sign slogan without its meaning.
Use mistakes to plan revision
Before calculating, predict whether the result should be larger or smaller than the starting value. Then check with a number line. If the prediction and answer disagree, review the meaning of the operation before repeating the arithmetic. Teachers can ask learners to explain two different starting positions with the same change. At home, attempt a short set and revisit only the method you could not explain; a long copied answer list does not show understanding.
Practice questions
Calculate minus 7 plus 10.
A temperature falls from 4 to minus 2 degrees. What is the change?
Which is greater, minus 8 or minus 3?
Answers and explanations
Move ten steps right from minus 7. The result is 3.
Final minus initial: minus 2 minus 4 equals minus 6 degrees, a fall of 6 degrees.
Minus 3 is greater because it lies farther right on the number line.
