See the idea
Before you start
Order whole numbers on a number line and interpret addition or subtraction as a change. Include zero and equal intervals before placing negative numbers.
Words used in this guide
- Negative number
- A number less than zero.
- Opposite
- A number the same distance from zero on the other side, such as 4 and −4.
- Absolute value
- Distance from zero; the absolute value of −6 is 6.
Why the method works
A number line separates position from distance. The number −6 is six units from zero, but lies to the left of −2, so −6 < −2. A larger distance from zero does not always mean a larger number. For addition, a positive change moves right and a negative change moves left. Subtraction means adding the opposite of the subtracted number.
Use position to compare
−5 lies to the left of −2, so −5 < −2. Thinking of temperature can help: −2 degrees is warmer than −5 degrees.
Add a positive amount
Start at −3 and add 5. Move five steps right to reach 2. Crossing zero does not change the size of a step.
Subtract a positive amount
Start at 2 and subtract 5. Move five steps left to reach −3. Keep the starting position, direction and distance separate when drawing the movement.
Worked examples, step by step
Example 1: Calculate −4 + 7.
- Move four steps right to zero, then three more steps right.
- −4 + 7 = 3.
Example 2: A temperature rises from −7 degrees by 10 degrees. Find the final temperature.
- Start at −7. Seven steps right reach zero, leaving three more steps right.
- −7 + 10 = 3 degrees.
- The rise is 10 degrees; the final temperature is 3 degrees. They are different quantities.
Example 3: Evaluate −4 − 3 and −4 − (−3).
- For −4 − 3, add the opposite of positive 3: −4 + (−3) = −7.
- For −4 − (−3), add the opposite of negative 3: −4 + 3 = −1.
- The brackets clarify that the second problem subtracts a negative number; it does not say to move left three times.
Example 4: Find the distance between −5 and 4 on the number line.
- There are five units from −5 to zero and four from zero to 4.
- The distance is 5 + 4 = 9 units.
- Distance is non-negative. The signed change from −5 to 4 is +9, while the reverse change is −9.
Common mistakes and how to repair them
“−9 is greater than −2 because 9 is greater than 2.”
−9 is farther left. Numbers increase to the right, so −2 is greater.
“Two minus signs always make plus.”
Only use a rule in its proper context. Subtracting a negative means adding its opposite; adding two negative numbers still gives a negative total.
Check your understanding
Choose an answer for each question. You can check again after reading the explanation.
Worked answers
Which number is greater? −2. −2 is farther right on the number line.
What is 3 − 8? −5. Move eight steps left from 3.
Practise independently
Work these out on paper. Include a diagram or a sentence where the question asks you to explain. Open each solution after making an attempt.
3. Order −1, −8, 3 and 0.
Show the reasoning
−8 < −1 < 0 < 3.
4. Evaluate −6 + 4.
Show the reasoning
−2; move four steps right from −6.
5. Evaluate 2 − (−5).
Show the reasoning
7, because subtracting −5 means adding 5.
6. A lift moves from floor −2 to floor 6. How many floor intervals does it travel?
Show the reasoning
8 intervals. Count movements between floors, not the number of floor labels including both ends.
If a method still feels uncertain, revisit the closest worked example, then try a fresh problem. A correct answer copied from a solution tells you less than an explanation you can give independently.
Learn it → Try it → Explain it
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Questions students and parents ask
Is zero positive or negative?
Neither. It is the boundary between positive and negative values.
Can a negative number have a larger absolute value?
Yes. −12 is less than 5 but its absolute value, 12, exceeds 5. Value and distance from zero are different.
Why does subtracting a negative move right?
Subtraction adds the opposite. The opposite of a leftward change is a rightward change.
Help at home: Separate starting point and movement
Draw a line from −10 to 10. For −3 + 5, ask your child to mark the start, identify the direction and then count five intervals.
If zero is counted as an extra step, move a counter physically from one tick to the next and count movements.
Ask for the distance between two points as a different question from their sum. This reveals whether the line is being read as positions or only a chant.
Keep the conversation focused on the reasoning you can hear or see. One short activity cannot establish lasting mastery or diagnose a learning difficulty.
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