Adding and subtracting integers on a number line
MathematicsNumbers & ArithmeticAges 11–12
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Numbers & Arithmetic
A number line with two arrows: the blue arrow goes from 0 to a, and the red arrow continues b steps further (to the right for adding a positive number, to the left for adding a negative one; subtraction turns into adding the opposite). Drag the arrow tips to change a and b and see the calculation and result update instantly; turn on absolute value to compare the arrow lengths.
Lesson: Addition and subtraction of integers
What it shows
Integers can be modelled as directed movements along a number line. The blue arrow starts at 0 and ends at a; the red arrow starts at a and has length |b|, pointing right when a positive number is added and left when a negative one is added. The point where the red arrow ends is the result. Subtraction is shown as adding the opposite, a − b = a + (−b), so one rule covers both operations. The information line states the sign rule in use: add the absolute values for equal signs, subtract them for different signs.
How to use
Start with Operation set to a + b and the default a = −3, b = 7. Drag the blue point to change a, or drag the red result point, and read the calculation below. Keep Show absolute value (arrow length) on to compare the lengths of the two arrows. Then switch to a − b, or press Flip sign of b, and check that a − b and a + (−b) end at the same point.
Parameters you can change
- Term a -12–12
- Term b -12–12
- Operation a + b, a − b
- Show absolute value (arrow length)
Questions to explore
- Why is the result of (−3) + 7 positive, and how do the arrow lengths show it?
- Use the number line to find 5 − (−4). Which way does the red arrow point, and why?
- For which values of b does a + b equal 0, and how are a and b related?
