How to teach rational numbers and the number line

Year 7 (ages 12 to 13)

How to teach it

1. Convert fractions to decimals by dividing, and decimals to fractions by writing the decimal over its place-value denominator and simplifying.
2. Plot a mix of fractions, decimals and negative numbers on the same number line to build a sense of their relative size.
3. Order a set of rational numbers by converting them all to a common form (usually decimals) first.
4. Find the midpoint between two rational numbers by averaging them, connecting this to the same skill used for coordinate midpoints later.
5. Use negative rational numbers alongside positive ones so the number line is not treated as starting at zero.

Worked example

Find the rational number exactly halfway between -4 and 10
(-4 + 10) / 2 = 6 / 2 = 3

Common mistakes

• Converting a fraction to a decimal by subtracting instead of dividing.
• Ordering rational numbers by comparing only the digits, ignoring the sign or the decimal point's position.
• Forgetting to simplify a fraction after converting it from a decimal.
• Assuming the midpoint of two negative numbers must also be negative, without actually calculating it.