Recall the rule for adding and subtracting fractions

What this is

A rule to be told and then rehearsed: To add or subtract fractions, keep the denominator, and add or subtract the numerators. It is the fourth step of adding or subtracting two fractions. Students have already decided whether the fractions are ready and, if they weren’t, written the lists and picked the pair with the same denominator. This rule says what to write next. They write it as a set-up, not an answer: (8 + 3) over 18, not 11 over 18. Working it out is the last step.

The routine

• Explain. Say the whole rule. Students repeat it.
• Frame. Say what the rule is for. Students give the rule. Press Reveal to check.
• Reframe. The rule is turned around. Say the rule on screen. Students say what it is for.
• Rehearse. Nothing on screen. Students give the whole rule, starting with what it is for.

Run it out loud first (individuals, then the whole class), then again on mini-whiteboards. You choose each time whether students say it or write it; the screen is the same either way. Reveal turns into Hide, so you can put the blank back and ask someone else.

Why the rule says what it is for

Knowing a rule is only half the job. Students also need to know when to reach for it, in the same way that they learn a formula and what the formula is for. That is why Frame gives what the rule is for and asks for the rule, and Reframe gives the rule and asks what it is for.

Why it can simply be told

Every idea in the rule is already secure or is plain English. “The denominator” comes from Are these fractions ready to be added or subtracted?; by now the two fractions share one. “Add or subtract” is whatever the question’s sign says. “Numerator” may be new to students: the earlier atoms only needed “denominator”. Check they know which number it is before you tell them the rule.

The rule says “numerators”, never “tops”: “add the tops and add the bottoms” is the chant behind the commonest mistake (4/9 + 1/6 = 5/15).