Here is a number trick. "I think of a number. I double it. I add 5. I get 17." What number did I start with?
Have a think: how could we work backwards from 17 to find the number I first thought of?
Take three hands-up answers, not open call-outs. Some pupils will guess-and-check; that is fine as an entry point. Do not reveal the letter-symbol method yet — the point of the hook is to leave them curious about a tidier way than trial and error. Give five seconds of quiet think-time before any hands go up.
We turn three number stories into equations, then solve them by undoing. In each one a letter stands for the number we are hunting for, and we work backwards to set it free.
Work each story live on the board. Do not read solutions off the screen. For Story 1, hold out until a pupil names the hook number, then show that 2n + 5 = 17 is that story in symbols.
Before Story 3, pause and pick a pupil to name what got undone first in the pencils problem, so the three-undo story lands on a fresh class. Slip to watch: undoing in story order instead of reverse, or dividing first when something was added last. Keep asking which operation happened last? before anyone touches the equation.
We walk through this worked example together on the interactive first, then work two more by hand on the board:
Then, together on the board:
For each one, name the unknown with a letter, write the equation, then undo step by step.
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.
Do the treble-and-take-away one on the interactive first. Then work the apples problem (6b = 30, one undo) and the chairs problem (4r + 3 = 27, two undos) by hand on the board, with pupils calling each step. The apples one is a deliberate breather after the two-step trick; the chairs one adds the second undo back in. Keep the three brisk — one interactive problem and two quick board problems is an eight-minute beat, not longer. Keep asking which operation do we undo first, and why? before anyone moves.
In your maths copy, for this problem write three things: the equation, your solution steps, and one sentence saying what the answer means in the real situation.
Work this one:
Finish with a sentence like "So the number I thought of was ___."
Done early? Try this one too:
Walk the room glancing for three things on the page — an equation, solving steps, and a sentence in words. This is whole-class copybook practice, not marking. Everyone completes the first problem well rather than rushing; the second is a fast-finisher extension, so slower writers are not left behind in the short slot. The interpreting sentence is the part pupils skip; nudge anyone who stops at the bare number. More of this practice, at each pupil's own pace, is on the printable worksheet.
Today we work through these Irish-context puzzles together, in order:
Write your own number-trick puzzle, then hand it up to swap with the class.
Form an equation for each Irish-context situation, solve it, and say what the answer means. The four core problems rise in difficulty; the final task is to invent your own.
Ways to start:
Stretch:
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
The taxi problem is the one that catches people: pupils want to write 2k + 4 but then divide by 2 first. Ask what was added last? so the €4 start comes off before the €2-per-km is undone. On the fundraising problem there is no fee to remove, so it is a single undo — a deliberate easier rung. Fast finishers write their own puzzle quietly while you circulate; do not send them to a device. The same four puzzles are on the printable worksheet for pupils to redo at their own pace.
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