Primary 6 · Investigation

Can you find the rule?

Nobody is going to tell you the formula for adding a long list of numbers. You are going to work it out yourself — by making pairs, collecting evidence, and testing your ideas.

1

First, the slow way

Add the numbers from 1 to 10, one at a time. Keep tapping. Count how many taps it takes.

0
Tap “Add the next number” to begin.
2

Make your own pairs

Tap any two numbers to join them into a pair. You choose which ones. Watch what each pair adds up to.

Finish the slow way first.

PairAdds up to
Make a pair to get started.
3

Predict before you check

You paired 1 to 10 end to end. Without adding them all up again, work these out.

Pair up all ten numbers the end-to-end way first.

4

Collect your evidence

One example proves nothing. Pair up these other lists too, and watch the table fill with clues.

Make your prediction first.

ListFirstLastFirst + last How many numbersReal total
No evidence yet — pair up a list above.
Collect at least three lists before moving on.
5

Which rule fits every row?

Here are four possible rules. Pick one and test it against your own evidence. Only one survives.

Collect at least three lists of evidence first.

6

You found it

Find the rule that works first.

Sum  =  ( first + last )  ×  how many numbers  ÷  2
You didn't get told this rule. You made pairs, spotted that every pair matched, and tested it until only one rule was left standing.
One last puzzle. Every list you tried had an even number of numbers, so the pairs came out neatly. What happens with 1 to 9 — an odd number of them? Try it and see whether your rule survives.
For the teacher. The order matters here: students feel the problem, make pairs by hand, predict, gather evidence across several lists, and only then choose between rival rules. Stage 2 deliberately lets them pair numbers any way they like — pairing 1 with 2 and 3 with 4 gives uneven totals, and noticing that is what makes the end-to-end pairing feel like a discovery rather than an instruction.