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Adding Plus

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Adding Plus


If you write plus signs between each of the digits $1$ to $9$, this is what you get:

$1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$

However, if you alter where the plus signs go, you could also get:

$12 + 3 + 45 + 6 + 7 + 8 + 9 = 90$

Can you put plus signs in so this is true?

$1\;$ $2\;$ $3\;$ $4\;$ $5\;$ $6\;$ $7\;$ $8\;$ $9\;$ $= 99$

How many ways can you do it?

Why do this problem?

This problem is one on which learners will need to practise much addition and subtraction! It will require systematic work using an approach of trial and improvement.

Key questions

What do the numbers from $1$ to $9$ add to? What do you still need to make $99$?
How about trying to make $90$ using the digits $1$ to $8$ and leaving the $9$ for adding on at the end?
Why not start by pushing the $1$ and $2$ together to make $12$?
Why not try pushing the $2$ and $3$ together to make $23$? What do you need now to make $90$?

Possible extension

Learners who find this straightforward could work out all the different numbers with less than four figures that can be made in the same way while still keeping the digits from $1$ to $9$ in order.

Possible support

Children could use a calculator to work out what the numbers from $1$ to $9$ add to and the differences made by putting two adjacent numbers together to make a two-digit number.