Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Have You Got It?

Can you explain the strategy for winning this game with any target?

Counting Factors

Is there an efficient way to work out how many factors a large number has?

Number Families

Age 11 to 14
Challenge Level

Why do this problem?

This problem gives students plenty of opportunity to explore and discuss patterns and properties of numbers. It would make a great starter activity as a prelude to some in-depth work on Factors, Multiples and Primes.

Possible approach

Show students the image above from the problem, or display this slide.
"From this set of numbers, can you find four or more that belong together?
Write down your set of numbers and a sentence to explain why they go together."

Give students a short while to find a set, and then collect together examples of sets on the board. You could invite students to tell you their four (or more) numbers and then ask the rest of the class to suggest the rule that describes the set.

A possible homework task could be to come up with as many different sets as possible, together with explanations.

Possible support

Students could start by listing as many properties of each number as they can, and then look for numbers which have the same property.

Possible extension

Students could then have a go at the Factors and Multiples Puzzle, Dozens and Shifting Times Tables

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