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Consecutive Numbers

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14 Divisors

What is the smallest number with exactly 14 divisors?

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Think of Two Numbers

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?

This problem can be solved by both trial and improvement and by using simple algebra. It is the intriguing kind of "puzzle-game" that can be taken from the maths classroom into the playground! A poster of this problem is available here.

Possible approach

This printable worksheet may be useful: Think of Two Numbers. 

You could introduce the problem as it appears on the site as a printed sheet or on a computer. Learners could first work individually to give them 'thinking time', then work in pairs to support each other and to give an opportunity for mathematical talk, and finally there could be a class discussion.
A concluding plenary could ask them to share any insights and strategies that helped them succeed at this task.

Key questions

Have you tried with several numbers to see what is happening?
What can you say about the answer and the first number that was chosen?
What can you say about the answer and the second number that was chosen?
Have you tried doing it with someone else whose numbers you do not know?
Have you tried using two letters in place of the two numbers?

Possible extension

Learners could go on to Multiply the Addition Square.

Possible support

Suggest trying with different numbers, thus practising simple calculation, even if the generalising is not done.