Patterns that lead to algebra and proof - October 2010, Stage 2&3

Mathematicians are fascinated by pattern - one writer has even described 'pattern sniffing' as a mathematical behaviour. In this month's activities and problems we invite you to discover patterns, describe them in different ways and begin to think about how you can convince yourself, and others that you have sniffed out all there is to find!

Problems

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Sitting Round the Party Tables

Stage: 1 and 2 Challenge Level: Challenge Level:1

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Carrying Cards

Stage: 2 Challenge Level: Challenge Level:1

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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Three Dice

Stage: 2 Challenge Level: Challenge Level:1

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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Which Is Quicker?

Stage: 2 Challenge Level: Challenge Level:1

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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Shapes in a Grid

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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Your Number Is...

Stage: 3 Challenge Level: Challenge Level:1

Think of a number... follow the machine's instructions. I know what your number is! Can you explain how I know?

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Your Number Was...

Stage: 3 Challenge Level: Challenge Level:1

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

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Special Numbers

Stage: 3 Challenge Level: Challenge Level:1

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?