Analysing - June 2009, All Stages

Analysing a problem in order to decide on appropriate mathematical procedures plays a key role in successful problem-solving. • Do we estimate or approximate or do we use more accurate methods of calculation? • Do we use diagrams or graphs? • Do we manipulate numbers or use algebraic techniques? • Do we check our working regularly? • Do we record our work, our solutions and our conclusions in the most effective way? These are some of the important questions that we may need to ask ourselves.

Problems

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Chain of Changes

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

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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Routes 1 and 5

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

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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Today's Date - 01/06/2009

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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Holes

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

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

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Cutting it Out

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

I cut this square into two different shapes. What can you say about the relationship between them?

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Which Scripts?

Stage: 2 Challenge Level: Challenge Level:1

There are six numbers written in five different scripts. Can you sort out which is which?

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Fractions in a Box

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

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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The Magic Number and the Hepta-tree

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

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!

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Keep it Simple

Stage: 3 Challenge Level: Challenge Level:1

Can all unit fractions be written as the sum of two unit fractions?

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Egyptian Fractions

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

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

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The Greedy Algorithm

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

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

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Power Countdown

Stage: 4 Challenge Level: Challenge Level:1

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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Take a Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

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Take a Square II

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What fractions can you divide the diagonal of a square into by simple folding?

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Six Discs

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

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Integration Matcher

Stage: 5 Challenge Level: Challenge Level:1

Match the charts of these functions to the charts of their integrals.

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Curved Square

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the area of the central part of this shape?

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PCDF

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When can a pdf and a cdf coincide?

Elsewhere...