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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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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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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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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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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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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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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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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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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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 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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Folding Squares

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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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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Curved Square

Stage: 5 Challenge Level: Challenge Level:1

Can you find the area of the central part of this shape? Can you do it in more than one way?

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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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PCDF

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

When can a pdf and a cdf coincide?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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