this month, Stage 3 & 4

January 2003

 

Problems

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Squaring the Circle

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

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an. . . .

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Overlap

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

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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NRICH Prime Squared

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

What is the first prime number greater than 3? Square it and subtract 1. What do you get? Do ths for the second prime number, then the third. Look at the three numbers you have ended up with. What do. . . .

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LOGO Challenge 7 - More Stars and Squares

Stage:3 and 4 Challenge Level:Challenge Level:1

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

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Excel Investigation: Number Pyramids

Stage:3 and 4 Challenge Level:Challenge Level:2Challenge Level:2

Use Excel to create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.

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Excel Investigation: Pascal Multiples

Stage:3 and 4 Challenge Level:Challenge Level:2Challenge Level:2

This spreadsheet highlights multiples of numbers up to 20 in Pascal's triangle. What patterns can you see?

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Excel Interactive Resource: Number Grid Functions

Stage:3 and 4 Challenge Level:Challenge Level:2Challenge Level:2

Use Excel to investigate the effect of translations around a number grid.

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Excel Technique: Triangular Arrays by Turning Off Zeros

Stage:3 and 4 Challenge Level:Challenge Level:2Challenge Level:2

Learn how to use Excel to create triangular arrays.

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Tree Graphs

Stage:4 Challenge Level:Challenge Level:1

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops). Prove that every tree. . . .

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A Tilted Square

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

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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Square Pizza

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

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

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Semi-square

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

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

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Take a Square

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

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.