January 2003, All Stages

Problems

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Little Squares

Stage: 1 Challenge Level: Challenge Level:1

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

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What's Left?

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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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Tangrams

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

Can you make five differently sized squares from the tangram pieces?

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Polydron

Stage: 2 Challenge Level: Challenge Level:1

This activity investigates how you might make squares and pentominoes from Polydron.

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Counter Ideas

Stage: 2 Challenge Level: Challenge Level:1

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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Cycling Squares

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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Two Primes Make One Square

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

Can you make square numbers by adding two prime numbers together?

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Geoboards

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

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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Penta Primes

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

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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Seven Square Numbers

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

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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Overlap

Stage: 3 Challenge Level: Challenge Level:2 Challenge 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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Squaring the Circle

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

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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 Technique: Triangular Arrays by Turning Off Zeros

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

Learn how to use Excel to create triangular arrays.

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Excel Interactive Resource: Number Grid Functions

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

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

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Excel Investigation: Pascal Multiples

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge 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 Investigation: Number Pyramids

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge 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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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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Take a Square

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

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Semi-square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge 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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Square Pizza

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge 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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A Tilted Square

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

Stage: 5 Challenge Level: Challenge Level:1

Prove that the sum from t=0 to m of (-1)^t/t!(m-t)! is zero.

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Cocked Hat

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

Sketch the graphs for this implicitly defined family of functions.

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Modular Knights

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Try to move the knight to visit each square once and return to the starting point on this unusual chessboard.