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The Mathemagician's Seven Spells

7 to 11

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?

problem

Pentabuild

16 to 18

Explain how to construct a regular pentagon accurately using a straight edge and compass.

problem

Time of Birth

11 to 14

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?

problem

Not a Polite Question

11 to 14

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

problem

Two Triangles in a Square

14 to 16

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

problem

The Koch Snowflake

16 to 18

Explore the strange geometrical properties of the Koch Snowflake.

problem

Half a Triangle

14 to 16

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

article

Digital Roots

7 to 14

In this article for teachers, Bernard Bagnall describes how to find digital roots and suggests that they can be worth exploring when confronted by a sequence of numbers.

problem

Sums and Differences 2

7 to 11

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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Always, Sometimes or Never? KS1

5 to 7

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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The Mathemagician's Seven Spells

Pentabuild

Time of Birth

Not a Polite Question

Two Triangles in a Square

The Koch Snowflake

Half a Triangle

Digital Roots

Sums and Differences 2

Always, Sometimes or Never? KS1