Squares

problem

Tetra Square

Age

14 to 18

Challenge level

2 out of 3

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
problem

Square Areas

Age

11 to 14

Challenge level

3 out of 3

Can you work out the area of the inner square and give an explanation of how you did it?
problem

Dissect

Age

11 to 14

Challenge level

3 out of 3

What is the minimum number of squares a 13 by 13 square can be dissected into?
problem

Pinned Squares

Age

14 to 16

Challenge level

3 out of 3

What is the total number of squares that can be made on a 5 by 5 geoboard?
problem

2001 Spatial Oddity

Age

11 to 14

Challenge level

3 out of 3

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
problem

Take a Square

Age

14 to 16

Challenge level

3 out of 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.
problem

Something in Common

Age

14 to 16

Challenge level

3 out of 3

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
problem

Logic Block Collections

Age

5 to 7

Challenge level

1 out of 3

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
problem

Square Surprise

Age

5 to 11

Challenge level

1 out of 3

Why do you think that the red player chose that particular dot in this game of Seeing Squares?
game

Seeing Squares for Two

Age

5 to 11

Challenge level

1 out of 3

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?