Squares

problem
Pinned squares

Age

14 to 16

Challenge level

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

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
Similarly so

Age

14 to 16

Challenge level

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
problem
Take a square

Age

14 to 16

Challenge level

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
Squaring the circle and circling the square

Age

14 to 16

Challenge level

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
problem
Something in common

Age

14 to 16

Challenge level

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
Paper patchwork 1

Age

5 to 7

Challenge level

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
problem
Logic block collections

Age

5 to 7

Challenge level

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

Age

5 to 7

Challenge level

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
problem
Chain of changes

Age

5 to 7

Challenge level

In this activity, shapes can be arranged by changing either the colour or the shape each time. Can you find a way to do it?