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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

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Fitting In

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ

Square It

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

This game can be played against the computer, or against a friend.

Players take it in turns to click on a dot on the grid - first player's dots will be blue and the second player's (or computer's) will be red. The winner is the first to have four dots that can be joined by straight lines to form a square.

Squares can be any size and can be tilted.

For an extra challenge, why not increase the size of the grid using the arrow buttons?

If you are not using the interactivity, you may like to print off some dotty paper.

Full Screen and Mobile Version