### Tangrams

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

### Three Squares

What is the greatest number of squares you can make by overlapping three squares?

### Chain of Changes

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

# Complete the Square

## Complete the Square

Can you complete the squares?
Use the pencil on the screen to finish the squares.

Full Screen Version

This text is usually replaced by the Flash movie.

If you are working away from the computer, you might like to print off this sheet of the squares to complete.

This activity comes from BEAM's Maths of the Month

### Why do this problem?

This problem is excellent for helping to reinforce the properties of squares and in particular for highlighting the fact that a square is a square no matter what orientation it is in.

### Possible approach

You could introduce this activity by showing the children a square piece of paper. Put the square on the board so that its sides are parallel to the sides of the board and ask the class what shape it is. How do they know? Then, invite one pupil to come up and pin the square on the board in a different way. Is the shape still a square? You might find that an interesting discussion ensues! It is common for children to call a tilted a "diamond" but the earlier we can encourage them to avoid this, the better.

Once pupils have tried the problem (whether on paper or using the interactivity), they could show each other their completed squares and discuss the drawings before sharing them with you and/or the whole class. Playing the game Square It would be a good way to end this lesson.

### Key questions

What do you know about squares?
What do you need to add to this to make it a square?

### Possible extension

You could give some learners a grid (for example $3$ by $3$ small squares) and challenge them to draw all possible squares on it, if all corners have to be on the grid.

### Possible support

Children may need rulers to convince themselves that the sides of the shape they have drawn are (or are not!) the same. Turning the page also helps!

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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