### Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

### Three Squares

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

### A City of Towers

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

# Change Around

## Change Around

Here is another triangular shape made from arranging circles.

Move just three of the circles so that the triangle faces in the opposite direction.

You could use this interactivity to try out your ideas:

### Possible approach

This activity can be approached several ways in the classroom. Each child can be given a set of ten counters, coins or discs and asked to set up the triangle and then physically move the objects. A more abstract approach is to ask the children to draw the shape and visualise what changes can be made and then try them out. A third alternative is to use the interactivity provided and allow the children to move the red circles to form the new triangle.

It is an idea not to set the task with its condition of only three moves to begin with. Let the children explore the activity and then ask how many changes they had to make to reverse the direction of the triangle. Based on their input set the challenge: Can it be done in five or even four moves? How about just three moves? Before they start to solve for three moves invite the children to think about, and then describe, which circles might be moved. As the task becomes more difficult the children are able to use what they have learned in the easier stages and visualise solutions to the more complex problem.

### Key questions

Can you picture what the new triangle will look like?
Try moving some counters/balls and see what happens.
Can you do it in fewer moves?