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?

Problem

Here is a set of shapes:

Image
The first row has a red circle, square, rectangle, and equilateral triangle. The second row has a yellow circle, square, rectangle, and equilateral triangle. The third row has a blue circle, square, rectangle, and equilateral triangle.

 

What do you see?

What do you notice?

If possible, talk to somone else about your noticings.

In this problem, we are going to arrange shapes in a line, in a particular order.

You may like to print and cut out a set of shapes from this sheet, or you could try out your ideas using the interactivity below.

Your challenge, as you add a shape to your line, is to change first colour, then shape, then colour again, then shape and so on. (Or first shape then colour...)

For example, if you put the yellow triangle after the blue one and so change the colour, next you must put another yellow piece and so change the shape.

To help you get the idea, below there are two pictures. Each picture shows the first four shapes of a sequence. 

Which sequence follows the rule and which does not? How do you know?

Sequence 1:
Image
Red circle, yellow circle, yellow rectangle, blue rectangle.

...

Sequence 2:
Image
Red square, yellow triangle, red square, yellow rectangle.

...

Have a go at creating your own sequence of shapes which follows the rule of changing first colour, then shape, then colour... (Or first shape, then colour...)

How many shapes did you use?

Have another go. How many shapes did you use this time?

Is it possible to use more shapes, still following this pattern?

Can you use all the shapes in this way? Why or why not?