Why do this problem?
encourages children to systematise and therefore ask themselves questions. Working on this problem is a great context for exploring the idea of combinations.
Ideally, it would be good if children had a set of the cards to work with in pairs.
You could introduce the activity by asking the children to describe the cards. Many will mention the coloured shapes and the fact that there are two shapes on each card. Encourage them to be more specific in their desciptions by asking them about the "rules" that they think were used to make the cards. They could talk about this in their pairs before sharing ideas with the whole group.
In order to find out whether all the possible combinations are included in the cards, again, allow them some thinking time in pairs first. How are they going to find out? Take a few minutes to discuss their ideas amongst the whole class - this might involve doing some recording, or arranging the cards in a particular way. There is no right way to go about it, but what is important is having
a system or order of some kind so that they know there aren't any missing.
Can you arrange the cards in a way that will help you find all the combinations?
Which shapes appear on a card with the yellow square? Are there any that don't appear with the yellow square?
Which shapes appear on a card with the red square ... the blue square ...?
Challenge children to create an equivalent set of cards. You could invite them to use any design they choose, but you could always have a few suggestions up your sleeve, for example three other shapes.
You could only use the cards which have, for example, red and yellow shapes.