Shaping Up
2 out of 3
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
Problem
For this activity, you'll need to print out these cards. There are 27 different cards in total. Here is a picture of just three of them:
What rules were used to make the 27 cards, do you think?
Have all the possible combinations of two shapes been included?
How do you know?
If the rules were changed so that a card has two triangles, what would the complete set of cards contain?
This problem is based on ideas from "It Makes You Think", a book and CD of mathematical puzzles and problems, produced by Jill Mansergh and available from The Association of Teachers of Mathematics (ATM)
Getting Started
It might help to arrange the cards somehow.
Which shapes don't appear on a card together?
How do you know what all the possible combinations are?
You might want to have a pen and paper handy for jotting things down.
Student Solutions
We haven't received any solutions to this problem yet and so we'd love to hear from you if you have any ideas.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
Shaping Up encourages children to systematise and therefore ask themselves questions. Working on this problem is a great context for exploring the idea of combinations.
Possible approach
Key questions
Possible extension
Possible support
You could only use the cards which have, for example, red and yellow shapes.