# Six Square Puzzle

### Task 68 ... Years 2 - 7

#### Summary

Each question in the puzzle begins with six squares arranged in two rows of three. Each challenge involves removing some sticks to leave a particular arrangement. Generally speaking the challenges become harder as you move through the card.
Note: Historically these challenges were parlour or pub tricks using matches. We have kept that history in the name, but provided material that is visually and kinaesthetically more satisfying.

#### Materials

• 17 sticks (matches)

#### Content

• 2D spatial perception
• problem solving and reasoning
• links to area and perimeter

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

Match stick puzzles help to develop spatial perception and logical reasoning. Spatial perception - or awareness - is the ability to view figures and objects within the mind and to transform the mental image so the object can be imagined from a different view point. This task offers only a selection from the many available match puzzles and builds them into a theme by using the same starting point in each case. Students will be using visualisation and reasoning strategies such as What happens if...? and Breaking a problem into parts, or Working backwards, to solve the puzzles.

The solutions are listed below. However, rather than just making them available to students, you could generate additional interest by declaring that you don't know any of the solutions, and that you will name each one after the pair who discovers it. It would also be appropriate to ask students to record the area and perimeter of each solution.

 Question 1 Are there only four squares? Question 2 There is another way! Question 3 Question 4 Question 5 Question 6
Further challenges include:
• Finding another way to remove sticks from the starting shape and leave an interesting design.
• What can be created if we move sticks but don't actually remove them?
(For the most part, these problems generally involve squares, rectangles and triangles.)
• Can you create a sequence of match stick puzzles using a different starting point?
• Research and report on match stick puzzles you find on the web.
(There's quite a lot actually and it can provide the basis for some interesting projects.)

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

It's easy to turn this task into a whole class activity - you just need plenty of matches, or their equivalent. Begin with the challenges on the card and discuss the reasoning students use to solve each one. Where possible, relate their comments to the Working Mathematically Process so they can see that they have been working like mathematicians. Encourage them to suggest further related problem solving challenges and investigations and look towards building a reasoning based project around their responses.

Some students might remember (or even have collections of) match stick puzzles from the back of matchboxes. The Redheads company in Australia has a long history of these matchbox puzzles and they have now a great interactive site with several match puzzles. The site would work very well on your electronic whiteboard. Again, the purpose would be to try to identify and analyse student reasoning and relate it to the process of working like a mathematician.

At this stage, Six Square Puzzle does not have a matching lesson on Maths300.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Six Square Puzzle task is an integral part of:

• MWA Space & Logic Years 7 & 8
This task is also included in the Task Centre Kit for Aboriginal Students.