# Octaflex

### Task 16 ... Years 2 - 10

#### Summary

Attractive, apparently straightforward, foam shapes offer spatial challenges which can be quite devilish. Problem solving strategies such as try every possible case are called on (albeit informally) as spatial perception develops.

#### Materials

• Panel of 8 foam shapes - some made from 7 squares and some from 6
• Playing board, marker and cloth

#### Content

• sorting
• spatial perception
• shape recognition
• perimeter & area
• factors

#### Iceberg

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

1. Place all the pieces on the table and mix them up. How many seconds does it take you to get them back into the frame. What is the class record?
2. Select any two shapes and fit them together in any way. Draw the perimeter of this combined shape on centimetre grid paper. Repeat until you have at least 10 puzzles on the page. Challenge someone else to solve your perimeter puzzles.
(Depending on student experience you might change this to 3 or 4 piece perimeter puzzles.)
Two examples are shown opposite. They were made in minutes using a black square created in a drawing program. The square was copied and moved to create the perimeter puzzle. A great opportunity to combine mathematical work on shapes with learning how to control features of technology such as the drawing tools in Word.
3. What is the longest possible perimeter of a 2 piece perimeter puzzle?
4. Use centimetre grid paper to make more puzzles like the ones on the task card. If each student produces one puzzle you will have class set of challenging spatial puzzles.
5. The eight pieces make a rectangle. How many squares are inside the rectangle?
6. If there were other rectangles shapes which could be made from the 8 pieces, what are the only sizes they could be? (Squares are rectangles too.)
7. Can any of these other sizes be made? How do you convince someone else?
8. Can you make rectangles without using all the pieces? How many rectangles can be made? How do you know when you have found them all?

#### 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.

The foam Octaflex sets shown in the photo are no longer available. However, you could turn this task into a whole class lesson by drawing the 8 Octaflex pieces using computer software. Draw them based 1cm squares and they will fit the challenge diagrams in the task. Print from the computer to card to make a class set. It helps to print each set on a different colour card (as far as possible) then each pair knows they need to pack up 8 pieces and they know their colour.

Now you only have to organise a team to carefully cut out the shapes; perhaps this can be the students in the first class that investigates the Octaflex challenges. The sets can be stored in envelopes for use year after year.

Another approach is to start by providing pairs with 1cm linking cubes and displaying the 8 pieces on the screen. The first challenge is to make the 8 pieces.

The notes above suggest several directions the whole class investigation could take. Experiences in spatial perception and reasoning underpin them all.

#### 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 Octaflex task is an integral part of:

• MWA Space & Logic Years 5 & 6
• MWA Space & Logic Years 9 & 10