# Where Is The Rectangle?

### Task 114 ... Years 2 - 8

#### Summary

Battleships & Cruisers is a game students probably play on occasion to pass the time. This task works in a similar way but includes a richer level of mathematics. Players take turns to be the Hider and Finder, deducing from clues the position of a hidden rectangle. They exchange roles when Finder has identified the co-ordinates of the four corners of the rectangle.
Note
The NRICH web site has a neat, software-based complement to this task which they call Poly Plug Rectangle. It offers several levels of challenge in the Teachers' Notes and video from classrooms.

#### Materials

• Geoboard with rubber bands
• Laminated grid, marking pen and cloth

#### Content

• Recognition and application of the ordered pair convention
• Recording data
• Application of problem solving strategies
• Making and testing hypotheses
• Factors, multiples and primes
• Area and length measurement

#### Iceberg

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

There is no specific answer to this task, which is perhaps part of the reason why students enjoy returning to it. In essence the task applies the mathematician's strategy of working backwards. Taking the example on the card, if you know the area of the rectangle is 12, the rectangle could still be 3 x 4 or 6 x 2. At least, on this geoboard, it can't be 12 x 1. However, prior to this thinking the finder has to first find a starting corner by 'guess, check and improve'.

If the children are looking for an additional challenge you could ask:

• What happens if the hidden shape is a rectangle or square with sides not parallel to the edges of the board?
The Hider will then have the first challenge. How will the area of the shape be calculated? This can be done by dividing the shape into squares and sections that can be combined to make squares. But it might also lead to a discussion of Pick's Rule (Maths 300 Lesson 171, Pick's Rule).

#### 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.

One way to develop the whole class lesson life of this task is to have enough geoboards and rubber bands for each pair. Students are even more likely to become involved in the task (and the many other uses of geoboards) if you have arranged with their craft teacher that they make their own maths equipment.

However, even if you have only one geoboard, the one supplied with the task, you can develop an excellent whole class investigation. One student is chosen as the Hider and you work with the other students to identify the rectangle. Working as a finder yourself provides opportunity to model efficient recording of the unfolding information. Square Dot Paper will be necessary for each student or pair of students.

Further, if you have Poly Plug you can easily develop a version of the same task as described in this section of Poly Plug & Tasks.

At this stage, Where Is The Rectangle? 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 Where Is The Rectangle? task is an integral part of:

• MWA Chance & Measurement Years 5 & 6
• MWA Chance & Measurement Years 7 & 8
This task is also included in the Task Centre Kit for Aboriginal Students.