# Mirror Patterns 1

### Task 100 ... Years 4 - 8

#### Summary

These are very visual puzzles showing students that mathematical thinking is not confined to numbers. Every one is a spatial problem solving challenge and tackling interesting problems is the work of a mathematician. Learning develops as the students work through the challenges. Success at the easier shapes creates learning which helps solve the harder ones. Internally, students are using the mathematician's strategy:
Have I seen a similar problem before?

#### Materials

• 2 mirror boards
• 1 dumbbell card
• 1 extra card with challenges for two mirrors

#### Content

• informal application of spatial properties such as length and angle
• properties of reflection
• problem solving

#### Iceberg

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

Students usually get a great deal of satisfaction and enjoyment from these challenges. There is a lot of problem solving involved, but feedback is immediate when they find the correct mirror positions. To create each shape, students need to experiment extensively with different angles for placing the mirrors. A bit of lateral thinking is required. Once they can make a 'square' with 2 mirrors, all the other polygons, triangles, pentagons, and hexagons, can be made by just changing the angle between mirrors.

Here are solutions to some of the harder challenges.

Puzzle H

Puzzle I

Puzzle K

Puzzle N

#### 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.

If you have a class set of mirrors you can turn this task into a whole class investigation. Rather than providing the diagrams, have the students develop their own. Build up a class record and encourage explanation of where the mirror or mirrors need to be placed to achieve each diagram.

Alternatively, consider creating a unit of work on 2D transformation geometry that includes this task and others such as:

Explore the Models & Structures link to find plans your colleagues have used to integrate tasks into a unit of work.

At this stage, Mirror Patterns 1 does not have a matching lesson on Maths300. However, a related lesson is Lesson 123 Mirror Bounce. For more ideas and discussion about this Mirror Bounce, open a new browser tab (or page) and visit 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 Mirror Patterns 1 task is an integral part of:

• MWA Space & Logic Years 3 & 4
• MWA Space & Logic Years 7 & 8

This task is also included in the Primary Library Kit. Solutions for tasks in the latter kit can be found here.