# Reflections

### Task 95 ... Years 4 - 8

#### Summary

Students explore the properties of symmetry by using one rubber band as the mirror line, making a figure with another on one side of the mirror, then trying to create its reflection.
• What happens if we create angles in the figure?
• What happens if the figure touches the mirror line?
• What happens if we change the orientation of the mirror line?
• What happens if the figure crosses the mirror line?

This cameo has a From The Classroom section which shows the fabulous reflections one class made using their Poly Plug.

#### Content

• spatial perception
• properties of reflection such as equal distance and angle from the mirror
• geometric concepts such as angle, right angle, perpendicular
• length measurement in sides or diagonals of a square
• rotational symmetry

#### Iceberg

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

Note: The word figure is used in this cameo to describe line drawings that don't enclose an area.

Students know when they are correct in this task because it looks right. There is a 'balance' around the mirror line. Encourage them to record their solutions, either directly into their journal or onto the dot paper first. It is easiest to sketch a border around 7x7 dots on the paper first to mark out an image of the geoboard.

Students tend to extend themselves by creating more difficult figures for each other. If not, encourage them to do so and point out that the examples on the card represent the What happens if...? questions above that a mathematician might ask. The last of those questions is not represented on the card so students will have to explore the idea without a drawing to guide them. Again, encourage recording of any creations.

A related challenge is to give the students a drawing such as:

and explain that Sarah has started to record the figure she made and its reflection, but hasn't finished. Their challenge is to choose a mirror line for Sarah, complete the figure and draw its reflection. You can also set challenges such as:

• Sarah finished her figure with one more side length and one diagonal. Draw three possible solutions for her.
• How many solutions are there?
• How do you know when you have found them all?
Note: There are actually many, many solutions for Sarah.
• She might complete the figure at its top or bottom.
• The mirror line could be either of the two diagonals or the horizontal or vertical central axis.
Consider building a class display of Sarah's Figures.

Show the students an example of rotational symmetry on the geoboard such as:

Challenge them to recreate and record this one, then create at least one more rotationally symmetric picture. Challenge students to explain the key features of rotationally symmetric figures.

If someone is looking for another challenge, try this:

• Use a 5 x 5 geoboard - restrict the one in the task by using a rubber band to mark out its perimeter.
• Think of the example above as four paths starting from the centre.
• There are exactly 24 figures with 90° rotational symmetry (Order 4) that can be made using these rules:
1. Paths begin at the centre nail and move from nail to nail until they reach a perimeter nail.
2. When a path reaches a perimeter nail it stops.
3. None of the four paths of a figure cross each other.
The challenge is to find all 24.

Extensions

• Reflection Dancing: Two children face each other as if they were mirror images and devise a dance in which they move as object and reflection.
• Making Reflections: This activity requires two boxes of Attribute Blocks and a one metre ruler. The ruler is the 'mirror'. Children take turns to place blocks. The partner has to place the exact same block in the mirror image position on their side of the ruler. Blocks may be stood up or built on top of each other. Photograph some of the results.
• Making Butterflies: by splodging paint and folding the paper. Cut the butterfly shape and decorate. Make a display garden and attach the butterflies. Alternatively make your own butterfly house as at the zoo.
• Shortest Routes: Choose 4 nails on the geoboard and mark their tops with chalk or sticky tack. Use string (or rubber bands) to find the shortest path that will join them all up. Can you find any rules? What happens if you choose more than 4 nails?

#### 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.

Person B completes a reflection
around the vertical axis.

If you have a class set of geoboards you can easily turn this task into a whole class investigation. If not, but you do have Poly Plug, you can put these to work exploring symmetry. Many patterns students make with the yellow/blue board are symmetric. Any of these is a starting point for discussion. When the properties of symmetric shapes have been identified, use two boards side by side (or corner to corner if you want a diagonal line of symmetry). Person A turns some plugs on one board. Person B turns the mirrored plugs on the other.

If you have neither geoboards nor Poly Plug, consider creating a unit of work on 2D transformation geometry using 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.

Visit Reflections on Poly Plug & Tasks. Also see the photos below from Year 6, Camberwell Primary School, where some students explored Poly Plug patterns created using a reflections and rotations.

At this stage, Reflections does not have a matching lesson on Maths300. However, a related lesson is Lesson 123 Mirror Bounce. For more ideas and discussion about 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 Reflections task is an integral part of:

• MWA Space & Logic Years 5 & 6
This task is also included in the Task Centre Kit for Aboriginal Students.

## From The Classroom

#### Camberwell Primary School

Year 6
Students worked in teams (usually four) creating multiple copies of a Poly Plug arrangement and then transformed the unit piece in various ways to make a tiling pattern. This was one Mathematics Week activity. Check Task 96, Networks, for more work on transformations created during this week, this time using Pattern Tiles as the tool.