Exploring Symmetry Years K - 6

### Summary

Children are introduced to the concept of symmetry and create their own examples in the yellow/blue board. Each creation has the potential to generate number work and in fact, multiplicative thinking, since every example will, at least, be a double. Suitable for threading.

### Materials

• 1 Poly Plug per person
• 1 drinking straw per person

### Acknowledgement

Viv Stagg, Jo Medcraft, Mayfield Primary School and Nancy Dear, Tania Webb, Glennis Everett, Rocherlea Primary School with Sue Morgan, Kingston Primary School

### Procedure

Beginning with one side of the board all yellow, turning over plugs so they are blue side up can create many patterns with line symmetry.

In the photo above Joshua was in Year 2. It was the first day he had used Poly Plug and this was the first pattern he made during a free play introduction. It is almost certain that in any class at least one child will produce a symmetric pattern like this in free play, so the activity can be seen to grow from children's own exploration.

• What do you notice about Joshua's board?
• Accept and discuss whatever is offered, but when the concept of symmetry comes up, use a drinking straw to show the line of symmetry.
• Would you like to know the mathematician's name for a picture like this?
Allow the children to explore as individuals or in groups using a straw to hunt for symmetry in their creations. Encourage recording on Poly Plug Paper or Poly Plug Frame. Coloured sticky dots on a photocopied outline of a Poly Plug Frame works well, because it saves time that children might uselessly spend colouring circles.

### Content

• 1:1 correspondence
• equations: creating/solving
• operations - whole number
• order of operations
• pattern interpretation
• pattern recognition
• recording - calculator
• recording - written
• transformations (rotations, reflections, flips)
• times tables
• visual and kinaesthetic representation of number

Once the symmetry pattern has been recorded, these questions give even more meaning to the recording:

• How many blue plugs are showing? (hidden?)
• How do you know?
• Can you check it another way?
• How many ways can you check it?
because the equations that result can be recorded with the pattern.

Unfortunately, we don't have a copy of Joshua's recording, but if you click the image, you will see a larger version which you could then save as a stimulus photo to model the range of equations that could develop from it. For example, blue plugs showing could be:

• 4 + 4 + 4 + 4 + 1 = 17
• 4 + 4 + 3 + 3 + 1+ 1 + 1= 17
• double 4 + double 4 + 1 = 17
• double 8 + 1 = 17
• double 2 + double 2 + double 4 + 1 = 17
• double 4 + double 3 + double 1 + 1 = 17
• double 4 + double 3 + double 1and a half = 17
• half of 17 = 8 and a half
• ...and so on
Recording can also be extended by combining it with recording on the calculator.
• How many times have you pressed 4 in 4 + 4 + 4 + 4 + 1? Can you use the calculator to write 4 + 4 + 4 + 4 + 1 another way?
• How can you write half of 17 on the calculator?
• How can you explain the answer?
We would be happy to receive photos or scans of your children's work.

#### Variations

• How many different symmetric patterns can the class find? Find a way to make a class display of them all.
• Children can make a symmetric pattern for their partner to copy. See Copy Cats.
• Child A makes a symmetric pattern and shows it to Child B for an agreed time, say 30 seconds, before it is hidden. Child B is then challenged to recreate the pattern from memory.

### Extensions

• Four children who combine their boards can make more extensive symmetric patterns.
• Try all the same ideas again with rotational symmetry. See the activity Rotation Challenges.
• The NRICH web site has a neat, software-based complement to this task which they call Poly Plug Pattern. It extends pattern making to a 5 x 5 array of boards and is supported by Teachers' Notes. It also has a 'smashing' pattern solution from Heather at Cottenham Primary School, which again confirms children's predisposition towards symmetry.
• Use the Task Cameo Content Finder to find Tasks that involve symmetry.

Calculating Changes ... is a division of ... Mathematics Centre