Visual = Number

Years 1 - 8

Summary

Wherever there is a visual pattern, there is a number pattern and vice versa. Poly Plug is a tool with which children often make patterns. This activity - described as it grew in one classroom - illustrates how a teacher can begin and extend an investigation from a child's pattern.

Materials

  • One Poly Plug per child
 Square Perimeters

Acknowledgement

This activity was contributed by Gay Lynch, Herdsman's Cove Primary School.

Procedure

This activity began when we were colouring 100 Squares in my Grade 1. Making them with Poly Plug is quicker. As the children made their patterns, a sentence from one of our Calculating Changes professional development workshops kept going through my head.
Wherever there is a visual pattern there is a number pattern; and wherever there is a number pattern there is a visual pattern.
Consider the arrangement of plugs in the photo. 		 

Content

  • multiplication
  • odd & even numbers
  • pattern generalisation
  • pattern interpretation
  • pattern recognition
  • problem solving
  • recording - written
  • square numbers
We decided to count the number of plugs in each concentric square, beginning from the outside:
36 ... 28 ... 20 ... 12 ... 4
I told my kids that because these numbers came from a pattern we can see in the plugs then there must be a pattern in the numbers. They started hunting.
  • Given it was a Grade 1, I was quite pleased when they noticed that each pair was 8 apart.
  • But I nearly fell over when one of my students said that they were 'four times numbers'.
That set us off looking at the fours in each one:
4 x 9 ... 4 x 7 ... 4 x 5 ... 4 x 3 ... 4 x 1
They were all four times an odd number!

I know not all my students were with me on this investigation, but they all did know that we were doing it because:

  • one of their classmates had made the suggestion
  • when you see patterns in shapes you can find patterns in the numbers that come from them.

Extensions

For older students, or even younger ones wanting to pursue this pattern, there is much to be learned by looking back to the visual pattern to find out why. For example:
  • Why must it be that each concentric square is a 'four times number'? (Is it sufficient explanation to say that squares have four sides? After all there are 10 plugs in each side of the outside square and the total isn't 4 x 10?!?)
  • Why is each concentric square four times an odd number?
  • Which 8 plugs 'disappear' each time you count the next square in?
  • How many plugs would be needed for the next largest concentric square?
  • If I told you any number for the largest concentric square (the picture only builds as far as five), explain how you would work out the number of plugs to make it.
    How many plugs would be needed altogether to make all the squares out to the one I tell you?

Use this picture to try a similar exploration of the link between visual and number patterns, or try with any other pattern the students make. Odds To Make Squares This investigation is explored in the activity Expanding Arrows. It involves similar mathematics and therefore can be seen as a partner to Visual = Number.


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