Tessellating Triangles

Years 3 - 6

Summary

Building on the children's experiences with folding paper to make equilateral triangles, this investigation explores visual patterns made with them. Then they hunt for numbers in the patterns because, wherever there is a visual pattern there will be a number pattern and vice versa.

Materials

  • Lots of coloured paper for folding
  • Markers and poster paper
  • Assorted decorative materials

Acknowledgement

This activity was contributed by Gay Lynch, Herdsman's Cove Primary School. It can be used at several levels, but the work shown is from her children in Years 3/4. Once again Gay shows us that:
Wherever there is a visual pattern there is a number pattern; and wherever there is a number pattern there is a visual pattern.

Procedure

Gay relates the sequence she used in her classroom...
The children had learnt how to fold paper to make equilateral triangles. Lots of learning related to shape, symmetry, angle and so on, and lots of fine motor skill practice. A simple way to do this can be found at this link on the Nrich site in Britain.

Now, what to do with this new found skill?
Mathematicians solve problems.
Mmmm, can I offer them a challenge that will lead to something more than just being able to do the folding?

 

Content

  • operations - whole number
  • pattern generalisation
  • pattern interpretation
  • pattern recognition
  • problem solving
  • recording - written
  • sorting & classifying
Challenge
  • Can you make a triangular tessellating design from our folded equilateral triangles?
  • Can you make it symmetrical?

Then came the detail:

Working in groups of 4:

  • Make a draft of the design you want to make.
  • Work out the number of pieces you will need of each colour.
  • Make up your design and point out any number patterns that you can find.
  • Use the computer to publish your group members and display this along with your draft and the finished product.

Here are some of the finished posters. (Click any poster to see it in larger size.) They are all visual patterns. If there is a visual pattern, there is always a number pattern connected to it. The children have indicated their number patterns.

  • Can you see what they see?
  • Can you predict the next line of triangles, ... and the next, ... and the next, ... and the 100th line?
  • Can you predict the next line of the number pattern, ... and the next, ... and the next, ... and the 100th line?
  • What other number patterns can you see?

The children then helped to design the rubric below
for assessing the Posters.

Extensions

  1. Explore Task 28, Plate Triangles, from the Mathematics Task Centre and the links within it.

Design
  • Clever design.
  • Looks great.
  • Is symmetrical.
  • Could have a more interesting pattern.
  • Poor design.
  • Is it symmetrical?

Presentation
  • Great effort.
  • Looks good.
  • Lots of colour.
  • Neat and tidy.
  • Not straight.
  • Too much glue.
  • Could be set out better.
  • Messy.
  • Not folded accurately.

Draft
  • Excellent plan.
  • Worked well when making up the real thing.
  • Not complete properly.
  • Poor planning.
  • Design is different to the draft.

Number Patterns
  • Good lateral thinking.
  • Lots of examples.
  • Clearly set out.
  • Didn't think as much as we could.
  • Not many examples.
  • Not accurate.
  • Hardly any examples - 'too hard'.

Group Work
  • Everyone co-operated.
  • Everyone had a job.
  • We had a few disagreements that were difficult to sort out.
  • Not everyone had a job.
  • Some people's feelings were hurt.
  • There were tears and tantrums.


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