Expanding Arrows

Years 1 - 8

Summary

Children make the plug board pattern shown, then investigate what happens to the number of plugs if the pattern continues. For some it might be enough to work out the result for a pattern that continues for 10 arrows. For others the search might be about finding the number of plugs to make any size board of arrows ... and there is more.

Materials

  • One Poly Plug board per pair
  • One calculator per pair

Special Note

This activity is a partner with Visual = Number. They don't need to be used together but they can be planned into the curriculum so children meet similar problem solving challenges at different times in their course.

Procedure

Before the lesson, make the pattern in the photo and show the students. Ask them to make it themselves.
Last year one of my students made this pattern in their plug board. It led us into an interesting investigation. I would like you to make this pattern now, so we can try the investigation together.
Ask the students to tell you what they can see in the board.
Why is this a pattern? Can you tell me how it is made? Can you use numbers to tell me anything about the pattern?
 

Content

  • fraction calculations
  • multiplication
  • odd & even numbers
  • pattern generalisation
  • pattern interpretation
  • pattern recognition
  • problem solving
  • recording - written
  • square numbers
Begin the investigation with a question like:

So there are five arrows on the board. The first one is really just a dot. If the arrows grew until there were 10 of them, how many plugs would there be altogether?
Once the children show interest in the problem, there is more that can be asked. For example:
  • Can you check your answer another way?
  • How many yellow plugs? How many blue plugs?
  • What fraction of the plugs are yellow?
  • What happens if there are 100 arrows?
  • If told you there were any number of arrows could you tell me the total number of plugs?
    • The number of yellow plugs?
    • The number of blue plugs?
    • The fraction of plugs that are yellow?
    • The number of red boards it would take to make the pattern?
  • Can you explain to someone else how you know these answers?
It doesn't really matter what the students investigate, or how long they remain interested in the problem, as long as they are working like mathematicians.


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