How Many Pieces This Time?
How many pieces of string have been used in these patterns? Can you
describe how you know?
Age
5 to 7
Challenge level
Problem
You might like to try How Many Pieces? before you have a look at this problem.
Image
You can see how many loops of string were used to make these string patterns because the strings are different colours.
In the next pictures can you work out how many loops were used?
Image
Image
Can you describe how you know?
You might like to print off this sheet of the pictures if you would like to work on paper.
Getting Started
You could print off this sheet and use a different coloured pencil to trace over each new loop of string.
Perhaps you can follow a piece of string just by looking?
Perhaps you can follow a piece of string just by looking?
Student Solutions
You decided that there is one piece of string used in the left-hand loop and two pieces used in the right hand loop below:
Image
And then you thought that there was one piece of string used in the left-hand loop and three used in the right-hand picture below:
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Not many of you explained how you knew, though. Here is what Lydia from Rickling C of E Primary said:
I decided this by following a bit of string. It ended completing the picture. I did this for all the others. Some of them ended without finishing the picture so I followed another bit. Then this finished the picture so there must be 2. I did this for all the others.
Well done also to Thea from John Young Elementary School, Luke from St Patrick's School and Olivia from Clitheroe Royal Grammar School who also told us how they went about doing this problem.
Teachers' Resources
How Many Pieces This Time?
You might like to try How Many Pieces? before you have a look at this problem.
Image
You can see how many loops of string were used to make these string patterns because the strings are different colours.
In the next pictures can you work out how many loops were used?
Image
Image
Can you describe how you know?
You might like to print off this sheet of the pictures if you would like to work on paper.
Why do this problem?
This problem is a more challenging version of How Many Pieces? and can be approached in similar ways. If you tried How Many Pieces? visually with your class, you may like to introduce this problem in a more practical way and vice versa.
The longer length of the pieces of string in this version make it slightly harder to solve.
Children may enjoy making up their own string patterns for a partner to work out the number of pieces used. It is quite a challenge to draw the patterns convincingly.
You might like to read the article Celtic Knotwork Patterns and share some of the ideas with your class, particularly the tips for drawing knots!
Key questions
Can you can follow a piece of string just by looking?
Why don't you use a different coloured pencil to trace over each new loop of string?
Can you explain how you decided on the number of loops there are?
Possible extension
Learners who found this easy might enjoy this more challenging problem.