How Many Pieces?
How many loops of string have been used to make these patterns?
Age
5 to 7
Challenge level
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
How many pieces of string do you need to make this string pattern?
Image
Can you explain how you decided?
Here is a pdf of the string images which you could print off if you find it easier to work on paper.
If you enjoyed this problem, you might like to have a go at How Many Pieces This Time?
Getting Started
What happens when you choose a starting point and follow the string from there?
You could print off this picture of the patterns and use a pencil to follow a loop.
You could print off this picture of the patterns and use a pencil to follow a loop.
Student Solutions
Thank you to everyone who sent in a solution to this problem. Most of you agreed that there was just one piece of string in the first picture, two in the second, one in the third and two in the fourth.
Thomas from St Luke's School in Frodsham explained how he worked out the number of pieces of string in the last picture:
I started at one point, followed the string round in one direction and found that I came back to where I started. I realised that I hadn't been everywhere, so I started from a place that I hadn't been and went around again. When I got back to the start again, I had been everywhere, so there are two loops.This is very clear - thank you Luke.
Well done also to Diana, Kate and Georgia from Danebank School who also wrote clear explanations of how they counted the pieces of string.
Teachers' Resources
How Many Pieces?
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
How many pieces of string do you need to make this string pattern?
Image
Can you explain how you decided?
Here is a pdf of the string images which you could print off if you find it easier to work on paper.
If you enjoyed this problem, you might like to have a go at How Many Pieces This Time?
Why do this problem?
This problem has potential in several different ways. You could focus on visualisation - asking the children to try and decide whether the patterns are made from more than one piece of string simply by looking.
Alternatively, you could make this a more practical task and encourage your class to recreate the patterns using prepared loops (large elastic bands could be useful perhaps, or bits of ribbon/string/thread tied into loops).
Here is a pdf of the string images which you could print off for the children to use.
Key questions
Can you explain how you decided on the number of loops there are?
What happens when you choose a starting point and follow the string from there?
Would it help to use a coloured pencil?