How Many Pieces This Time?
2 out of 3
How many pieces of string have been used in these patterns? Can you describe how you know?
Problem
You might like to try How Many Pieces? before you have a look at this problem.
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?
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?
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:
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:
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
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
Key questions
Possible extension
Possible support
Suggest staying with the simpler problem How Many Pieces?