Four Triangles Puzzle

Zac and Olly from  Pendragon School Cambridgeshire sent in the following:

I have attached a solution two of my year 6 children came up with to the 'four triangles' problem. They spent three lessons talking about it before coming to their agreed solution!

 

Orchards Primary in Wisbech (who say they often like to work together in pairs or groups) sent in solutions from their different (tree) classes: 

Laburnum Class worked really hard to try to explain how they made their shapes.
The first photograph is Ciara-Rose and Zarah's work. Then Hawthorn Class' solution.

  

Below is just one picture from Juniper Class' solution

 

 and the rest of their excellent work can be seen here Juniper Y4.docx

The teacher of Year 5 in Bute House Prep School sent in the following:

The Year 5 girls worked in groups to investigate how many arrangements they could find.  They considered the different ways they could classify the shapes they made and whether or not they could prove they had them all. The attached document is the conclusions Maya, Kyra and Amelie came to. 

 

You can see more of their work here. What do you make of the key they've created using different symbols to sort particular groups of shapes? 

Thank you for these good ideas of working with the triangles. I wonder what happens if you add one more triangle?