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Let's Investigate Triangles
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Stage: 1 Challenge Level: 
If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on ...
Arrange the numbers $1$ to $6$ in each set of circles below.
The sum of each side of the triangle should equal the number in the centre of the triangular shape.
Once you've had a chance to think about it, click below to see how three different pupils began working on the task.
Dan said:
"I used counters which had $1$ to $6$ on them.
I put the counters in a triangle in any old way, then I added up the sides.
Then I moved the counters around to try and get the right total on each side."
Emma said:
"I noticed that three of the numbers are odd ($1, 3$ and $5$) and three of the numbers are even ($2, 4$ and $6$). I thought this might help.
I know that $9$ is an odd number so it can be made using odd + odd + odd or using even + even + odd."
Farah said:
"If I want a small total on each side, I'll need small numbers in the corners of the triangle."
Can you take each of these starting ideas and develop it into a solution?
A practical version of this activity is included in the Year 3/4 Brain Buster Maths Box which contains hands-on challenges developed by members of NRICH and produced by BEAM. For more details and ordering information, please scroll down this page .
NRICH is part of the family of activities in the Millennium Mathematics Project.