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Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-5
Featured UK Key Stage 3-5; US Grades 6-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3-5
Featured UK Key Stages 3 & 4; US Grade 6-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
These triangles belong to three different families.
All the triangles in a family are the same shape.
But they may not be the same size or the same way up.
Can you sort them out and explain how you did it?
You may want to use this interactivity to sort the triangles:
This text is usually replaced by the Flash movie.
Or you could print off pictures of the triangles (
here as a Word document
here as a pdf
), then cut them out and sort them practically.
Why do this problem?
is a good one to try with young children once they are familiar with the properties of a triangle. Often, they associate the name "triangle" with a shape in a particular orientation and this problem is an excellent way to challenge this assumption. Other children may dismiss all three-sided shapes as triangles without looking at their other attributes. The activity will require pupils to look carefully at each shape and scrutinise its properties.
You could start by asking the group to tell you what they know about triangles. You could then ask one child to draw a triangle on the board and ask someone else to draw a different triangle. Invite the group to talk about what is the same and what is different about them. In this way, the discussion will include shape, size and orientation, but you could draw some triangles yourself to bring out certain aspects.
Next you could show the group the interactivity on an interactive whiteboard or show them the triangles on
. (The first page has the triangles in colour, the second in black and white so that it can be photocopied.)
After this you could encourage the group to work in pairs so that they are able to talk through their ideas with a partner. This could be done at a computer or using the sheets of triangles to cut out and sort. Listening to their justifications can reveal a lot about their understanding of similar triangles, even though this terminology is not used.
What do you see if you turn this triangle round? Do the two look the same shape now?
What is the difference between these two triangles and what is the same?
Children could draw their own families of triangles and label the differences and similarities.
one of these sheets
so that the triangles can be cut out, then rotated and placed on top of one another. (The first page has the triangles in colour, the second in black and white.)
Addition & subtraction
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the
Millennium Mathematics Project