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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 1-4
Featured UK Key Stage 3-5; US Grades 5-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Count the Trapeziums
Why do this problem?
It's quite easy to hazard a guess about how many trapezia there are in
but to be absolutely certain (and convince someone else that you have all the possible solutions) requires some really systematic work.
You could begin with a whole class challenge of a similar but simpler kind - for example how many trapezia in this shape?
Check that all the children know what a trapezium is and ask for a system for finding all possibilities in this diagram. Emphasise working systematically and what this means in practice - for example starting at the top and working clockwise.
for those who want it - and scissors for them to cut out the variations and re-order them to check for missing diagrams. Working systematically does not come naturally to young children so being able to impose a structure onto randomly generated pictures can be a valuable step in learning how to be systematic.
Where will we start?
What story can we tell which will convince a friend that we have them all? How do we know?
Is there another way of arranging them in a pattern?
Adding another layer of triangles to the bottom of the diagram increases the complexity, but for children who are already working systematically this will be only slightly more challenging.
There is a collection of similar style problems
Reducing the picture by one layer can be helpful for children who find visualising difficult. Provide a
so that they can model the same ordering strategy as in the main activity.
Factors and multiples
Multiplication & division
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