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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
A Patchwork Piece
Why do this problem?
encourages learners to develop their spatial reasoning. The fact that they are asked to recreate the pattern pieces gives the opportunity for mathematical construction which is perhaps quite rare at this level.
By the far easiest way to do this construction is to start with an octagon and draw the square round it. Drawing an accurate regular octagon in a set sized square requires mathematical knowledge beyond primary level. Otherwise children can make a design in which the octagon is not regular.
A nice way to start this activity might be to put up a picture of
the final design
and then of a
Invite the group to talk about what they can see. (Children will often call this a diamond which gives a good opportunity to discuss the properties of a square.)
When the class begin to work on the problem itself, encourage them to work in pairs. Their conversations will help you to assess their knowledge and understanding of properties of 2D shapes, and how readily they use vocabulary associated with shape and position.
What you can see in this design?
What different shapes are there in the picture? Tell me about them.
Which shapes are the same and which are different?
What can you tell me about the shape in the middle?
How are you going to draw regular octagon?
What size are the eight internal angles?
Learners could try to make
using the same pieces or even this one called
Suggest making a design in which the octagon is not regular so the triangles can be any shape. Starting with a square with sides that are readily divided into three will make a pleasing pattern.
Ruler & protractor constructions
STEM - General
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