Developing a spatial proof for some angle properties of triangles.
Analysing patterns in terms of lines and shapes.
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Resources |
Vocabulary |
Large, common 2D shapes
Variety of different triangles
Card
Scissors
Rulers
A3 sheets of paper
Thick felt tip pens
Copies of the notesheet (scalene triangle
template) on card or thick paper
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tessellation, repeating pattern, overlap, spaces, rotate, turn, reflect, flip, translate, straight, transformation, parallel, parallelogram, rhombus, quadrilaterals, composite, shape, infinite |
Organisation |
Near ability pairs on mixed ability tables
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Whole Class Preparation: (about 10 mins) |
What does ‘tessellating’ mean? Covering space with no gaps or overlaps. Emphasise not just pattern but creating a repeating pattern that could be infinite.
Where might we see tessellating shapes? Paving on floor, tiling on walls, patchwork...
How do you know if shapes tessellate?
Which common 2D shapes will tessellate with themselves? Squares, rectangles,hexagons, triangles. Ask children to demonstrate the different tessellations. This could be modelled using plastic shapes.
Let’s concentrate on triangles. What different kinds of triangles are there? Right-angled, scalene, equilateral, isosceles.
Go over the properties of the different types of triangles very briefly.
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Paired Work: (about 10-15 mins) |
Give out plastic or card triangles, A3 paper (one sheet per pair), felt tip pens
and scissors. The children use the shapes as templates to create more.
Find out how your triangle tessellates. Children sort equilateral triangles on one
table, right-angled triangles on another, and isosceles on another.
Remind children to note anything that they have noticed about the patterns that are made by the tessellation and the new shapes that are produced.
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Class Sharing: (about 10-15 mins) |
Ask for feedback, starting with right-angled triangles.
What shapes have you made? New shapes made will be rectangles from the right-angled triangles. Get children to show their sheets to demonstrate this.
When tessellating your triangle, describe the patterns made. The shapes will create continuous straight or staggered lines that are parallel. Get a few pairs to hold up their sheets to demonstrate this.
Repeat this for the equilateral triangles and the isosceles triangles. The new shapes made will be parallelograms and rhombi from the equilateral and isosceles triangles, as well as inverted kites.
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Paired Work: (about 10-15 mins) |
Distribute Remind children of the properties of an irregular (scalene) triangle and ask a couple to sketch examples on the board. Give out the notesheet.
Cut out scalene triangles from the notesheet. Establish that scalene triangles tessellate. Give children a few minutes to try this out with their triangles.
Remind the children about the patterns of lines they noticed with the previous triangles. Is it possible to create a pattern of straight lines without tessellation?
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Class Sharing: (about 15 mins) |
Collect Show the patterns you have made. Did you create continuous parallel straight lines without producing a tessellating pattern? Why is this the case? Because the straight lines are created by using the same sides of the triangle.
Why do we need to use the same side each time? So that the triangles can fit in with each other, you fit the corners of the triangle together each time.
How do the corners help create the straight lines? They can colour-code their template and repeat this colour coding on the paper tessellations.
Ask the children to describe what they notice about the colour coding along a line or around a point.
What have we done – how did we investigate all the different triangles?
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