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Broad Topics > Angles, Polygons, and Geometrical Proof > Triangles

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Paper Patchwork 2

Age 5 to 7 Challenge Level:

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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Walking Round a Triangle

Age 5 to 7 Challenge Level:

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

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Data Shapes

Age 5 to 7 Challenge Level:

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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Sorting Logic Blocks

Age 5 to 11 Challenge Level:

This interactivity allows you to sort logic blocks by dragging their images.

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Jig Shapes

Age 5 to 7 Challenge Level:

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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Repeating Patterns

Age 5 to 7 Challenge Level:

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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Overlaps

Age 5 to 7 Challenge Level:

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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Inside Triangles

Age 5 to 7 Challenge Level:

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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Matching Triangles

Age 5 to 7 Challenge Level:

Can you sort these triangles into three different families and explain how you did it?

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Can You Explain Why?

Age 11 to 14 Challenge Level:

Can you explain why it is impossible to construct this triangle?

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Fraction Fascination

Age 7 to 11 Challenge Level:

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

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More Transformations on a Pegboard

Age 7 to 11 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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Triangle Animals

Age 5 to 7 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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Property Chart

Age 11 to 14 Challenge Level:

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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Shapely Pairs

Age 11 to 14 Challenge Level:

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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Nine-pin Triangles

Age 7 to 11 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

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Isosceles Triangles

Age 11 to 14 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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Hexy-metry

Age 14 to 16 Challenge Level:

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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Transformations on a Pegboard

Age 7 to 11 Challenge Level:

How would you move the bands on the pegboard to alter these shapes?

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Rectangle Tangle

Age 7 to 11 Challenge Level:

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

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Egyptian Rope

Age 7 to 11 Challenge Level:

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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Lens Angle

Age 14 to 16 Challenge Level:

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.

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Cut it Out

Age 7 to 11 Challenge Level:

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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Triangle Midpoints

Age 14 to 16 Challenge Level:

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

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Chain of Changes

Age 5 to 7 Challenge Level:

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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Colouring Triangles

Age 5 to 7 Challenge Level:

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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Let's Investigate Triangles

Age 5 to 7 Challenge Level:

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?

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Bracelets

Age 7 to 11 Challenge Level:

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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Regular Rings 1

Age 7 to 11 Challenge Level:

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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Folding Flowers 2

Age 7 to 11 Challenge Level:

Make a flower design using the same shape made out of different sizes of paper.

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Board Block for Two

Age 5 to 11 Challenge Level:

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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Peg and Pin Boards

Age 5 to 11

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

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Constructing Triangles

Age 11 to 14 Challenge Level:

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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Calculating with Cosines

Age 14 to 18 Challenge Level:

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

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Cutting it Out

Age 5 to 11 Challenge Level:

I cut this square into two different shapes. What can you say about the relationship between them?

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Logic Block Collections

Age 5 to 7 Challenge Level:

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

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Animated Triangles

Age 5 to 7 Challenge Level:

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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Triangle Relations

Age 7 to 11 Challenge Level:

What do these two triangles have in common? How are they related?

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Putting Two and Two Together

Age 7 to 11 Challenge Level:

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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Triangle Shapes

Age 5 to 11 Challenge Level:

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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Impossible Triangles?

Age 16 to 18 Challenge Level:

Which of these triangular jigsaws are impossible to finish?

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Notes on a Triangle

Age 11 to 14 Challenge Level:

Can you describe what happens in this film?

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Lighting up Time

Age 7 to 14 Challenge Level:

A very mathematical light - what can you see?

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The Square Hole

Age 14 to 16 Challenge Level:

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

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Equal Equilateral Triangles

Age 14 to 16 Challenge Level:

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

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Interacting with the Geometry of the Circle

Age 5 to 16

Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.

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Number the Sides

Age 7 to 11 Challenge Level:

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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Wedge on Wedge

Age 14 to 16 Challenge Level:

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

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Making Maths: Test the Strength of a Triangle

Age 7 to 11 Challenge Level:

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

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Making Maths: Equilateral Triangle Folding

Age 7 to 14 Challenge Level:

Make an equilateral triangle by folding paper and use it to make patterns of your own.