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Broad Topics > 2D Geometry, Shape and Space > Angles

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Turning

Stage: 1 Challenge Level: Challenge Level:1

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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Six Places to Visit

Stage: 2 Challenge Level: Challenge Level:1

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

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How Safe Are You?

Stage: 2 Challenge Level: Challenge Level:1

How much do you have to turn these dials by in order to unlock the safes?

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Orbiting Billiard Balls

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

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Estimating Angles

Stage: 2 and 3 Challenge Level: Challenge Level:1

How good are you at estimating angles?

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Watch the Clock

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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Bisecting Angles in a Triangle

Stage: 3 and 4 Challenge Level: Challenge Level:1

Measure the two angles. What do you notice?

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Witch's Hat

Stage: 3 and 4 Challenge Level: Challenge Level:1

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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Olympic Turns

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

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Cylinder Cutting

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

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Link Puzzle

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A metal puzzle which led to some mathematical questions.

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Interacting with the Geometry of the Circle

Stage: 1, 2, 3 and 4

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

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Dotty Circle

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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Flight Path

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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Overlapping Squares

Stage: 2 Challenge Level: Challenge Level:1

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

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Spiroflowers

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.

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Spirostars

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

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Making Maths: Clinometer

Stage: 3 Challenge Level: Challenge Level:1

Make a clinometer and use it to help you estimate the heights of tall objects.

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Making Maths: Equilateral Triangle Folding

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

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Three Tears

Stage: 4 Challenge Level: Challenge Level:1

Construct this design using only compasses

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Pegboard Quads

Stage: 4 Challenge Level: Challenge Level:1

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

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Angle Measurement: an Opportunity for Equity

Stage: 3 and 4

Suggestions for worthwhile mathematical activity on the subject of angle measurement for all pupils.

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Watch Those Wheels

Stage: 1 Challenge Level: Challenge Level:1

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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Sweeping Hands

Stage: 2 Challenge Level: Challenge Level:1

Use your knowledge of angles to work out how many degrees the hour and minute hands of a clock travel through in different amounts of time.

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Right Angle Challenge

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

How many right angles can you make using two sticks?

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Pythagoras

Stage: 2 and 3

Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music.

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Maurits Cornelius Escher

Stage: 2 and 3

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be. . . .

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Lunar Angles

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?

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LOGO Challenge 8 - Rhombi

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

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Take the Right Angle

Stage: 2 Challenge Level: Challenge Level:1

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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Hand Swap

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

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On Time

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

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A Problem of Time

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

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Square World

Stage: 5 Challenge Level: Challenge Level:1

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

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Clock Hands

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.