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Resources tagged with Angles - points, lines and parallel lines similar to Semi-regular Tessellations:

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Broad Topics > Angles, Polygons, and Geometrical Proof > Angles - points, lines and parallel lines

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Semi-regular Tessellations

Age 11 to 16 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate?

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Right Angles

Age 11 to 14 Challenge Level:

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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Angles Inside

Age 11 to 14 Challenge Level:

Draw some angles inside a rectangle. What do you notice? Can you prove it?

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Estimating Angles

Age 11 to 14 Challenge Level:

How good are you at estimating angles?

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Right Time

Age 11 to 14 Challenge Level:

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

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A Problem of Time

Age 14 to 16 Challenge Level:

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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Pythagoras

Age 7 to 14

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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Triangles in Circles

Age 11 to 14 Challenge Level:

Can you find triangles on a 9-point circle? Can you work out their angles?

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Which Solids Can We Make?

Age 11 to 14 Challenge Level:

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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Link Puzzle

Age 7 to 16 Challenge Level:

A metal puzzle which led to some mathematical questions.

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Maurits Cornelius Escher

Age 7 to 14

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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Subtended Angles

Age 11 to 14 Challenge Level:

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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On Time

Age 11 to 14 Challenge Level:

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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Shogi Shapes

Age 11 to 14 Challenge Level:

Shogi tiles can form interesting shapes and patterns... I wonder whether they fit together to make a ring?

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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.

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Quad in Quad

Age 14 to 16 Challenge Level:

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

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Making Maths: Clinometer

Age 11 to 14 Challenge Level:

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

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Arrowhead

Age 14 to 16 Challenge Level:

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

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Robotic Rotations

Age 11 to 16 Challenge Level:

How did the the rotation robot make these patterns?

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Pegboard Quads

Age 14 to 16 Challenge Level:

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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Orbiting Billiard Balls

Age 14 to 16 Challenge Level:

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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Hand Swap

Age 14 to 16 Challenge Level:

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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Angle Trisection

Age 14 to 16 Challenge Level:

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

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Same Length

Age 11 to 16 Challenge Level:

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

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Round and Round and Round

Age 11 to 14 Challenge Level:

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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Parallel Universe

Age 14 to 16 Challenge Level:

An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.

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Similarly So

Age 14 to 16 Challenge Level:

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

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Making Sixty

Age 14 to 16 Challenge Level:

Why does this fold create an angle of sixty degrees?

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LOGO Challenge 7 - More Stars and Squares

Age 11 to 16 Challenge Level:

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

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Witch's Hat

Age 11 to 16 Challenge Level:

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

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Three Tears

Age 14 to 16 Challenge Level:

Construct this design using only compasses

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LOGO Challenge 1 - Star Square

Age 7 to 16 Challenge Level:

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

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Angle Measurement: an Opportunity for Equity

Age 11 to 16

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

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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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LOGO Challenge 8 - Rhombi

Age 7 to 16 Challenge Level:

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