What kinds of triangles do these points form? Join your point to two adjacent corners, and measure the angles as shown in the GeoGebra applet below. Lunar Angles Age 16 to 18 Challenge Level: PQ has length 1. What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? You may also like Clock Hands This investigation explores using different shapes as the hands of the clock. Right Time Age 11 to 14 Challenge Level:

Weekly Problem 15 – How many of the five properties can a heptagon have? Qualifications and Curriculum Authority National curriculum tests Olympic Turns Age 7 to 11 Challenge Level: What is the size of the marked angle? You may also like Floored A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. Find the distance marked on the diagram. I wonder whether they fit together to make a ring?

anhles Can you prove Alison’s conjecture? The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots.

Given four of the angles in two triangles, can you find the smallest angle overall? Weekly Problem 44 – A garden has the shape of a right-angled triangle. Can you find triangles on a 9-point circle?

Orthogonal Circle Age 16 to 18 Challenge Level: Prove that proboem triangle with sides solviing length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. A similar task could be repeated for different point-circles – those with eight or twelve points are relatively straightforward to construct. What is the sum of the interior angles of the resulting polygon?

Can you make images which show the turnings described? This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles. Olympic Turns Age 7 to 11 Challenge Level: Shogi tiles can form interesting shapes and patterns These problems are ideal for primary school children to work on with others.

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.

# Angle Please :

How often in a 24 hour day will the second hand be parallel to either of the two other hands? What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? Weekly Problem 41 – Three straight lines divide an equilateral triangle into seven regions.

Filter by resource type problems games articles general resources interactive environment projects Lists Filter by age 5 to 7 7 to 11 11 to 14 14 to 16 16 to Cartesian Isometric Age 7 to 11 Challenge Level: Weekly Problem 45 – The diagram shows a regular pentagon with two of its diagonals.

Half a Minute Age 11 to 14 Challenge Level: Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

## Angle Hunt

Age 11 to 14 Challenge Level: Well, initially, pupils could be invited to draw, by joining points on the six-point circle, different triangles and then encouraged to measure their angles.

I don’t practice hitting nails into blocks of wood just for the sake of it – at least not in the world I inhabit.

What mathematics do I need to know to be able to do it? Advice nfich problems to help your students become more resilient. What kinds of triangles do these points form? How many right angles can you make using two sticks?

## Estimating Angles

Can you work out the size of the marked angle? National Flags Age 7 to 11 Challenge Level: Weekly Problem 17 – The diagram shows an equilateral triangle touching two straight lines.

Interactive Games – Upper Secondary Age 14 to 18 Games and computer room activities suitable for upper secondary school students. This collection of games focus on the concepts of shape, position and movement. PQ has length 1.

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.