# NRICH PROBLEM SOLVING ANGLES

Olympic Turns Age 7 to 11 Challenge Level: Weekly Problem 46 – The diagram shows two parallel lines and two angles. Can you work out the fraction of the tiles that are painted black in this pattern? How large is this acute angle? Follow the track of a pool ball around the table. Weekly Problem 26 – The diagram shows two equilateral triangles. Being Resilient – Geometry Geometry problems that may require resilience. How many pentagons will be needed? How did this help? How did the the rotation robot make these patterns? This investigation explores using different shapes as the hands of the clock. In so doing, I hope I have gone part-way to convincing colleagues that such tasks are accessible at a range of levels and, therefore, appropriate for mixed ability working.

Which ones are impossible? Given four of the angles in two triangles, can you find the smallest angle overall?

Interior angles can help us to work out which polygons will tessellate. Three Tears Age 14 to 16 Challenge Level: Students can discover angle relationships. What is the side length of the original triangle?

## Angles, Polygons and Geometrical Proof Short Problems

During the lesson, as pupils were working their way through one of the most turgid exercises imaginable, I began thinking about how such work might be made more relevant to such classes – that is classes where the evidence shows that a substantial number of children can sngles manage, with competence, the skill being taught.

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What proportion of the area of the tessellation is shaded? Find the sum of all of the angles denoted by letters in this diagram. Join the midpoints of a quadrilateral to get a new quadrilateral. Ironically, the nricj in which the task was presented meant that no measurement was needed – pupils could simply read off the required angle from the scale. Quad in Quad Age 14 to 16 Challenge Level: Weekly Problem 44 – A garden has the shape of a right-angled triangle.

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# Angle Hunt :

Centred Age 14 to 16 Short Challenge Level: Olympic Turns Age 7 to 11 Challenge Level: Filter by resource type problems games articles general resources interactive nrkch EYFS Resources projects Lists Filter by age 5 to 7 7 to 11 11 to 14 14 to 16 solging to How can an identical hexagon be made by cutting the corners off a different equilateral triangle? Investigate the different shapes that the quadrilateral can take. Tessellating Hexagons Age 11 to 14 Challenge Level: This problem explores the shapes and symmetries in some national flags.

Use your mouse to move the red and green parts of this disc.

This article gives an wonderful insight into students working on abgles Arclets problem that first appeared in the Sept edition of the NRICH website. Register for our mailing list.

Weekly Problem 16 – Can you figure out how far the robot has travelled by the time it is first facing due East? What is the distance between the centres of the circles?

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How long will it be before they are at right angles again? Such invocations concern me, not because I have a principled objection to the sentiments, but because they are presented in ways that suggest that familiarity with units oslving measurement and practice in using scales are worthwhile ends in themselves.

Interactive Games – Upper Secondary Age 14 to 18 Games and computer room activities suitable for upper secondary school students. Some questions they could be asked might include:. How well can you estimate 10 seconds? Use your mouse to move the red and green parts of this disc. Make an equilateral triangle by folding paper and use it to make patterns of your own. Pupils could be asked to repeat the exercise with six-point circles drawn with a different radius.