What is the size of the angle FAE? Weekly Problem 47 – What is the sum of the six marked angles? Can you do this without drawing them? 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. What do you notice? Four rods are hinged at their ends to form a convex quadrilateral.

I would not use a protractor like the one above for work like this. What is the side length of the original triangle? Why does this fold create an angle of sixty degrees? Weekly Problem 47 – What is the sum of the six marked angles? Challenging problems to get stuck into! If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas. How well can you estimate 10 seconds?

Can you find the area of the yellow square? This task looks at the different turns involved in different Olympic sports poblem a way of exploring the mathematics of turns and angles. This investigation explores using different shapes as the hands of the clock. Olympic Turns Age 7 to 11 Challenge Level: Discover some angle relationships. The other method involves looking at the farthest right angle in the diagram.

## Angle Hunt

Spirostars Age 16 to 18 Challenge Level: 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. Weekly Problem 13 – The diagram shows contains some equal lengths.

Robotic Rotations Age 11 to 16 Challenge Level: What kinds of triangles do these points form? The exercise itself was repeated twice more over the page.

Probldm Angles Age 11 to 14 Challenge Level: Being Resilient – Geometry Geometry problems that may require resilience.

Turning Age 5 to 7 Challenge Level: Cubestick Age 16 to 18 Challenge Level: Weekly Problem 41 – The diagram shows a square, with lines drawn from its centre. Just from the diagram, can you work out the radius of the smaller circles?

How did the the rotation robot make these patterns? An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

## Estimating Angles

What is the smaller angle between the hour hand and the minute hand on an accurate analogue clock? Lunar Angles Age 16 solviing 18 Challenge Level: 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. In this particular lesson pupils were working anglss a text which contained, on one page, a picture similar to that in figure 1, albeit with a greater number of labels.

Weekly Problem 18 – Draw an equilateral triangle onto one side of a square. Can you explain why and does this rule extend beyond angles of 90 degrees?

# Angle Measurement: an Opportunity for Equity :

Weekly Problem 21 – What is the angle between the two hands of a clock at 2. Geometry Stage 6 Age 7 to 11 Challenge Level: Weekly Problem 45 – What is the obtuse angle between the hands of a clock at 6 minutes past 8 o’clock? Why does this fold create an angle of sixty degrees? What is the angle between the triangles? What is the bearing of the nrih from the church?

What is the shaded area? At the time of writing the hour and minute hands of my clock are at right angles. Work out the angles in each quadrilateral you make.