### NRICH PROBLEM SOLVING ANGLES

You may also like Consecutive Numbers An investigation involving adding and subtracting sets of consecutive numbers. Follow the track of a pool ball around the table. If the shape on the inside is a rectangle, what can you say about the shape on the outside? Can you decide whether two lines are perpendicular or not? Pupils could be asked to repeat the exercise with six-point circles drawn with a different radius.

Quadrilaterals Age 7 to 11 Challenge Level: Bow Tie Age 11 to 14 Challenge Level: Isosceles Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. What is the size of the marked angle? Weekly Problem 10 – If you know how long Meg’s shadow is, can you work out how long the shadow is when she stands on her brother’s shoulders? What is the length of TU? It is what many teachers believe children need and, sadly, what many parents and school managers think is indicative of good teaching.

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. The linkage is moveable so that the angles change. A similar task could be repeated for different point-circles – those with eight or twelve points are relatively straightforward to construct. What is the size of one of the angles?

Draw some quadrilaterals on a 9-point ahgles and work out the angles. Also, I wanted a means by which practice could be embedded within a more meaningful and mathematically coherent activity. Ratty Age 11 to 14 Challenge Level: What is the length of TU? Weekly Problem 44 – Extend two of the sides of a nonagon to form an angle. Four rods, two of length a and two of length b, are linked to form a kite.

Can you work out their angles? Weekly Problem 38 – A quadrilateral can have four right angles.

# Angle Hunt :

Linkage Four rods, two of length a and two of length b, are linked to form a kite. Geometry problems for primary learners to work on with others. Make five different quadrilaterals on a nine-point pegboard, without using the centre prohlem. Is there a theorem? Weekly Problem 21 – What is the angle between the two hands of a clock at 2. Weekly Problem 18 – The diagram shows a regular pentagon.

You can find more short problems, arranged by curriculum topic, in our short problems collection. Can you do this without qngles them? How can an identical hexagon be made by cutting the corners off a different equilateral triangle?

Investigate sklving our timing tool. Can you find triangles on a 9-point circle? Can you work out the means of these distributions using numerical methods?

## Angle Measurement: an Opportunity for Equity

Weekly Problem 27 – Ten stones form an arch. Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses? Among these might be. Shogi Shapes Age 11 to 14 Challenge Level: Pupils could be asked to repeat the exercise with six-point circles drawn with a different radius. Can you work out problfm shaded area in this shape? What if the triangle is on the surface of a sphere? What is the size of the other angle? If all the probelm are drawn in, into how many areas will the pentagon be divided?

How many pentagons will be needed? What is the sum of the interior angles of the resulting polygon? Strange Rectangle 2 Age 16 to 18 Challenge Level: Weekly Problem 28 – Zolving lines meet at a point.