Dewch i Feddwl Mathemateg (9 i 11 oed) Gwers H. Cwpanau a Soseri
| Introduction |
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| An activity on exploring the circle. Children formulate the size relationship between the radius, the diameter and the circumference. They then explore the reasons for the constant relationship between the diameter and circumference using intuitive and approximate methods followed by a ‘pure’ geometric investigation. |
| This activity has two episodes. Each episode consists of an introduction, paired or group work and whole class sharing. The session must finish with a whole class reflection phase, regardless of how far the class has got. |
| Episode 1: Finding the relationships between elements of any circle, practically |
| Children compare sizes of circles and cylinders, focusing on the use of radius, diameter and circumference. They discover the accurate relationship between radius and diameter and explore the approximate one between diameter and circumference in any size circle. Children use lengths of string to find the relationship directly, recognising that the ‘bit’ in the ‘3 and a bit’ is not fixed but is a fractional part of the diameter. |
| Episode 2: A mathematical reasoning approximation of the circle ratio |
| Children investigate circles enclosed by a square with an inscribed triangle and hexagon, using the relationship between diameter and perimeter. This provides another perspective from which to formulate the circle ratio (pi) as much nearer to 3 than to 4. The circumference value will lie between the perimeters of the hexagon and square (with values 3 and 4 times the diameter of the circle). Children sketch their own inscribed regular polygons, describing how increasing the number of sides brings the perimeter nearer to the circumference, and the fact that the circumference value is the upper limit. |
| Reflection |
| Children discuss the different ways they investigated the relationships within the circle in each of the two episodes and note that the end result was the same for both. |
| BEFORE YOU TEACH |
| There is no need to emphasise accuracy or the irrational nature of pi, as the lesson’s focus is on the general nature of the relationship between pi and circumference and, in particular, the ‘bit’ of ‘three and a bit’. |