Digging deeper into … the Circle (5th & 6th)

While the circle, as a topic, is not a specific strand unit in itself, it traditionally has been dealt with separately, and more in depth, in 5th and 6th class. It is in these classes that the children begin to explore the circle as something more than just a 2D shape, and rather as a shape which has specific parts that can be named (eg diameter, radius, etc) and specific properties that can be explored. Fifth class is also the first time that the children have encountered degrees as a measurement of rotation (they first meet degrees in the strand unit of lines and angles). Fifth class is also the first occasion when the children would be required to use degrees to construct pie-charts in the strand unit of representing and interpreting data, for which the children require knowledge of constructing circles and dividing them into sectors prior to creating pie charts.

Thus, in Operation Maths, this chapter is placed after the chapters of Lines and Angles and 2-D Shapes and before the chapter of Data.

CPA Approach

As is typical in Operation Maths, A CPA approach is taken to this topic where the emphasis at the introductory stages is on the children exploring and examining circles in their environment and then using the manipulation of cut-out circles to identify the parts of circle and label them using the correct mathematical terminology. Indeed the children themselves can be used to model a circle, as outlined below. This type of activity will also greatly suit the kinaesthetic learners.

When looking for circles in the environment, it is also important to accurately identify circles, which are examples of 2D shapes, as distinct from cylinders, which are examples of 3D objects. So, if a child suggests that a coin is an example of a circle, emphasise that the face of a coin is indeed a circle, but that the coin itself is a cylinder.

Integrating maths and literacy

When introducing this new terminology, ask the children to suggest examples of words with similar prefixes/rootwords so as to foster connections and deepen meaning eg diameter coming from dia meaning across, through and thus connected with diagonal, diaphragm, dialogue; radius as being related to radiate, radio, radar (originating from a central point and moving outwards), etc. Etymology websites, such as Etymonline can be very useful to research and collect related words.

Measuring and constructing circles

The children should be provided with ample opportunities to measure the radius and diameter of circles of various sizes and, in doing so, be guided to discover for themselves that the measure of the diameter is twice the radius.

In a similar way, in 6th class, through comparing the measurement of the circumference and diameter of various circles, it is hoped that the children realise that the circumference of a circle is always just over three times the measure of the diameter. They can explore this in a very concrete way by measuring the circumference of various circles using string/wool and then cutting the string into lengths that equal the diameter, as show in the image below from K-5 Math Teaching Resources

Again before constructing circles using a compass, the children should be asked to suggest ways to draw circles that they may have used previously and to identify the pros and cons of these methods. When ready to use a compass, it can be a good idea to use a video to demonstrate, such as the ones below.

Circles in art

Once the children have mastered the basics of constructing a circle, they could be encouraged to look and respond to circles in art, for example the work of Kandinsky, Anwar Jalal Shemza or the multitude of circle themed pieces available to view on the internet (just search google images for circles in art). The children could even look and respond to crop circles (in particular the activities of John Lundberg) or the use of circles in famous brand logos. For more ideas, check out this Pinterest board which includes circle themed art lessons. Using circles in such a way provides purposeful opportunities to use and reinforce the specific circle terminology e.g. diameter, circumference, arc, etc.

Further Reading:

Shape and Space Manual from PDST, p.154-157