The topic of co-ordinate geometry of circles is a new addition in the latest syllabus update for Cambridge IGCSE™ Additional Mathematics (0606). As teachers, we can become anxious when a syllabus changes, especially if there are new topics added. We know we need to take special care to check out the detailed descriptions of the new topic, and how to teach it, to help prepare our students for the new exam. In this blog post, I hope to help alleviate some of your anxieties by sharing ideas on how to teach this new topic, using the resources from the Cambridge IGCSE™ and O Level Additional Mathematics series.
Ideas to build inquiry lessons for the topic
In a recent mathematics series launch by Cambridge University Press in Southeast Asia, I shared how we can introduce the equation of circles using DESMOS Classroom. This DESMOS activityis an improved version of the original one, and is easier for students to observe the pattern for the centre and radius of a circle. The activity makes use of the Class Discussion on page 155 of the student coursebook.
It serves as a quick introduction to the standard equation
and leads students to think about how to find the centre and radius of a circle when given the expanded form of the equation.
One important concept in co-ordinate geometry of circles is for students to understand that the centre of a circle will always lie on the perpendicular bisector of any chord in the circle. This second activity, created with the help of Mark Smith using DESMOS, can help students discover that. It provides a seamless transition to Worked Examples 5 and 6 in the student coursebook.
There are many useful features in the new edition of the student coursebook, especially the Class Discussion, which not only provides opportunities for students to think deeper, but also paves the way to build meaningful social interactions. Students can engage in small group discussion where they can bounce off each other’s ideas and understanding. There are also useful reminders to highlight key concepts to solving exam problems. This coursebook is a fantastic resource for building classroom inquiries. The two DESMOS activities above come from a Class Discussion and a useful reminder from the chapter in the coursebook.
Let Cambridge do the research for you!
Building your own activities and resources can be very time consuming. Ironically, when we feel that we don’t have enough time to create our own activities, we find ourselves sitting in front of a computer for hours, searching the internet for relevant resources. Some of these ‘search missions’ are fruitful while others are not. The digital teacher’s resource helps you save time by providing many suggestions on where you can get relevant resources for each topic. This activity (Finding Circles), from Underground Mathematics by Cambridge, is one such suggestion that is a good continuation from the two DESMOS activities I have shared.
The digital teacher’s resource is great for teachers because it not only provides a plethora of links to online resources, but it also proposes classroom activities you can conduct in your lessons. These activities can be adapted to support your weaker students or challenge the stronger ones. It’s a resource created for teachers by a teacher who understands the demand of our work.
I hope the three activities shared here will help you build your lessons for teaching co-ordinate geometry of circles. For more teaching ideas for Additional Mathematics, check out the Cambridge IGCSE™ and O Level Additional Mathematics series.
Have you enjoyed reading this blog post? Watch the below video to gain more useful tips from Jasmine Teo and explore how our new resources support your teaching strategies.
Jasmine Teo graduated with a Master of Science, specialising in Mathematics for Educators. She has over two decades of teaching experience, both in public as well as international schools in Singapore. A creative teacher, she likes to experiment with digital tools and inquiry in her teaching. She lives to learn and loves exploring new ideas in teaching.
