This collection of lesson plans are part of my coursework for EDN550 Transition to Teaching, the initial intensive unit of the Graduate Diploma in Education at Murdoch University in 2018.
There are five lessons. For each lesson there is an original lesson plan with the Lesson Evaluation part at the end completed (in red), and a revised lesson plan with changes highlighted in red.
Year 8 Mathematics – Geometry
This lesson has students finding 𝜋 (pi) and the formulae for circumference and area of a circle. I have found that students are often already familiar with the concept of 𝜋, a mathematical constant for circles. What they lack, however, is an intuitive understanding of the diameter–circumference ratio and the formulae. The main activity in this lesson involves cutting up circles into sectors and rearranging them into rectangles, which can be measured to obtain 𝜋 and analysed to derive the formulae for circumference and area of the circle (given that they already know circumference and area of a rectangle).
A possible future variation of this activity could be to give students three rectangles of different width-to-length ratios which they cut into thin triangles and arrange into circles. The shortest rectangle does not make a complete circle. The longest rectangle makes a complete circle and then some. The middle rectangle makes a circle exactly (because its dimensions were made with the ratio 𝜋).
This was a fun and easy lesson to plan and deliver. However, I found that the ultimate objective of the lesson (deriving the formulae for circumference and area of a circle) were not easy to achieve. It was necessary to revise the lesson plan to provide greater scaffolding for the students to help them make the final connections.
Year 8 Mathematics – Financial mathematics: Discount
Download: EDN550 Lesson Plan 6 2018.02.16 Revised (PDF)
Download: EDN550 Lesson Plan 6 2018.02.16 (PDF)
Download: The Incredible Products Amazing Discount Day (PDF)
I had originally planned to do a Year 12 Specialist Mathematics lesson plan. Unfortunately, I couldn’t find anyone with the required background knowledge to act as my student. Instead, I created another Year 8 lesson plan (hence this is number 6).
This lesson was also easy and fun to plan and deliver. The trickiest part was getting students to understand the calculation of original price from sale price and discount percentage. That is the highest objective of the lesson. The revised lesson plan adds explicit teaching of the calculations involved with examples and some practices.
I think what really made this lesson fun and effective is that students get to use their imagination to come up with a product and a product name. Then, collecting the incomplete data from other students (myself in this learning experience) involved interacting with the creative work of other students.
The ‘Incredible Products Amazing Discount Day’ worksheet I made to go with the activity meant allows the students to quickly transition from the chaotic creative part of the lesson to the serious mathematical part.
Year 9 Mathematics – Probability
This lesson was fun for me but I could possibly liven it up a bit more for the students. The subject is chance draws of black and white stones from a back. Without encouraging gambling, it could make the class more interesting if, throughout the lesson, we periodically stop to draw another stone from a ‘big black bag’ of perhaps 10 black stones and 10 white stones. At the start of the class, students could place bets of different sorts of outcomes. For example, at least 3 black stones or no more than 5 white stones. If I wanted to get clever, I could create a list of outcomes and assign them point value, then give each student a fixed number of points to spend. They choose spend their points on choosing the outcomes they think are most likely. Of course, I will already have assigned the points based approximately on their likelihood, with some a little more likely than others.
But I digress. The lesson was mostly effective. The only change needed was to add a section for explicitly teaching drawing tree-diagrams and adding probabilties for an example with replacement and then without replacement, including calculating the priobabilities of the three outcomes.
Oh, also I didn’t end up using my ‘My Big Table of Probabilities’ worksheet because of the small class size (one). But I believe it would be valuable in a larger class.
Download: My big table of probabilities (PDF)
Year 10 Mathematics – Algebra: Polynomials
This is a fascinating topic for me because it is the second time in mathematics when students start to do things with things that are not number which they previously thought could only be done to numbers. The first is algebra—You can’t add letters together! In this lesson, students learn to do long division with remainders using not numbers but complete polynomial expressions.
It’s a significant conceptual leap but my student impressed me with her ability to accept the idea and give it a go. However, I had initially planned to be introducing the language around polynomials and stress that polynomials are a new and important kind of thing. This never happened and I concluded that that was better left to a later lesson. The concept of polynomial long division with remainders is so crucial to understanding the factor and remainder theorems. If students are confused about doing long division with polynomials and at the same time trying to understand the nuances of two new theorems… well, cognitive overload. So, updated the lesson plan to focus exclusively on polynomial long division with an empasis on practice rather than discussion.
Year 11 Mathematics Applications – Trigonometry
This lesson was inspired by a recent examination problem I saw. At first glance, the problem seemed to call for application of the advanced sine or cosine rules. However, by simplifying the non-right-angled triangle into two right-angled triangle parts, it is easier to solve using the basic trigonometric ratio rules. The objectives of this lesson plan fall perfectly in between the two stated curriculum content descriptions, which I feel makes for an excellent segue. Furthermore, this kind of problem really highlights the importance of considering approaches to problem-solving instead of just jumping in. That aligns this lesson really strongly with the general capability of critical and creative thinking and the mathematics proficiency strand of problem-solving.
I had initally assumed to much about my students’ fluency with the prior knowledge and skills (using sine, cosine and tangent to find unknowns in a right-angled triasngle). Although in practice this would have been very recent learning, I still concluded that a solid review of those important facts was needed in this lesson.
A lot of work went into developing and delivering these lessons but I feel it was beneficial. While I might never teach these exact lessons again, I will definitely recall what aspects worked and what didn’t. The two main themes were (1) properly reviewing prior knowledge and skills, and (2) providing explicit teaching of new skills with examples and practices.