Spotlight on Classroom Excellence

Each week in ‘Spotlight on Classroom Excellence’, Mrs Melissa McMahon, our Director of Teaching Excellence, will give you a window into some of the engaging and innovative teaching and learning happening in our classrooms across the College. 

This week we are shining a light on Year 10 Accelerated Mathematics. The article is written by Mrs Amy Kydd, Mrs Julia Squires and Mrs Katie Jackson.

Mrs Melissa McMahon

Director of Teaching Excellence (K-12)

Excellence in Mathematics

Year 10 Accelerated Mathematics students have been undertaking a Mathematics Enrichment Course in 2021. They have studied topics such as Exponentials and Logarithms, Linear Programming, Circle Geometry and Polynomials with a focus on richer problems to solve.

Their assessment task for Term 3 was an investigation and we had three entries into a Mathematics Competition run by the Mathematical Association of NSW (MANSW). The Investigating Mathematics Competition is very open-ended and allows students to experience working as mathematicians.

The girls were given the investigation task in the last week of Term 2 and used the holidays and Weeks 1 to 3 of this term to plan, investigate and report on their findings. All students in Year 10 Accelerated Mathematics enthusiastically engaged in the task. It was extremely difficult to choose entries for the competition as the standard was so high. An amazing variety of mathematical concepts were investigated including Infinity, Pascal’s Triangle. Mathematics in Sport, Fractals, Euler’s number, safe levels of noise exposure and Archimedes and volume by displacement. Some groups performed experiments, others researched and posed their own questions about the mathematics that they were investigating. All students are to be commended for the high-quality investigations produced. Special congratulations to the entrants selected for the competitions. You can read about their projects and the results below.

The three investigations chosen to represent Pymble were:

The Fight To Prevent Death (Highly Commended)

Eloise Kinchington, Charlotte Hartin and Hayley Johnston

Our mathematical investigation focuses on the question, ‘Which vaccine (AstraZeneca, NovaVax or Pfizer), provides the lowest herd immunity threshold within Australia with the current Alpha and Delta variants?’ The coronavirus vaccines explored in the investigation were AstraZeneca, NovaVax and Pfizer. We utilised various mathematical equations, involving the SIR Model in order to reach our conclusions. Our equations ultimately revealed that the Pfizer vaccine was the most effective against the Alpha and Delta variants at the time of the investigation. This vaccine was followed by NovaVax then AstraZeneca. 

Mass vaccination is the solution to the recent coronavirus outbreaks within Australia, which are becoming increasingly prevalent after the appearance of the Delta strain within Sydney and Melbourne. COVID-19 is having a profound impact on society as a whole. Vaccination programs are the only hope for the world to return to normality. Internationally, effective vaccination rollouts have enabled countries including America and Britain to return to normality, despite experiencing severe coronavirus outbreaks. In the recent example of Wimbledon in London, stadiums were filled to capacity, with almost no masks or PPE perceived necessary for protection against the virus, due to effective vaccination programs. Mathematics is an integral aspect of epidemiology. Mathematical methods are implemented to forecast the spread of disease and make conclusions regarding vaccine efficacy and herd immunity. Epidemiology was the focus of this investigation due to its relevance in mathematical and real-world situations.

The Honeycomb Conjecture

Piper Markson, Angelina Lu and Jocelyn Mar

This investigation looked at bees and the hexagonal shape of the honeycomb and asked if this was the most efficient shape. The project looked at tessellations and used a bubble experiment to show how the honeycomb shape is produced. They discovered that a hexagon uses the smallest perimeter in a circle and hence is the most efficient shape for bees to use. The group even researched notable scientists in this area and reached out to Professor Hale who wrote about The Honeycomb Conjecture. The girls were very excited when he took time from his day in America to write back to the group. This group received a participation certificate.

MathsDonalds (First Place)

Rose Haran, Alie Windybank, Ava Olesen and Saskia Willoughby-Winlaw

How does the per cent of the volume of product delivered to the consumer versus maximum potential volume, and price per g/ml vary between certain items on the McDonald’s menu, indicating the best value for consumers?

This group came first in the competition! They were excited about having a reason to go and buy McDonald’s. They purchased a number of items and worked out the volume of the packet/box/cup and they compared the volumes of different sizes for drinks and chips. They identified four nugget shapes (they termed the types ‘bell, ball, bone and boot’) and calculated the average mass of each type of nugget. They then calculated the probability of getting each type of nugget in your box of nuggets. They concluded that as the sizes of the milkshake and fries increase, the cost per mL/gram respectively will decrease, indicating that the best value for the consumer is larger sizes which is what they hypothesised. They also found that the percentage of maximum volumes filled was always less than 100 per cent, besides the small fries as the fries are filled to go outside the packet.