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Incidental Maths

I’ve always loved numbers. Upon reflection on my own journey with Mathematics, I believe two key experiences contributed to my mental maths ability. These helped me to succeed in high school maths.

It became obvious early on that my mathematical ability and interest didn’t come from my mother. I distinctly remember, whenever we were shopping she was regularly asking me to calculate discounts, “How much will this be if it’s 15% off?”, or to compare items, “This is $2.50 for 2L or $2 for 1.25L, which is the better deal?”. As a parent and teacher now I am a little suspicious that in retrospect, Mum may have been feigning ignorance to make me work. This repeated practice helped me to identify the best methods and shortcuts to use for quick calculations.

Later, I started my first job in a doughnut shop. The boss felt that having to go to the register to add amounts after taking an order and then returning to collect money added an unnecessary and inefficient step to the process during busy times. This meant we were expected to add everything up in our head. After being abused by customers a couple of times for attempting to overcharge them, you soon became very good at these calculations.

My mum’s repeated questioning and the mental maths required at the doughnut shop led to a mastery of the basics which in turn helped me to succeed in class. A solid foundation and ability in the basics frees up the mental space required to learn the new information and skills during lessons. A student who is continually struggling with adding fractions, or performing basic multiplication, will find it far more difficult to focus on the new skill being taught. In these circumstances, students find themselves becoming further and further behind, experiencing little success and eventually switching off to the subject. How can we help the boys to ensure this doesn’t happen?

Fitness professionals often talk about incidental exercise being a key component of good health and physical wellbeing. Taking the stairs instead of the elevator. Parking in the furthest carpark. These simple tasks, embedded in daily routines help to maintain a good baseline fitness level.

What if the same principle were applied to Maths? The incidental mental calculations that occur every day can help students to see the relevance of maths beyond the classroom, improve their speed and accuracy and help them to find the mental maths shortcuts that can be taken in calculation and estimation. Some examples of opportunities for developing mathematical thinking include:

Car trips
Working out when to leave if you need to arrive by a set time and will travel at an approximate average speed.
Estimating the distance between petrol stops given the cars fuel consumption and size of tank.
Reading maps and plotting the most efficient routes.

Gardening
Estimating the distance between and the depth of holes required for planting trees.
Organising vegetables into arrays, for example, when planting 3 rows of 4 seedlings, asking “how many will we need?”

Cooking
Calculating new quantities of ingredients if a recipe serving 4 is required to serve 6.
Measuring in fractions. For example: If you require 1 1/2 cups of sugar, ask “How can I create this using these 1/4 cup and 1/3 cup measures? How else could I do it?”

Shopping
Budgeting, calculating change and estimating/calculating amounts. For example: “I need 200g of ham and it’s $17.00 per kg. How much will I pay?” You could make this a competition between siblings with the closest estimate getting a prize.

Mathematics is skill-based and like all skill-based pursuits, the more practise we get, the better we perform. Providing opportunities like this and asking questions of your children will help develop and maintain their basics, which allow them to focus fully on the new skills being taught in class.

Mark Watson, Head of Senior School Maths
watsonm@atc.qld.edu.au