Thinking and Working Mathematically: Using Numbers in Geography

© Beverley Paine, August 2007

[this article forms part of a series on Geography you can buy as a Practical Homeschooling booklet from Always Learning Books]

There isn't a subject in the homeschool curriculum that can actually be studied in isolation. No matter what you are studying you are learning so much on so many different levels. Not only that, you are using so many different skills from across the curriculum as you learn. How we use - and improve - our reading and writing skills is usually obvious, but not many people realise they are thinking and working mathematically when studying geography. That's probably because most of us are maths phobics and tend to avoid anything to do with maths! However, mathematically speaking, we're a lot smarter than we think we are...

How are some of the ways we can use numbers when studying geography? Think about the maths embedded in some of the following questions. Questions like these come up all the time in conversation in homeschooling families.

• How far is it to Grandma's house?
• Which is the shortest route between our house and the swimming pool?
• How high is Mount Everest? How much higher is it than Mount Kosciusko?
• Which way will our pet mouse have to go to get through the maze we built?
• How did we get to the zoo?
• How busy is this road, and when is it the busiest? Why is that?
• What does scale mean?
• Which places will we visit and how far will we go today?
• How do you use a compass?
• How is everyone going to get to the homeschool camp?
• How long will it take and how far will we travel?
• How big is one kilometre?
• Why is our town this big and the next town that big? Why are different towns different sizes?
• How far is it around the world?
• What time is it it in London right now?
• How high above sea level do we live?
• How can a compass be used with a map to help us find our way?

Doing geographical explorations often means we need to make measurements and these can involve talking and learning about the use of scale, as well as the different measuring tools and devices (and how they were invented and how they are used by different profressions for different reasons). Geography often means looking at how things change over time: time is a mathematical concept. Recording changes over time is a scientific process that teaches a great many mathematical skills.

We had lots of fun making various measuring tools, including a metre stick, a trundle wheel, and a really long tape measure! Working out how to build 'square' or using different angles met using protractors and a pair of drawing compasses. Trigonometry came into some calculations when planning and designing major projects... as did using algebra. Working 'professionally' was always a challenge but it gave the children the opportunity a taste of what working in different careers was like. Playing and modelling with LEGO slowly scaled up to building pieces of furniture and drawing and making parts for car engines... Real life projects can be supplemented with lots of interesting investigations in every area of culture, history and environmental studies.

Various units of measurement are used in geographical investigations. We can simply use them and let our children become familiar with them in this very hands-on practical way or we can do a little research and let our children know how and why these units came into being. Most of the time our children aren't really interested enough to do the research themselves and a quick explanation at the right moment is usually not forgotten. I'm amazed at how much my children learned without any kind of repetition or drilling. Homeschoolers are lucky to capitalise on learning when our children's interests are at their highest. Information and skills learned this way require very little consolidation or practice.

Thinking mathematically means developing skills in the area of number, measurement, shape and space, probability, data.

Making models, drawing, designing, planning - these all develop skills and knowledge in shape and space. Creating and giving directions and instructions also develop and practice spatial concepts. Introduce and use technical terminology so that your children become familiar with using these concepts in their everyday language. Orienteering is a great way to teach a great number of geography skills as well those related to space and shape in mathematics.

Children handle data every day without thinking about it and there usually isn't much call for them to naturally record this information, but if they want to make predications or make decisions often they need to have some kind of record to which they can refer. Mapping changes by recording - either with graphs, flow charts, in tables or graphs - is an invaluable skill. As is using information and communication technology such as spreadsheets and databases to transform the information into formats that can be easily interpreted. When children are young they enjoy charting their growth, the weather, how many jobs they've done (to earn their pocketmoney), how many 'sleeps' left on the calendar before a special event, etc. When they get older they can be introduced to bus timetables and routes.

If doing maths is a chore for your children consider adding in more geography investigations. It's like mixing zucchini and carrots into that yummy cake - your children won't know they're getting all that goodness and nutrition. Geography makes maths easy!