This post is inspired by one of the workshops I participated at the One-Day Conference for the Teachers of Secondary Mathematics. The workshop was about how Singapore students are taught to use some sort of graphical method to solve increasingly complex problems such as ratio, percentage change or simultaneous equations.
This method is called the Singapore Bar Model. The only important part in all of this is to make children use bar models to represent different types of problems. I have a couple of examples bellow:
- Two apples and a banana cost £1.95. Two apples and 3 bananas cost £3.45. How much does an apple cost? This is a typical algebra – simultaneous equations – type questions. Generally students are taught to start writing the 2 equations. The complains I normally get from pupils at this stage is that they do not really know what to do first. This graphical method seems to access their intuition more and give a purpose to the algebra that comes after. The bar representation for this problem is easier than you think:
- The ratio of the number of Katie’s marbles to Emma’s marbles is 4:5. Katie is given 12 more marbles. Katie now has twice as many marbles as Emma. How many marbles did Katie have to begin with? Again another more algebraic question, which most of the students find quite hard to start it. Their intuition is a little lost at the start and even though they know what ratio is, starting the question is not straight forward. Using this bar method, the question gets very easy. The only problem I would say is reading the question paying attention to details and then making the bar:
- Alison gave 1/6 of her sweets to her Mum and 2/5 of the remainder to her Dad and has 6 sweets left. How many sweets did she have at first? This is another example which could go wrong if we go straight to algebra notation. Here is the bar model option:
We have done many other examples during the workshop, but there a couple of things which are very important. The method gives the students a way to use their intuition better by giving them the opportunity to represent it graphically. Moreover, it gives them a good way to start thinking about a problem. Also, it is a great way to start explaining the algebra that follows normally after using the drawings. If you want to find out more about this method, I recommend Bar Modeling: a Problem Solving Tool: Professional Development Book by
If you want to read more about my day at the conference, read One Day in Stirling.
Have you ever used this method? Or maybe you have similar that you use from time to time. Just let me know in the comment box bellow. I would love to find out more. Hope you enjoyed this post and that you are excited for the future ones. Have a great week. You can find me on Facebook,Tumblr, Google+, Twitter and Instagram. I will try to post there as often as possible.
Don’t forget that maths is everywhere! Enjoy!