Below are two activity sheets to help you understand how to use the excellent nvlm and Wisweb FREE websites and suggest some ways in which you can use them.

These sites have loads more fun activities, browse around after you've complete these activities. Can you work out the weight of the gold bars in the picture on the left?

Why we like this activity....
Mathematics is a language, just as confusing to many as the first time you read chinese, german, arabic etc. This activity allows you to play around with some scales and understand how and why, if you take objects that weigh exactly the same as each other off both sides, the scales stay balanced. Imagine you are a salesman or at the market buying your food and supplies in the middle ages and you want to check the weights of the bags are what you think they are: how are you goint to work it out using a pair of scales?

How this activity can be used....
Equations are NOT abstract ideas, they define and enable us to evaluate the relationships between any given variables. Balloons pull the scales upwards making the goods on that scale seem lighter than they actually are! If you take off a ballon you make the scale heavier! If you take off a weight, which pushes the scales down, you make the scale lighter. The equals sign means exactly that, the things represented either side of the equals sign are the "same as" or equal to each other. This is how you must think or the equals sign, showing two things are equivalent, the same, just like hello and hi are two different ways of saying the same thing. The equal sign does NOT mean: "what is the answer".

Once you've mastered, through play, this concept of the equals sign as the centre point of a balanced set of scales, you can then focus on understanding that letters represent unknown numbers and numbers known weights. This is where you start to learn the language of the physical, non-human, non-emotive (emotional) world = mathematics. Hopefully you can appreciate that it is much easier to write an equaiton than to draw a picture of a set of scales and weights you know and don't know! However, if you're ever stuck trying to solve an equation, you can always convert the equation back into the picture it represents!

What to expect when using this activity, from our experience...
With the second activity from Wisweb, without the balance scales, you may have difficulty understanding what to type in and how the programme works. Get help from your teacher, by the end of a one hour lesson we've had almost no students who didn't understand how it works and once you know how these two internet sites work, if you are genuinely motivated to learn how to solve equations, and are committed to practicing at home, with these sites, there is no reason why you cannot, and will not, finally understand how to solve equations. Best of luck!

Extra notes

 

Oliver Bowles 19.08.09

Web resources from: Freundenthal Institute for science & mathematics, Netherlands and National Library of Virtual Manipulatives, USA