This the fourth post in a series about using cups and counters to introduce concepts in algebra. In my last post I started to describe a teaching sequence. We got to the point where the students were writing expressions for the number of counters in a diagram.

It’s a good idea to mention to the class that if two cups are marked with different variables they *may* have a different number of counters but they also could have the same number of counters. One misconception among students who are being introduced to algebra is that different variables always stand for different numbers.

As the lesson progresses students may offer different correct answers to a question. They may change the order of addition (3+x or x+3). If this happens I often refer them back to the first example and point out ’3+5′ and ’5+3′ are both correct sums. You might also have students who suggest multiplication as an alternative to repeated addition. For example:

Here some students may answer ’a+b+b’ and other might answer ’a+2 x b’ . It’s a good opportunity to remind students of the relationship between multiplication and repeated addition. I usually provide some more examples and ask for both answers. I always leave the multiplication symbol in the answers at in my early algebra lessons as it can mimise confusion. At this stage we’re not concered about simplification so there’s no need to omit the multiplication symbol.

With these points in mind it’s time to start handing out the cups and counters to the class. I’ll describe how I like to do this in my next post in this series.