Substitution: so what does it mean?

Substitution is taught every year and yet it is always
causing problems. In particular when we ask a student to substitute a number
into 2a then a

^{2}.It is not the act of substituting that causes the problem but the understanding of algebra. Common misconceptions when substituting into a term happens time and time again. This activity helps to identify those that do, and do not understand, algebra particularly when those difficult areas of powers and brackets are used.**Step 1**

A bit of preparation, but once done it is a resource that
can be used time and time again. Each pupil needs a set of cards numbered 0 to
9. Make them big get them laminated, held together with an elastic band and
stored in a cheap envelope.

**Step2**

Hand out a set of cards to each pupil or give them a set
between two if you want a more collaborative approach. Write an expression on
the board such as

2

*a*

Emphasise that this is an expression not an equation. You
may have to tell them what the difference is, again another big problem what is
an expression, what is an equation.

**Step 3**

Now tell them

*a*= 4, using the cards show the answer. Hopefully they will all demonstrate they know the answer is 8, if not you have an opportunity to rectify any misconceptions. Now put the following on the board*a*

^{2}
Once again the same process is followed you can ask the
class show me the answer. It is now some confusion occurs, some will give you
the answer 16, others 8 again. Now is the opportunity to find out who
understands and who doesn’t. Dependent on the answers it is up to you how you
progress. Try other numbers and other powers. This quick simple exercise will
inform your assessment and guide future lessons.

**Extension**

Once you have successfully rectified
any problem with these issues, and it is a major problem to be solved if you
want them to progress in algebra, you can now try something like these more
challenging terms 3

*a*and (3^{2 }*a*)^{2}. This starting activity will provide the basis for much useful discussion.