Putting the fun into algebra
I work with a brilliant support teacher who helps with a small group of pupils from my Year 8 set 3 in maths. Soon we will be doing an algebra module from our scheme of work. Have you any suggestions for a fun activity that will help their understanding of substitution into algebraic expressions?
The following activity can be done by individuals or in small groups; I have even done it with whole classes playing in teams. The activity is based on ordering a set of six cards showing different algebraic expressions. The order is determined by substituting a particular value into each expression.
The number of copies of the cards for the activity obviously depends on the size of the group. For this article, I have assumed that the support teacher will be working with a group of four pupils. A photocopiable sheet with solutions is available at www.mathagonyaunt.co.ukarticlesindexJan312003.html The pupils play in pairs. Each pair needs four sets of the 6 circle cards (with each set on different colour card) and one set of the 4 rectangular substitution cards. For demonstration purposes you will need another two sets of 6 circle cards and an n = 4 card. Laminate the cards and then cut out. I have found that the organisation of "handing out" and "collecting in" is made easier by placing each set of sets in a re-sealable plastic bag. Pupils also need a calculator and paper for any rough working.
First demonstrate the activity using a set of the circle cards and the n = 4 card.
Explain that the purpose of this activity is to determine the order of the set of circle cards (from smallest to largest) for substitutions using different values of "n", as indicated on the rectangle cards.
Take one demonstration set of six circles and the n = 4 card and ask the pupils, as a group, to decide what order they think the circle cards would be in if the "n" in the expression had a value of 4. In each case ask them why they think the cards should be in that order.
Follow this by demonstrating the values that are created by correct substitution for each circle, writing the value in washable pen on the circles. Lay the second set of circles in their correct order beneath the pupils' chosen order, placing the n = 4 card at the end. Discuss the differences, pointing out why these might be different. There is a great deal that pupils can learn from this interactive discussion.
Now the pupils work in pairs for each of the values given on the rectangular substitution cards to create the correct order of the expressions on the circle cards. Let your support teacher know that pupils are allowed help as they need it.
When they have finished check their solutions with them and discuss those that are incorrect.
Your support teacher might find it helpful to have some notes about what pupils might have forgotten or still not understood;I have given some examples of some common problem areas.For example, 8n is 8 x n (that is, 8n = n + n + n + n + n + n + n + n). Pupils sometimes find it useful to see this with numbers, and it helps to solve any misconception.
n2 is n x n; pupils often mistake this notation and work out 2 x n instead of multiplying the number by itself. One way to help them is to encourage them to write n x n and then substitute the numbers beneath. For this exercise they can also use a calculator using the x2 button. For example for 22, type then on the calculator.
2n is 2 V n. The mistake pupils tend to make here is to read the calculation bottom to top: "n divided by 2". You should stress that it should be read from the top to the bottom as "two divided by n", and they should write it down in symbols as they say it: 2 V n.
n2 is n V 2. The mistake here is similar to that given above.
8 - n. This becomes a problem when the value to be substituted is negative.
Sometimes it helps to write the sum out: for example, when n = - 1 we have 8 - (-1) = 8 + 1 = 9. Similarly for - 2n, when n = - 1 this becomes - 2 x - 1 = 2.
The support teacher might need to be shown how to use the fraction button on the scientific calculator prior to the session so that they can remind pupils how this is done.
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses. Email your questions to Mathagony Aunt at firstname.lastname@example.orgOr write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX