A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful. Each account refers to one or more of the values and principles in the report.

Lesson Account 20 - Introducing Algebra

Written by

Janet Pass

Organisation

Stockport Continuing Education

Age/Ability Range

Adult 20 – 50+. L2 / GCSE group. 15 on the register – 12 learners present.

How was the session/task introduced? 30 minutes group session in a 2½ hour teaching session. Individuals work at own tasks informed by syllabus and ILP (individual learning plans).

Adult Core curriculum Ref N1/L2.4

Task introduction of algebra. – Group were asked to draw the following on a piece of paper and told the rules.

3 consecutive numbers are placed in the triangles – definition of consecutive question and answer.

The values of the circles are found by adding numbers in the triangles connected to the circles.

The value of the square is found by adding all the values in the circles.

Demonstration of above rules with first set of numbers.

Learners were given opportunity to try a set of 3 numbers they had chosen.

Introduced as a trick, I then asked for a further set of 3 numbers and told them (without visibly working it out) what number would appear in the square box.

Students then had to find out if I was correct. The group wanted a number of different sets of 3 numbers to check whether I had really been able to answer.

How was the session/task sustained? The algebra came next. – by introducing x, x + 1, x + 2 (for any three consecutive numbers) and discussing how it could be shown that the number in the square box would always be 6x + 6, so as long as you had the first number it was fairly easy to work out final number.

Students then got opportunity to try it out for themselves.

It was easy to sustain interest. Plenty of opportunity for feedback from students.

How was the session/task concluded? No answer.

What were the critical moments? By introducing algebra in this way ensured the students didn’t shut off before start of session. Quite often this happens, especially with adults who can’t always see the benefits of being able to manipulate equations. As the students could follow where the x, x+1, x+2 had come from and why it may be used they seemed more open to the concepts trying to be introduced.

Evidence was supplied by each student being able to work out what went in the square box using formulae.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning? No answer

How was that mathematics learnt? No answer

Other memorable outcomes One of the learners said she had always hated algebra at school and if I said that’s where the session was going would have shut off. As it was she enjoyed it!

Resources None specified

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Values & Principles

Conceptual understanding and interpretations for representations

Strategies for investigation and problem solving

Exposes and discusses common misconceptions and other surprising phenomena