Lesson 2 Text ‘n’ talk

# Episode 3

Reasoning Resources
Whole class preparation
Two ideas combine to show ubiquity of mathematical structures:

• A situation can be expressed in algebra,
• An expression can represent many situations.
• Engage the pupils in a story using an algebraic expression, for example: There are 71 children in a class but three are away (71 — 3). Now make up a different story for the same expression, e.g. n pounds in my purse and I take three pounds out. Explain that we don’t know how much money is left (n — 3) unless we know how much we started with. But that could be any number, a variable.

Give out Worksheet 1 and talk it through. You may wish to let pupils work at five questions at a time, according to the ability profile. Some questions ask for expressions and some give expressions.
Pair and small group work
A general approach to simple algebra is conveyed: an expression is a concise story, each of its bits corresponds to some detail, so a solution is similar to working things out through talk. Pupils solve the problems on Worksheet 1 by writing expressions and making up new stories for given algebraic expressions.
Whole class sharing and discussion
More advanced algebra allows manipulation without reference to detailed meanings at each step, therefore it is a quicker and more flexible method for solving a problem. Ask the pupils to share their solutions, ensuring that at least two versions are aired for each question, Distinguish questions that ask them to symbolise, and others that ask them to make up a story for an expression.

How can we work out the numerical value for the expression? Remind the pupils of the example of the money: you can’t know how much is left unless you know how much you started with. So each expression can be understood as a story that needs to be unravelled.

The usefulness of writing of equations as opposed to sentences in words may be discussed. For example, the equation for question 8 could be p = 5z + 35 so if we know p we can work out z and if we know z we can work out p. It is possible to do the same with words in sentences, but the equation is neater.