## This learning unit gives you the opportunity to:

- understand how formulae are used to represent relationships between variables.
- use some practical examples with your learners to create simple formulae in everyday contexts.
- work backwards to solve equations with your students once the formulae have been created.

### Resources you will need for this online learning unit

Squared paper, calculators, access to computer spreadsheets.

### Setting the scene - what is algebraic thinking?

Writing formulae using letters and numbers and solving equations often involves little numeracy.

Formulae are just one way to represent generalisations. Graphs are another.

A generalisation is a statement about something that happens all the time, although sometimes mathematicians qualify the situations in which it happens. Generalisation allows learners to transfer their knowledge. That is numeracy!

For example, the commutative law of multiplication can be written as: .

The commutative property works all the time when multiplying numbers in real life situations.

### Setting the scene - what are variables?

Formulae are usually statements about variables. Variables can take up different values.

For example, in the formula , a can be 6 and b can be 5. In fact with integers and fractions, a and b can take up any value and the equation is still true. In fact a and b can be the same value!

Unfortunately, solving equations like a + 7 = 13 can cause students to think of letters as “specific unknowns”, i.e. numbers in disguise.

### Setting the scene - what is number sense?

Number sense is really a feel for numbers. Numerate adults have number sense.

This involves an understanding of the quantities that numbers represent, the strategies that can be used to solve number problems, and the ability to estimate when an approximate answer is appropriate.

Number sense implies understanding. Calculating an answer without any sense that the answer is reasonable is not number sense.

### Ideas for teaching around formulae

For many courses and vocations, an obvious place to embed numeracy teaching is around the various formulae that are used to calculate values.

When teaching around formulae we have two basic options:

1) ‘teach’ learners how to **use** the formula, i.e., plug these numbers into your calculator and push = button.

or

2) use the formula as a vehicle to build number sense by getting learners to explore what the formula means and does.

Option 2 is the only option that offers an opportunity for embedded numeracy teaching. Drilling learners on how to simply use a formula is not improving or building their numeracy.

Option 2 allows students the opportunity to generalise how formulae are used to represent relationships between variables and to transfer their understanding in one situation to another.

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