Algebra Ideas

Just the mention of the word algebra can strike fear into the hearts of many adults which is why it is so important to make primary pupils aware that they are starting to think algebraically when they are are looking for patterns and relationships.

Asking pupils which two numbers can be added together to produce a sum of 10, will result in several different numbers that can satisfy that relationship.

## Pattern

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From an early age, pupils work with pattern in a very practical way when carrying out activities such as building towers and joining beads. Pupils generally enjoy spotting patterns and this can be encouraged early on when looking at visual images of the odd numbers or even numbers up to ten, by asking pupils what is the same about each number in the pattern.

Allow time for pupils to build their own sequences and let other pupils work out the rule for continuing the pattern. Also ask whether certain numbers will occur in the sequence, which makes pupils think about the features of the numbers in the pattern which leads to generalising rather than just focusing on how to get from one term in the sequence to the next.

Provide opportunities to explore connections between a sequence and its connected multiple pattern, when applicable, which helps when pupils are trying to find a general rule for a sequence.

Make sure to include some sequences where the numbers decrease rather than increase.

As well as arithmetic sequences (numbers - including decimals and fractions - where terms have a constant difference between them) also explore sequences such as those of square and triangular numbers, Fibonacci numbers and the place value headings sequence. It has always surprised me how some older pupils can write out the square number sequence but have never associated them with a square shape so ensure that this happens. They can also be linked back to the multiplication grid, where the square shape of the numbers can be clearly seen.

See Algebra Sequences in Resources

## Language

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Work on the language and definitions used in algebra that we often assume pupils understand: evaluate, for example, often confuses pupils as do words such as expression. Games involving matching cards could be played to help avoid this confusion.

Provide pupils with basic calculators and scientific calculators to work out expressions containing a mixture of multiplication / division and addition / subtraction and get them to discuss why the calculators provide different answers; what order have they used for the operations?

Use examples from real life for formulae such as mobile phone tariffs, car journeys or cooking food.

## Equivalence

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Emphasise that the equals sign means the same as rather than makes, to avoid pupils always expecting a numerical value on the right hand side of the equals sign.

Ensuring that pupils understand the idea of a balance, where both sides are equal, also means picking up on written statements such as 3 x 8 = 24 - 6 = 18 and exploring why this needs changing.

Encourage pupils to write simple equations in different ways so that they appreciate that a + 5 = 12 can also be written as:

12 = a + 5, 12 = 5 + a, 5 + a = 12, 12 - 5 = a, 12 - a = 5, a = 12 - 5, 5 = 12 - a.

Work with numbers first and revisit ideas for flexible calculating such as: 58 - 19 = 59 - 20 or 37 + 28 = 35 + 30, where pupils use number lines to explain why this is true. Missing number problems can then be introduced.

## Real Life

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Use examples from real life for formulae such as mobile phone tariffs, car journeys or cooking food.

Pupils can also make up their own formulae for situations that affect them at school, such as planning a trip (which provides a link to measures) when investigating the cost of a coach or entry into a place of interest, which could involve a standard fee plus the cost for each pupil.

During a topic on money, simple formulae can be used to illustrate how much money has to be paid back when using credit or store cards to pay for items, rather than debit cards. Similarly, if it is close to holidays, pupils can work out the cost of using money abroad in different formats, using various formulae.

Visitors are useful here for explaining how they use formulae in their jobs (such as the nurse mentioned in measures).

When working with variables, pupils sometimes think that the letters stand for abbreviations (as in m for metres) rather than unknown numbers; providing examples helps pupils to grasp this. When converting inches to cm, we can use the relationship that 1 inch is the same as 2.5 cm. Asking pupils to express this relationship can result in them writing I = 2.5C. However, if we insert numerical values such as C = 1, we have 1cm being equal 2.5 inches. The correct relationship is of course C = 2.5I and it is well worth allowing time for a discussion about this. Apart from measures, formulae also make good use of relationship tables.