Factorise the expression to quickly reveal more information about an algebraic expression
Factorising will ultimately be used to solve equations.
Practising, and becoming fluent, with expressions is the first step on this road.
The result from factorising a quadratic expression is hidden at first glance, but with a bit of determination, the pattern is revealed.
Extend your learner’s knowledge of factorising by looking for the patterns
Your learner will already be familiar with the fact that expanding and factorising are opposites.
Expanding is useful for simplifying expressions where there are multiple like terms.
Factorising is essential for solving equations.
Looking for the patterns in the problems you solve will make light work of the increases in challenge your learner is certain to experience.
Quadratic expressions can include negative numbers and fractions, but they all follow the same basic pattern, when factorising.
Without the awareness that comes from pattern spotting, factorising quadratic expressions will rely on memorised steps without meaning or purpose.
Sadly, some learners forget the order, forget a step, or do something extra from a related procedure
For emerging learners
A good start is to revisit expanding brackets and try reversing the operation.
This way, they know what the answer is supposed to be before they begin to factorise.
Then, encourage them to think about what you need to do to get back to the binomials. It might help to rewrite the expression to show how each of the terms were formed.
Try this with several other binomial expansion problems to support factorising the quadratic expression.
For learners needing extension
For those who are becoming more confident, identify how you made the middle term in the quadratic expression.
Identify how you made the last term.
Have a think if there is more than one way to make the last term and more than one way to make the middle term.
Now, investigate if there is more than one way to make the end terms and the middle term using two numbers.
This is pattern spotting, which will support all future work with quadratics.
At this point in S3, it’s helpful to continue to focus on:
- Factorising quickly
- Knowing your tables – recalling them without having to count
- Finding patterns in processes
S3 pupils who become familiar with the process of expanding and factorising will develop their flexibility with algebra.
This will greatly support the variety of concepts they are going to experience, this year and next.
Next week, I’ll be hosting a small group session to address any questions you might have up until now.
It is limited to six participants to maximise interaction and individual questions.
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Each week, I’ll continue to focus on one important aspect of the National 5 pathway, supporting you and your learner as they continue to expand their ability.
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