How Brackets Make It Easier to Solve Equations (Reveal the Secrets)
Instead of 3x + 10 = 50, write 3(x) + 10 = 50
Podcast is AI generated, and will make mistakes. Interactive transcript available in the podcast post.
Using brackets to both express multiplication, and to reveal secret multiplication, is a game changer in more ways than one.
Take a simple equation like this one:
That expression:
Creates a lot of problems for novice learners.
To you and me (and some of our students,) obviously it means ‘three lots of x,’ or ‘three times x,’ or ‘three multiplied by some unknown quantity,’ or ‘the coefficient of x,’ where in turn we understand coefficient to imply multiplication.
To the novice learner - most children in school today - if we say ‘x is four,’ or:
Then there is no immediately obvious reason that this:
Shouldn’t mean this:
Yes, you can learn that it implies multiplication, that there’s a secret cross symbol there, and many students eventually do, but we can make this faster and easier to learn for all students.
For example, if we start off writing this instead:
Then it is immediately obvious that it must mean this, when ‘x is four’:
Which we have already learned, since we replaced the cross symbol with brackets ages ago now, means ‘3 times 4,’ or ‘12.’
From here, we can start to see how this simplifies the process of learning to solve linear equations by rearranging.
We’ll also see how it simplifies other mathematical routines that seem to simple to us, but provide a real challenge to students.
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