For many of you things were going great in math – well maybe you'd say "OK" – but things got crazy around 7th grade when one particular thing changed in math class.
Letters.
Letters started to replace numbers! I know you asked, Why are there letters in math???
Great question. Let’s look at an example. Yes, one with a letter in it. Grab a pencil and paper. Pause here if you need to, but come back. It’s important that you participate. As I like to say, math is not a spectator sport.
OK, write down this short equation: x + 0 = x
A quick note before I continue: most math teachers would agree starting with numbers, looking for patterns and then writing equations like this is the best way to approach teaching.
So why am I starting with an equation with a letter in it??
Because this is the problem you face in math. The letters are thrown at you and POW you’re confused. I am going to show you how to make sense of those stubborn little equations with letters. Then the next time you see one you’ll know what to do.
OK, so x + 0 = x.
Maybe you’ve seen that before. Perhaps it was last week or 20 years ago, who knows. I can almost hear you groaning. And that um, yearning, you feel for actual numbers is good. Use that. In fact, write these other equations directly below the first equation.
2 + 0 = 2
10 + 0 = 10
57 + 0 = 57
OK, that’s enough. If you didn’t align them one directly under another, take a minute and do it again. Don’t bother erasing.
I think we can all agree these numerical equations are pretty obvious. I mean if you have $10 and you earn $0 you have $10.
But we come back to the big question: why replace the numbers with x?
Because that one little letter, x, which we will call a “variable”, represents ALL numbers, or ANY number. In that equation , we could say that the could be any number: Any number plus zero equals that same number.
I like to say that the variable is “able to vary”.
Get it? Variable… “able to vary”.
So why is a simple equation like even a thing? It’s so obvious. What’s the point? It turns out that little equations like that are tremendously important in more complex math like algebra and even calculus.
What is the one number you can add to ANY number and the result is the same as what you started with? You guessed it – ZERO!
So we could add ZERO to anything and not change its value. In math class you will hear the word identity; identity means value.
An equation like x + 7 = 23 actually requires this concept. You would ask What number, when you add 7 to it, becomes 23? Would it be more than 23 or less than 23? If you said LESS, you’re right. Well then, how much less? 7 less! So you would subtract 7 from 23.
But here’s the thing. If you only subtract 7 from 23 your equation would be x + 7 = 16 and that’s different from what we started with.
You should subtract 7 from the left-hand side of the equation as well, which gives you x + 7 – 7.
But of course 7 – 7 = 0 so the equation would be x + 0 which as we know equals ... x.
And in this case x = 16. And you have solved the equation.
There you have it, the first episode of Strength in Numbers.
You learned what a variable is and how they represent any number.
You explored that in an example you will definitely see in math class.
Finally, if you didn’t follow everything here that’s OK. Be encouraged. Your brain is powerful! Listening to this even once will help you make new connections whether or not you fully master it. And that helps you develop understanding and build confidence.
Now YOU have Strength in Numbers.
Thanks for learning.
Letters.
Letters started to replace numbers! I know you asked, Why are there letters in math???
Great question. Let’s look at an example. Yes, one with a letter in it. Grab a pencil and paper. Pause here if you need to, but come back. It’s important that you participate. As I like to say, math is not a spectator sport.
OK, write down this short equation: x + 0 = x
A quick note before I continue: most math teachers would agree starting with numbers, looking for patterns and then writing equations like this is the best way to approach teaching.
So why am I starting with an equation with a letter in it??
Because this is the problem you face in math. The letters are thrown at you and POW you’re confused. I am going to show you how to make sense of those stubborn little equations with letters. Then the next time you see one you’ll know what to do.
OK, so x + 0 = x.
Maybe you’ve seen that before. Perhaps it was last week or 20 years ago, who knows. I can almost hear you groaning. And that um, yearning, you feel for actual numbers is good. Use that. In fact, write these other equations directly below the first equation.
2 + 0 = 2
10 + 0 = 10
57 + 0 = 57
OK, that’s enough. If you didn’t align them one directly under another, take a minute and do it again. Don’t bother erasing.
I think we can all agree these numerical equations are pretty obvious. I mean if you have $10 and you earn $0 you have $10.
But we come back to the big question: why replace the numbers with x?
Because that one little letter, x, which we will call a “variable”, represents ALL numbers, or ANY number. In that equation , we could say that the could be any number: Any number plus zero equals that same number.
I like to say that the variable is “able to vary”.
Get it? Variable… “able to vary”.
So why is a simple equation like even a thing? It’s so obvious. What’s the point? It turns out that little equations like that are tremendously important in more complex math like algebra and even calculus.
What is the one number you can add to ANY number and the result is the same as what you started with? You guessed it – ZERO!
So we could add ZERO to anything and not change its value. In math class you will hear the word identity; identity means value.
An equation like x + 7 = 23 actually requires this concept. You would ask What number, when you add 7 to it, becomes 23? Would it be more than 23 or less than 23? If you said LESS, you’re right. Well then, how much less? 7 less! So you would subtract 7 from 23.
But here’s the thing. If you only subtract 7 from 23 your equation would be x + 7 = 16 and that’s different from what we started with.
You should subtract 7 from the left-hand side of the equation as well, which gives you x + 7 – 7.
But of course 7 – 7 = 0 so the equation would be x + 0 which as we know equals ... x.
And in this case x = 16. And you have solved the equation.
There you have it, the first episode of Strength in Numbers.
You learned what a variable is and how they represent any number.
You explored that in an example you will definitely see in math class.
Finally, if you didn’t follow everything here that’s OK. Be encouraged. Your brain is powerful! Listening to this even once will help you make new connections whether or not you fully master it. And that helps you develop understanding and build confidence.
Now YOU have Strength in Numbers.
Thanks for learning.
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