This Week on ByMoms4Moms: Understanding Unknowns… without Fear, Uncertainty, or Doubt

understandingunknownsThe next step, after you have taught your children to understand and not be afraid of algebra word problems is to introduce the concept of the unknown.

My kids love pokemon and so “the unknown” to them is that crazy looking black and white pokemon. It was a great surprise to discover that mathematicians had their own class of “unknowns.”

So if you can relate the concept of unknown to a pokemon character you have a leg up. But if not, you can sit your kids down at the table with a pile of pennies, a pile of crayons, and a pile of raisins. You then explain that the game is to calculate the total number of items on the table without counting them all up. You tell them that there are 2 pennies and 3 crayons and 5 raisins, but since we want to know the total number of items in the group, we can use the concept of an unknown, or x to represent a generic item. X could be a penny or a crayon, or a raisin, it really doesn’t matter in this case. So the total number of items is 2 x’s plus 3 x’s plus 5 x’s, or 10 x’s (if you do the addition).

(I have always said it aloud like this: “two xes plus 3 xes plus 5 xes makes 10 xes,” so that it really drives home the concept)

If your child resists the idea of x as an unknown use an object that she really likes, say a ball or an ice cream cone. Then lay the objects out on the table and ask her to pretend that they are all ice cream cones, even though they are pennies and crayons and raisins. Once she buys that and using her imagination adds up the items, you point out to her that the ice cream cone in this case is actually an unknown object and is just like the x, only she is currently using the word “ice cream cone” instead of “x”.

You can show your child that using an unknown is a much faster way of finding out how many when problems get complicated and numbers are really large. You should probably also tell her at this point that understanding this point of abstraction is fundamental to doing complex algebraic problems and she is well on her way to understanding how algebra works now.

And then you should repeat this little exercise with different objects and different numbers, saying it out loud each time, until your child innately gets it.

Finally, if you have a kid who understands the concept of x as an unknown immediately, praise her and end the lesson. If and when you realize that she understands you need to stop teaching it and move on. (I think this is the same idea as the key to success for the businessman: when you hear the customer say, “Yes,” stop selling and ask for the money)

If you want to teach algebra using a pre-written curriculum in the style I described in this post, you are welcome to download lessons from my algebra curriculum site at The book is called “Doodles Do Algebra” and I post a new worksheet each weekday along with an answer key and teacher’s guide.

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