This Week on ByMoms4Moms…Wrapping Your Head Around “Mental” Algebra

wrapping your headA good part of algebra requires thinking through problems in your head. This type of mental work is not taught anymore in school (not even in the dark ages of the 1970’s when I was in middle school). So learning to teach it to your own children first requires that you understand how it works.

Let’s start at the beginning.

One important type of mental “algebra” problem is focused on solving the typical type of “so-and-so has twice as many apples as his friend, if together they have such-many apples, how many does each person have?” problems.

The key here is to mentally count up how many “units” there are in total.

As an example,

My sister and I have 18 cents, and I have twice as many as my sister; how many cents do each of us have.

So you need to help your kid think about it like this:

  • There are 18 cents total
  • You are dividing that 18 cents a total of 3 ways. DoodleTwo (my boy) gets 2 of those parts (or ways) and DoodleOne (his sister) gets the last 1 part.
  • So if you are dividing 18 into 3 equal parts, then each part is 6 cents because 18/6 is 3.
  • That means that DoodleOne (sister) gets one part, or 3 cents
  • and DoodleTwo gets two parts, or 2×3 cents, or 6 cents.
  • Now if you think of dividing the 18 cents “x” ways instead of using the word “parts”, you are now doing mental algebra!

It is really easy unless you had a traumatic middle school algebra experience and then fear, uncertainty, and doubt creep in at odd moments.

Don’t worry, your kids will have a much easier time with this than you think.

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.

Find more posts like this at


Leave a Reply

%d bloggers like this: