Doodles Do Algebra – Lesson 13


Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.


Teacher’s Notes:

DoodleCat takes your child through the concept of ‘less than’ (from an algebraic standpoint) today.

There are two basic operations at work here, the first is dealing with addition/subtraction across a complete equation, and the second is multiplication/division across a complete equation, both in order to solve an equation for an unknown. The goal is for your child to intuitively understand what is going on and why when he is solving these problems. When I grew up, we learned that you need to remember to “do the same thing to both sides of an equation,” but it wasn’t until I tried teaching this to my own kids that I realized how arbitrary and ultimately useless this method was. Algebra books used by people in the 1600’s, 1700’s, and into the 1800’s (from Cocker’s to Ray’s) teach in a much more straightforward and clear manner by showing why you are learning at each step of the way through algebra. You reason your way through instead of memorizing facts. This works for my family as one of the basic principles of the classical education methods we use is that the memorization stage (or grammar stage) of learning is only the first step in the process of learning and by the time most children are ready for algebra, they are more than ready to learn the why instead of blindly memorizing the what.



Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra


If your kiddo is having trouble seeing how to solve these types of problems, you can get back out the pennies, or jellybeans. For solving a problem like x-1 = 3, you can make one pile of 3 beans/pennies and ask your child to count out an equivalent pile of their own (your child now counts out 3 beans). “But,” you say, “I am going to need to take one of your beans away. So now how many do you need to put out in the first place so that after I take one away, there will be three left?”

You can follow the same process so that your child can easily see the answer to 2x = 6: Make a pile of 6 pennies. Then ask your child to make their own pile of pennies that is equal to yours. Now tell your child that you are going to double their pile before you check to see if they have the same number in their pile as you have in yours, so how many pennies do they need to put out in that case? Right, 3.


1. This one is possibly a bit tricky: ‘a number less 1’ means the number minus 1 equals 3, or x-1=3. Once you show this to your child, assuming they are having issues getting it, it is easier to see that x=4.

2. This problem is the same as the first one, only it isn’t a word problem. The idea is to show your child how the word problem describes the algebraic problem, and vice versa. So the answer is 4.

3. 2x=6, and x=3

4. 3x=12 and x=4

By now your child will be understanding how to manipulate and solve real problems using basic algebra. In a few lessons, we will switch gears and spend a while learning the vocabulary of algebra using some poetry and games. After that your child will be ready for more complex problems.

As always, please leave any feedback you have.