The Four Basic Math Laws

Every year in our homeschool community, our students review the four basic laws in math. They learn additional formulas and measurement details, but the four basic laws seemed to stump our family the first few years. This past year, I finally thought through the laws and what the words mean in order to create the memory peg for my children.

The Four Basic math laws-3

Here is what I say!

Associative Law

(a + b) + c = a + (b + c)
(a x b) x c = a x (b x c)

Who “associates” with whom? In the first section, a associates with b, but on the other side b associates with c. This shows you where the parenthesis need to go. You “associate” with the letter inside the parenthesis with you!

Commutative Law

a + b = b + a
a x b = b x a

This law is simple. My husband works from home in an office upstairs. In the morning, he leaves the bedroom (a) and “commutes” to his office upstairs (b). In the evening, he leaves his office upstairs (b) and heads back to our room (a). The commute is the same, but the starting and ending points switch/reverse in order. This would work for any commute. It just needs to be simplified to 1 starting point and 1 ending point.

Distributive Law

a(b + c) = a x b + a x c

This one is the hardest to explain. What I tell my children is that the a is “distributed” out to the b and to the c. In the first part, the b and the c work together and then get the a involved. In the second part, the a is “distributed” to each of letter individually, and then they are added together.

Identity Law

a x 1 = a
a + 0 = a

This law really is simple without an explanation. The one thing I do throw out is this question – in each situation, what does a have to do to remain a (or to keep its identity)?

Another fun thing to do with the math laws is actually try them out! I love to sit down with my students at home and plug in a number for each letter. Then they are able to see the truth behind the laws.

Note: I would never explain this in detail in our homeschool community classes as we introduce the memory work, but do not teach about it at the younger ages. It’s a fun and simple way to discuss the laws at home while you memorize them!

Related Posts

  • 10000
    One of our favorite things to do is read fun math books. It all started when my mom retired from teaching and brought her math books home from the classroom. After reading several books to her grandkids at her house, she sent a few our way. Now, I'm always on the…
  • 10000
    This post may include affiliate links. See my full disclosure policy for more details. When I began homeschooling, I was beyond clueless. In a matter of 3 months, I decided to homeschool, joined a classical homeschool community, (Classical Conversations) and quit my job in Human Resources (over 15 years in the field).…
  • 10000
    For a moment, I considered titling this blog "Five Reasons You Shouldn't Join Classical Conversations (CC)," but I admire the program too much to disparage it - even in the name of creativity. The reason I considered this is because classical education and CC go against the grain of what…
  • 10000
    Setting up for our year in the Classical Conversations Essentials program has been a trial and error for us over the last two years. I encourage new moms to ask those ahead of you what they have done - and then make it your own! There are three areas of…
  • 47
    Classical Conversations programs have given us a much needed method to tackling the idea of classical homeschooling. Are we perfect at it? Oh, far far from it! But the parameters are more than helpful in determining what we will learn and how we will learn it. Not to mention the…
    Tags: students, year, math

Leave a Reply

Your email address will not be published. Required fields are marked *