How to Teach Addition, Subtraction, Multiplication, Division, and Fractions in One Easy Lesson

When my oldest was little I had no clue what I was doing and used the same math program that all the other smart people I knew were using.

Because math was all of these disconnected parts for me: fractions, addition and subtraction, multiplication and division, we never saw how any of it is connected.

My youngest is getting a completely different education. Tear free and fun.

And so can yours.

Over on the left we have two images of the number 8. At the top is an 8 block. We have one 8 (1 x 8) and we can count and know it is 8. We also have 2 four blocks and that also makes 8. 4 + 4 = 8. What else can we see?

• 2 x 4 = 8  Two groups of 4 is the same as  8.
• If I had 8 units in the image we could see that 8 x 1 is the same as 8.
• There are 2 fours contained in the number 8. Or 8 divided by 4 is the same as 2.

In this image we can easily see that:

• If you have 8 and you remove 4 you are left with 4. 8 – 4 is the same as 4.
• If we divide the 8 in half we get 4 on each side. 4 is 1/2 of 8.

Now we have 4 of the two kind. And that also is the same as 8 or 4 x 2 = 8. And what else can we see?

• 2 + 2 + 2 + 2 = 8
• There are four 2’s contained in 8. Or 8 divided by 2 is the same as 4.

 Now if we take 2 away from 8 we are left with 6. And what else do we know?

• There are four 2’s in 8. One 2 is 1 block out of 4. Or 1/4 of the number 8.
• 6 is the same as 3 two’s. Which is 3 blocks out of the 4 total blocks. Or 6 is the same as 3/4 of the number 8.
• 2/4 of 8 is exactly the same as 1/2 of 8.

If you are starting out with a pre-schooler I wouldn’t use this language.

I would ask a lot of questions:

• How many two’s make 8?
• If we take away a two, how many 2’s are left?
• We made 8 with two’s.
• What other blocks can we make an 8 with?
• We have 8 in this rectangle. How many across? How many down?
• Let’s skip count these two’s: 2, 4, 6, 8.

If I had an older student, we would play a lot of blocks before doing a lesson like this one. This is a lot of information to cover at one time. But when playing with the blocks, it is easy to see that numbers are made up of other numbers and it is all organically connected.