AskDrCallahan Blog

Grade school math prep for higher math is actually quite simple. Children
need to see math more than do math.  The basics needed are;

Addition
Subtraction
Multiplication
Division
Fractions
Geometric shapes
Time
Space

Granted that can include a lot of stuff such as mastery of addition includes
knowing the placeholders of base 10 number system. The one’s place, the
ten’s place, etc. Fractions are going to take you into the 1/100 place and
such. But still its addition, start simple and grow.

Basically, all of those concepts can be taught at home without purchasing much at all. Paper, pencil and a clock can get you a long way. But doing math as you go throughout the day gets you a lot further. We wrote a lot on chalk boards and made lots of games out of numbers and shapes and time. We are always noticing shapes and calling them by their correct names. We add as we go along -”We counted 10 steps. There are 5 floors. How many steps are
there to the top?”

One thing we do that I haven’t seen in any curriculum for grade school is to use the alphabet for blank spaces to make formulas.  Use the word ‘formula’
and use X, Y or something else. This is critical to make the move to Algebra easy. Such as

1+ X = 2

Write this on your chalkboard (we wrote it on the driveway), and say something like “what do you need to add to 1 to get 2?”

Out on the driveway it’s a game and a mystery, then when they get to the course called Algebra, they have already done it. We were always told that
children had to reach a certain age to understand this abstract notation. I have found this is not the case. My son could do this as soon as he could
and 1 and 1. I just wrote it with a blank first  1 + ____ = 2 and later with the X and told him the X was the blank. He got that. I left all sorts of
mysteries on the driveway or large cardboard boxes and the chalkboard. He had a blast figuring them out.

See this picture:

This is our son learning sums and geometry. Some of the math is more than he currently comprehends and he has no idea that he’s learning, but when he gets there it won’t scare him or look odd.

We did math this way only through the 2rd grade. Our cover school requires taking the SAT beginning in the 4th grade (each cover is different), so we
decided 3rd grade was a good time to begin expressing math on paper. So after looking around a lot, we finally picked http://www.mathmammoth.com
worksheets. It does a great job of moving into new techniques and concepts as well as continuing to enforce prior skills. It approaches problems in a
common sense way so that the math can easily be applied to the real world. For example, it teaches to add in a way that can be done in your head not
just on paper. Such as adding 16 and 20 you don’t just pull down the 6 on the right side and add the 1 and 2 to get 36.  You add the tens and get 30
and the ones and get 6 for 36. That can be done in your head and is useful for adding in life when paper and pencil and desk are not always readily
available. We do these sheets and still do the activities as well as pointing out math everywhere we see it.

Think of math like you think of language. First you learn to speak it before you read and write it. Kids should be able to speak math and understand it

before they are reading and writing it.  Its not just an activity, it is a language that explains a lot of things in this world that words just can’t do.

Don’t get bogged down on when to move children to Algebra. If they understand the basic math concepts outlined above, then they can go on to
express math in algebraic terms. Its just a more sophisticated way of expressing math. The higher you go in math the more detailed you can express how something in this world works.