Learning the 4 operations

Some educators advocate delaying formal maths until aged 10. There are many books that help to make maths part of family life.  There are a series of books called Family Math and here ( presently out of stock at Book Depository but Amazon has them) which will help you, we owned one of them for a while. There are probably some similar books at your local library. Because maths is part of everyday  life; coins, cooking, playing board games, telling the time, playing shop with pretend money etc  we found that we didn’t need a book. I just needed to take the time to talk about numbers: we counted cutlery when setting the table together, cut the sandwich in 1/2, played games like monopoly etc.  We found that one son at 5 years old knew most of his addition sums to 12 because he liked to play board games with his older siblings and didn’t trust their addition on the die! He loves doing math sheets for fun. (He thought it more fun than colouring!). But another of our children struggled with any written addition until over 7 years old.Use wisdom when to start

One thing I would recommend for puchase is an abacus. ( I prefer one that is 10 rows of 10 and has then in groups of five). 

Below is a summary of the basic approach we have taken once we felt a child was ready to do written math . The  ideas are gleamed from a variety of places but most of the credit must be given to ProfB maths.

We used math sheets downloaded from here.

Our first goal was to achieve mastery in the four basic operations.

“Arithmetic operations should be memorized and over-learned to the point that they become automated procedural processes, fully automated and perfectly accurate. Students who have the mechanics of calculation automated (able to run with out conscious attention) will inevitably be able to allocate more attention to problem solving” (Quoted from Don Potter).

Addition We start with 1+1, 1+2, 1+3 … up to 1+9. 2+1, 2+2, 2+3 … up to 2+8. and so on.

The child is encouraged is use an abacus and fingers. They do these sums until they are mastered.

Some sheets are available for printing here that just cover these facts.

Subtraction Similar to addition, a sheet of 20 sums was given until mastered while continuing to do drill sheets in addition. With some of my children they started all 4 operations together. Others one at a time.

Higher addition (over 10) e.g. 6+7

We taught the concept that “the teens are ten” by counting this way … teen (10), one and teen (11), two and teen (12), three and teen (13), four and teen (14) etc.

When adding make the largest addend up to a 10 (teen) as below:

Note the arrows with the numbers, moving for example, from the 3 to the 9.

When we first start this, the child draws in an arrow. With the number on top of the arrow being the amount that needs to be moved to make 10. Now we see how important it is to master adding up to 10.

They do drill sheets until the arrows are not used (These usually drop away by themselves)

and the abacus is not needed.

Higher subtraction

15-2 is easy. 15-9 is a little harder.

Separate the 15 into five and teen again. You can’t take 9 from the 5 but you can take it from the 10. What is 10-9? 1! Now add back the 5. Again, this is easy to see with an abacus.

When the child writes this I have them write 10 + 5 above the 15 (as illustrated above). They do drill sheets until the abacus is no longer used and it can be done by rote.

We continue with addition and substraction drill sheets and go on with …

Multiplication We start with skip counting: by twos – 2,4,6, 8, … and 20 by threes – 3, 6, 9, 12 etc

Then we introduce the x symbol as for example 4×2 is 4 groups of 2 or 2+2+2+2.

Again do lots of drill sheets.

My children usually wrote out numbers at the top of their page at first: 7,14,21, …

I taught them that if count 3 along this would be 3 groups of whatever you are skip counting.

Continue until mastered.

Division 49/7 is how many groups of 7? It should come easily to mind but if not out comes the abacus or they can skip count in 7s, 7, 14, 21… up pop the fingers until 49.And how many fingers are up? Thats the number of 7s needed. They are now completeing 4 sheets daily, taking about 5 minutes each: a total of 30 minutes (allowing for finding a pencil etc).

Once they are able to do this and are reading independantly they begin Saxon 54.