Musings

Mood: Stressed

Get  your child to make up   75 pennies, bagging them as usual.

Put out 21 pennies, i.e. 2 bags and 1.
Now put out  11 pennies. i.e. 1 bag and one unit.

Ask you child how many  pennies are in total?   Start taking the pennies out of  the bag to count then.

If you do this a few times, (or maybe the even first time) the child will object as he starts thinking of a bag as a group.  He sees that he can save time.
Praise him and tell him that mathematics is all about saving time and learning lots that is not  immediately obvious.  That this is how computer work and most of the  everyday things he sees around him: phone, TV, CD player, DV, PC.

When this moment occurs, he has made the discovery that makes arithmetic easy.

He has realized that you can count the bags without opening them.

Now play a game giving him   23 and 31  in bags and pennies and let
him tell you how many he has.

Write 9 cards 5 cm high with the numbers   1,2,3  ... 9 on a card.

Get him to show you how many bag and how many units (pennies) he has.

Write  a card   with the following:  
 BAG  
 of
 10      Units

Place the number under the correct column.

Show him that  25 is different from 52  i.e. 2 bags of 10,  that the
position of the numbers is what matters.
When you get to 100.  point out that the o allows you to have
no bags of 10  , or no units.   

This is a huge concept, invented by the Arabs.


Soon he will realise that you can add the numbers instead of the bags.

Make one Bag of 100  pennies.

Now her can see that this is just another group.

From this you can start back to the sheet with a million.

you may want take a sheet of 1/4inch or   5mm squared paper.

The 8 1/2 x 11 inch has 32 x 44 squares.
   Mark off
1 unit
a row of 10
a square of 10 x 10   i.e. 100, 200, 300, 400 up to 1000 etc.

Now you child is thinking in an abstract way.

The next idea is to get him to think in terms of carrying
i.e.  replacing a 10 units with 1 bag of ten; 10 bags of 10 with 1 bag of one 100 etc.

We are well on the way to teaching addition and subtraction multiplication
and division.

Mood: Happy
Listening to: Elgar's Pomp ...

Give your child some small cloth or paper bags, each to hold 10 pennies.
Take a  sheet of paper. 
 Mark 10 circles on the paper from left to right "1", "2", "3", ... ,"10".
Let your child use this to count groups of 10 pennies from a pile of pennies.

Show him how to make bags of ten pennies.  Call it a "Bag of Ten".
Give him 25 pennies for him to count.
When he done so say: "You are counting as big people do", and
 "You have 2 Bags of Ten and 5 pennies."

Write down 20 and show him this means 2 "Bags of Ten".

Take another sheet of paper and mark 100 circles with 10 rows of 10 circles,
writing 1 2 3 ... 10 on the first row,
and    11 12 13 ... on the 2nd row,
and    21 22 23 on the 3rd row.
Continue up to 100.

On the left side put a big "0" beside the first row
a "1" beside the 2nd row; a "2" beside the third row etc.

Now let him count piles of pennies by covering up
the circles and then lift off the last coin to see
how many coins are in the pile.

Point out that each row is a "Bag of Ten".
Tell him that 20 means that you have 2 Bags of Ten and no units. (0 units).

Play this game for 10 minutes each dayfor a week.

Name the numbers:
"One-ty", Two-ty, "Three-ty", "Four-ty" etc.  This is consistent and
lets the child learn the rules.

After a week you can explain that adults have different words for
the numbers from 11-20, and 30. i.e. tht it is called "Twenty" not "Two-ty" etc.