Monthly Archives: June 2014

Another way to do subtraction

No more borrowing and paying back, or the new alternative

Use addition and then simple subtraction, naturally there are several steps

Example     234 – 187

234

-187  (should be lined up!)

Now 7 is greater than 4,  so we add 3 to both numbers, giving a zero in the units position of the second number

234 -187 = 237 – 190   (must be able to add 3 to 187 !!!)

moving to the 10’s position, and very formally, 90 is greater than 37 so add 10 to both numbers, giving

237 – 187 = 247 – 200, which is now simple, with result  47

Of course, if the lower digit is less than the one above just subtract it from each number

234 – 117 = 237 – 120 = 214 – 100 = 114

It is best to keep the “one above the other” layout, but I have fought with the editor enough today.

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Long division, the explanation.

Since the kids have to explain everything in the new CCSS math standards,

they better have this under their belt, even if they have to learn it and parrot

it out in some test or other (careful, cynicism is not always just round the

corner).

So, here is a long division calculation for you, 32 divided into 2768, or if you

prefer the old fashioned, only used in schools notation,   2768 <the old

fashioned division sign, not on my keyboard>  32. (and < and > are not

representing inequalities at this point).

Division is at bottom repeated subtraction, so we do it:-

32)2768    100×32 = 3200 is too big
2560   so take a smaller multiple (in 10’s)
——   Choose from 90×32=2870, 80×32=2560 (OK!)
208   and subtract,leaving 208, and 10×32=320
192   So try 6×32=192 (OK!). 7×32 is too much.
—-   Subtract again, leaving 16,which is less
16    than 32 and so is the remainder.

So 2768 = 90×32 + 6×32 + remainder,
which is  96×32 + 16,
and so 2768 divided by 32 is 96  with remainder 16

The End

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In the future (tomorrow?)

“Mommy, teacher says we all have to get the new eyepad”.

“Why? What’s wrong with the one you’ve got?”.

“She says it’s much better, the screen goes right to the edge, and we can use the Ruler App to measure things”.

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Fractions are parts of the same whole, part 3

When is a whole not a whole? (again)

When it’s two wholes (or more) :-

John eats 1/2 of his pizza, Mary eats 3/4 of her pizza. So between them they ate 1/2 + 3/4 of a pizza, or 5/4 of a pizza.

So which whole are we referring to ? John’s pizza ……. No.   Mary’s pizza ……. No.    Both pizzas …….. No.    John’s pizza and  Mary’s pizza and  both pizzas …….. No.

Conclusion: What we are referring to as “the same whole” is an abstract unit of one pizza, and the fractions are measurements using this unit. Wouldn’t it be a good idea to start off like this, with fractions as measurements, and avoid years of misunderstanding, stress and confusion.

Is this so different from adding whole(adjective!) numbers , as when  adding two numbers they have to be counts of the same thing (or whole(!) before it is chopped up).?

Fun arithmetic:        3 apples + 4 bananas = 7 applanas

Desperately fun arithmetic :  1/2 of my money + 1/2 of your money = 1/2 of our money

 

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Fractions are parts of the same whole, part 2

When is a whole not a whole ?

When it’s a hole.

(which half of the hole shall we fill first, the top half or the bottom half?)

Besides, I thought whole was an adjective.

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Fractions are parts of the same whole

Just a bit of math fun :

Image

For each triangle, what fraction of the triangle is the (partially) shaded bit ?

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