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Using base ten [ 10 ] blocks and centimeter grid paper,
we will model the multiplication problem: 15 в 13.
This rectangle is 13 centimeters by 15 centimeters.
As we fill in the rectangle with base ten blocks,
we can fit a hundred block there.
As we continue to fill in this side,
we have ten, [ 10 ]
twenty, [ 20 ]
thirty, [ 30 ]
forty, [ 40 ]
and fifty. [ 50 ]
And we fill in down here another ten, [ 10 ]
twenty, [ 20 ]
and thirty. [ 30 ]
We'll then fill in this last small rectangle with ones.
As we do this, not only do we demonstrate
multiplication of two digit numbers,
but we can then use this model
to demonstrate the place value that comes into play
when we're multiplying multiple digits.
So, we have ten here, [ 10 ] and three [ + 3 ] more
makes thirteen. [ 10 + 3 = 13 ]
We have ten here, [ 10 ] and five more [ + 5 ]
makes fifteen. [ 10 + 5 = 15 ]
The ten times the ten [ 10 x 10 ]
gives us a one-hundred block. [ 10 x 10 = 100 ]
This ten times the five [ 10 x 5 ] gives us
the ten, twenty, thirty, forty, fifty [ 10, 20, 30, 40, 50 ]
that fits in this space.
This ten times this three [ 10 x 3 ]
gives us the ten, twenty, thirty [ 10, 20, 30 ]
that fit into that space.
And this three times this five give us the fifteen [ 3 x 5 = 15 ]
that fit into the small rectangle at the bottom.
By drawing lines on the grid paper,
we can then show our separate regions.
We have this region which is ten times ten [ 10 x 10 ]
which equals one-hundred. [ 10 x 10 = 100 ]
This region is ten times five [ 10 x 5 ]
which equals fifty. [ 10 x 5 = 50 ]
This region is ten times three [ 10 x 3 ]
which equals thirty. [ 10 x 3 = 30 ]
This region is five times three [ 5 x 3 ]
[ 5 x 3 = 15 ] which equals fifteen.
If we add all those four regions together,
we have one-hundred, [ 100 ] one-hundred fifty, [ 150 ]
one-hundred eighty, [ 180 ] one-hundred ninety-five. [ 195 ]
For a product [ 195 ] of one-hundred ninety-five.