Friday, July 18, 2008

Singapore Math Strategy Area Model to solve Multi-digit Multiplication

Another concept at the Singapore Math conference that I attended this past week was using what is called the Area model to solve multiplication problems.

You set the problem up as such: 3 x 77

Step one: Draw a box with two parts
[ ]
[__]
[ ]

Step two: write the single digit multiplier at the top of the box.
3
[ ]
[__]
[ ]

Step three: write out the second multiple breaking it out into place values down the side of the box
3
70 [ ]
[__]
7 [ ]

Step four: multiply
3
70 [210]
[___]
7 [ 21]

Step five add
3
70 [210]
[___]
7 [ 21]
______
231

Your answer is 231

Here is another example, but this time both of the multiples have a digit in the tens place

You set the problem up as such: 54 x 68

Step one: Draw a box with four parts
[ ][ ]
[__][__]
[ ][ ]

Step two: write the first multiple at the top of the box, breaking it out into place values.
50 4
[ ][ ]
[__][__]
[ ][ ]

Step three: write out the second multiple breaking it out into place values down the side of the box

50 4
60 [ ][ ]
[__][__]
8 [ ][ ]

Step four: multiply
50 4
60 [3000][240]
[____][___]
8 [ 400][ 32]

Step five add, on problems like this it is easier to use the Z method,
50 4 3000+240+400+32 = 3672
60 [3000][240]
[____][___]
8 [ 400][ 32]
_______________
Your answer is 3672
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