MULTIPLICATION Egyptian and Chinese and more
Pre requisite skills ■Can you double a number? ■Can you add? ■If you can do these things you can do Egyptian multiplication
Lets start with something easy. 21 x 5 ■You start by making a table
Lets start with something easy. 21 x 5 ■You start by making a table 215
Lets start with something easy. 21 x 5 ■You start by making a table
Lets start with something easy. 21 x 5 ■You start by making a table
Lets start with something easy. 21 x 5 ■You start by making a table
Lets start with something easy. 21 x 5 ■You start by making a table
Lets start with something easy. 21 x 5 ■You start by making a table
PAUSE ■How long do we need to make the table? ■The table needs to have all the powers of two that are smaller then the first number (in our case 21) ■This means we can stop at 16 because our next power of 2 is larger than 21.
So we have a table now what? ■Now we need to look at our table and decide how we can make our first number (21) by adding powers of two together
So we have a table now what? ■Now we need to look at our table and decide how we can make our first number (21) by adding powers of two together =
So we have a table now what? ■Once we have identified which powers of two we need all we have to do is add up the corresponding doubles = =
So we have a table now what? ■Once we have identified which powers of two we need all we have to do is add up the corresponding doubles = = 105
Lets practice representing numbers as sums of powers of 2. ■9 ■14 ■23 ■44
Lets do another problem 23 x 132 ■First make our table
Lets do another problem 23 x 132 ■First make our table
Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to
Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to =
Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to =
Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to 23 ■Third: Add corresponding doubles =
Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to 23 ■Third: Add corresponding doubles =
With your teams try these: ■25 x 31 ■38 x 45 ■12 x 63
Lets try another one 14 x 1962
Chinese Multiplication ■Chinese multiplication involves drawing pictures to help solve multiplication problems. ■We look at where line segments intersect and count those.
Chinese Multiplication ■Lets start with an easy problem 12 x 11 ■What is this going to look like?
Chinese Multiplication ■So how does this picture help us?
Chinese Multiplication ■We have to remember what the different lines represent
Chinese Multiplication ■We have to remember what the different lines represent The stuff in the red circle represents 1 x 2
Chinese Multiplication ■We have to remember what the different lines represent The stuff in the grey circles are 1x10 and 2x10
Chinese Multiplication ■We have to remember what the different lines represent The stuff in the green circle is 10 x 10
Chinese Multiplication ■We have to remember what the different lines represent So all together we have: 2 x 1 10 x 1 10 x 2 10 x 10
Chinese Multiplication ■We have to remember what the different lines represent So all together we have: 2 x 1 = 2 10 x 1 = x 2 = x 10 = 100
Now what? ■So all together we have: ■2 x 1 = 2 ■10 x 1 = 10 ■10 x 2 = 20 ■10 x 10 = 100 ■Now all we do is add. ■ ■132
Lets try another one ■Using the Chinese method multiply 23 x 111
And another one 121 x 121
Lattice Multiplication (coms from 10 th century India) ■First we need a problem: 43 x 92
Lattice Multiplication (coms from 10 th century India) ■First we need a problem: 43 x 92 ■Draw a rectangle and divide it up like so
Lattice Multiplication (coms from 10 th century India) ■First we need a problem: 43 x 92 ■Draw a rectangle and divide it up like so
Lattice Multiplication (coms from 10 th century India) ■First we need a problem: 43 x 92 ■Draw a rectangle and divide it up like so
Lattice Multiplication (coms from 10 th century India) ■Now we label the rectangle with our numbers
Lattice Multiplication (coms from 10 th century India) ■Then multiply all the mini problems
Lattice Method
And another one 7219 x 341
Which do you like best?
Which do you like best? Using your favorite method do the following ■173 x 59 ■341 x 27 ■1563 x 11