Math Mojo - Making Math Meaningful

These are some hints about how to make the table explained in the lesson on long division.

(Anything written in green is something that can be done with Math Mojo methods that you should learn to make it go even quicker and easier.

To make a table of the first 10 multiples of any number:

First - Make a list of the numbers from 1 - 10, then follow the steps below.

For example, let's make a table of the first ten multiples of 47.

(In each of the steps, the number in red is the answer to the step you are working on. The number(s) in purple are the ones you use to get that answer).

Step 1: use the original number
in order to get the original # times 1 (Duh!)

1
47
2
3
4
5
6
7
8
9
10

Step 2: double the original # (using left-to-right multiplication by 2)
in order to get the original # times 2

1
47
2
94
3
4
5
6
7
8
9
10

Step 3: Double what you got in the previous step (using left-to-right multiplication by 2)
in order to get the original # times 4

1
47
2
94
3
4
188
5
6
7
8
9
10

Step 4: Double what you got in the previous step (using left-to-right multiplication by 2)
in order to get the original # times 8

1
47
2
94
3
4
188
5
6
7
8
376
9
10

Step 5: add the multiples of 1 and 2 together (from left-to-right)
in order to get the original # times 3

1
47
2
94
3
141
4
188
5
6
7
8
376
9
10

Step 6:Double what you got in the previous step (using left-to-right multiplication)
in order to get the original # times 6

1
47
2
94
3
141
4
188
5
6
282
7
8
376
9
10

Step 7: add the original number to to what you got in the previous step (from left-to-right)
in order to get the original # times 7

1
47
2
94
3
141
4
188
5
6
282
7
329
8
376
9
10

Step 8: add original number to the multiple of 8 (from left-to-right)
in order to get the original # times 9

1
47
2
94
3
141
4
188
5
6
282
7
329
8
376
9
423
10

Step 9: add a zero to the end of the original #
in order to get the original # times 10

1
47
2
94
3
141
4
188
5
6
282
7
329
8
376
9
423
10
470

Step 10: Divide what you got in the previous step by 2 (using short division)
in order to get the original # times 5

1
47
2
94
3
141
4
188
5
235
6
282
7
329
8
376
9
423
10
470

You're done!

You deserve a break. Click here for a very weird mathematical anagram.

Below is a table of all the steps in a nutshell. (Do the steps in the order listed in the far-left column). Check the table out, but don't commit it to memory. Learn it by using them to do lots of division examples.

A good exercise, is any time you have a free few minutes, take a long random number (5 or more digits) and make a table of the first ten multiples of them. It is a great execise in manipulating numbers, and simple addition, multiplication by 2 and division by 2. Those skills are the rock-bottom basis of arithmetic, and you can never practice them enough.

To get a list of random numbers, open any phone book.

Step #:
In order to get:
Here's what what you do:
1
the original # times 1
 use the original number
2
the original # times 2
 double the original # (using left-to-right multiplication by 2)
5
the original # times 3
 add the multiples of 1 and 2 (which you got in steps 1 and 2) together (from left to right)
3
the original # times 4
 Double what you got in the previous step (step 2) (using left-to-right multiplication by 2)
10
the original # times 5
 Divide what you got in the previous step (step 99 by 2 (using short division)
6
the original # times 6
 Double what you got in the previous step (step 5) (using left-to-right multiplication)
7
the original # times 7
 add the original number to to what you got in the previous step (step 6) (from left-to-right)
4
the original # times 8
 Double what you got in the previous step (step 3) (using left-to-right multiplication by 2)
8
the original # times 9
 add original number to the multiple of 8 (which you got in step 4) (from left-to-right)
9
the original # times 10
 add a zero to the end of the original #

Of course, improvement and thought never end. There are many more hints besides this. This is just one more step along the way to gaining great numeracy (number sense) skills.

The next step in Math Mojo is to check each of the above steps to make sure you make no mistakes along the way. There is a simple way to do this, although, like most of Math Mojo, it takes effort to explain than it does to learn. And once you learn it and practice it a bit, it takes almost no effort to use.

This method of checking will be in a forthcoming booklet. The booklet will cover an amazing way to check all your arithmetic (addition, subtraction, multiplication, division and exponents) using one simple system (and it is NOT using the reverse of the operation you originally used!) It has nothing to do with the way you learned in school, and it is quicker than using a calculator, It is the best thing I could possibly teach you for use on standardized math tests (although that should never be the main incentive).

I hope to have the booklet available by the spring of 2003. If you really are curious, or you need it for upcoming tests, you can send me an e-mail to hurry me along.

Hint: Speed-multiplication by 2 from left to right, and speed-division by 2 from left to right (which is also know as short division by 2) are essential skills to anyone who is beyond the kindergarten stages of manipulating numbers. If you need to learn how to do them, e-mail me requesting that I get lessons on them up right away.

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