Tic-Tac-Toe Multiplication
A person who knows this method can put the entire system on paper in two minutes. Then, the multiplication
tables can be used during any classwork or test.
Step 1: Draw six tic-tac-toe boards.
Step 2: In the upper left-hand corner of each tic-tac-toe board, write the following numbers: 3, 7, 9, 4, 6, 8. 2’s or
5’s are not included since most students do know these facts.
Put the odd numbers in the top tic-tac-toe boards and the even numbers in the bottom tic-tac-toe boards.
3
Odd Numbers
7
9
4
Even Numbers
6
8
Step 3: Double the number in the upper left-hand corner, and put the “double” on the center spot in the left
column.
3
6
7
14
9
18
4
8
6
12
8
16
Step 4: Add the two numbers in the left-hand column and put the sum in the bottom spot in that column.
3
6
9
7
14
21
9
18
27
4
8
12
6
12
18
8
16
24
Step 5: You are now going to add to ten. Remember that when you are adding to ten, you only look at the
number in the ones’ place.
We will begin with the first tic-tac-toe board and start with the diagonals.
Look at the number in the upper left-hand corner, which is a “3.” You need “7” to add up to “10.” You write a
“7” in the lower right-hand corner (the box diagonal to the first box).
Now look at the number in the lower left-hand corner, which is a “9.” You need “1” to add up to “10.” You write
a “1” in the upper right-hand corner (the box diagonal to the left, bottom box).
Then look at the middle box in the left-hand column, which in the first tic-tac-toe is a ”6.” To add up to “10,” you
need a “4,” which goes in the right middle box (the box across from the “6”).
In the second board, the left-hand middle box is “14,” so looking at just the “4,” you need “6” to add up to “10,”
so you write “6” in the right middle box.)
You fill in the right column in the rest of the boards the same way.
3
6
9
1
4
7
7
14
21
9
6
3
9
18
27
3
2
1
4
8
12
8
2
6
6
12
18
2
8
4
8
16
24
6
4
2
Step 6:
If the number in the upper left-hand corner is odd, put a five in the center of the board.
If the number in the upper left-hand corner is even, put a zero in the center.
3
6
9
4
8
12
5
1
4
7
7
14
21
0
8
2
6
6
12
18
5
9
6
3
9
18
27
0
2
8
4
8
16
24
5
3
2
1
0
6
4
2
Step 7: Now, we start looking for patterns.
We are just going to do the odd numbers at the beginning.
For the first tic-tac-toe board, “3”, the pattern goes  (right to left), for the “7” board, it goes  (left to right) and
for the “9” board, it goes ↑ (bottom to top).
Can you see the 4, 5, 6 in the “3” board, reading from right to left in the middle row?
You need to finish the pattern by counting 1, 2, 3 and 4, 5, 6 and 7, 8, 9 (right to left in each row).
(The pattern numbers we added are highlighted so you can see them more easily.)
Now complete the other tic-tac-toe boards in a similar way, counting 1, 2, 3 and 4, 5, 6 and 7, 8, 9 in the direction
of the pattern for those boards.
Ignore the tens’ place and just look at the ones’ place when you look for the 1, 2, 3 and 4, 5, 6 and 7, 8, 9 patterns.
3
2 1
6
5 4
9
8 7
Right to Left
Pattern 
4
8
12
0
8
2
6
7
8 9
14 5 6
21 2 3
Left to Right
Pattern 
6
12
18
0
2
8
4
9
6 3
18 5 2
27 4 1
Bottom to Top
Pattern ↑
8
16
24
0
6
4
2
Step 8:
Now, go down each of the columns and “count.” For the “3” board, you start counting 3, 6, 9,….
Going down the next column, the next number is “2,” so we need to insert a “1” before it to make it “12,” so that
the numbers are increasing.
Then, we insert a “1” to make 15 and another “1” to make 18.
Going down the next column, the next number on the “3” board is “1.” When counting, the next number with a
“1” following ”18” would be “21,” so we insert a “2” in front of the “1.” We don’t “skip” count. We actually ask,
“When you are counting and have said “18,” when would you next see a “1”?
Continue this process for the sevens and nines boards.
3
6
9
12 21
15 24
18 27
4
8
12
0
8
2
6
7
14
21
28
35
42
49
56
63
9
18
27
36
45
54
63
72
81
6
12
18
0
2
8
4
8
16
24
0
6
4
2
Step 9: Now, we will do the even numbers. Their pattern is different from that of the odd numbers. Again, we
are just going to look at the ones’ place and ignore the tens’ place.
Ignoring the middle box and looking at the 8 outer boxes, you will notice that there are duplicates of two of the
numbers. So we need to complete this pattern and have duplicates of the remaining two numbers.



For the “4” board, the pattern is two 8’s, two 2’s, so we need to insert another 6 and another 4.
For the “6” board, the pattern is two 8’s, two 2’s, so we need to insert another 4 and another 6.
For the “8” board, the pattern is two 4’s, two 6’s, so we need to insert another 2 and another 8.
There are two empty spaces to fill. We don’t want identical numbers next to each other, so we need to insert the
missing numbers into the empty space in the row different from the row the number is in.



For the “4” board, the “6” should go in the empty space in the top row and the “4” in the bottom row.
For the “6” board, the “4” should go in the empty space in the top row and the “6” in the bottom row.
For the “8” board, the “2” should to in the empty space in the top row and the “8” in the bottom row.
3
6
9
12 21
15 24
18 27
4
8
12
6
0
4
8
2
6
7
14
21
28
35
42
49
56
63
9
18
27
36
45
54
63
72
81
6
12
18
4
0
2
8
4
8
16
24
2
0
8
6
4
2
6
Step 10: You finish the even tic-tac-toe boards the same way you finished the boards of the odd numbers. Go
down each of the columns and count to find what number comes next.
3’s table
3
6
9
12 21
15 24
18 27
7’s table
7
14
21
4’s table
4
8
12
16 28
20 32
24 36
28
35
42
49
56
63
6’s table
6
12
18
24
30
36
42
48
54
9’s table
9
18
27
36
45
54
63
72
81
8’s table
8
16
24
32
40
48
56
64
72
Now you have your multiplication tables for 3, 4, 6, 7, 8, and 9. You can use this method to reproduce them
quickly whenever you need them.