Multiplication: An Adventure in Number Sense
Times Two
Student: I am going to color the facts about multiplication by two:
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
1 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
2 |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
3 |
3 |
6 |
9 |
12 |
15 |
18 |
21 |
24 |
27 |
30 |
4 |
4 |
8 |
12 |
16 |
20 |
24 | 28 |
32 |
36 |
40 |
5 |
5 |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
6 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
7 |
7 |
14 |
21 |
28 |
35 |
42 |
49 |
56 |
63 |
70 |
8 |
8 |
16 |
24 |
32 |
40 |
48 |
56 |
64 |
72 |
80 |
9 |
9 |
18 |
27 |
36 |
45 |
54 |
63 |
72 |
81 |
90 |
10 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
100 |
Student: When you multiply a number by two, you just add the number to itself. It is so easy to do, I do not have to memorize the answers, so I can color another part in the big table:
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
1 |
1*1=1 |
1*2=2 |
1*3=3 |
1*4=4 |
1*5=5 |
1*6=6 |
1*7=7 |
1*8=8 |
1*9=9 |
1*10=10 |
2 |
2*1=2 |
2*2=4 |
2*3=6 |
2*4=8 |
2*5=10 |
2*6=12 |
2*7=14 |
2*8=16 |
2*9=18 |
2*10=20 |
3 |
3*1=3 |
3*2=6 |
3*3=9 |
3*4=12 |
3*5=15 |
3*6=18 |
3*7=21 |
3*8=24 |
3*9=27 |
3*10=30 |
4 |
4*1=4 |
4*2=8 |
4*3=12 |
4*4=16 |
4*5=20 |
4*6=24 |
4*7=28 |
4*8=32 |
4*9=36 |
4*10=40 |
5 |
5*1=5 |
5*2=10 |
5*3=15 |
5*4=20 |
5*5=25 |
5*6=30 |
5*7=35 |
5*8=40 |
5*9=45 |
5*10=50 |
6 |
6*1=6 |
6*2=12 |
6*3=18 |
6*4=24 |
6*5=30 |
6*6=36 |
6*7=42 |
6*8=48 |
6*9=54 |
6*10=60 |
7 |
7*1=7 |
7*2=14 |
7*3=21 |
7*4=28 |
7*5=35 |
7*6=42 |
7*7=49 |
7*8=56 |
7*9=63 |
7*10=70 |
8 |
8*1=8 |
8*2=16 |
8*3=24 |
8*4=32 |
8*5=40 |
8*6=48 |
8*7=56 |
8*8=64 |
8*9=72 |
8*10=80 |
9 |
9*1=9 |
9*2=18 |
9*3=27 |
9*4=36 |
9*5=45 |
9*6=54 |
9*7=63 |
9*8=72 |
9*9=81 |
9*10=90 |
10 |
10*1=10 |
10*2=20 |
10*3=30 |
10*4=40 |
10*5=50 |
10*6=60 |
10*7=70 |
10*8=80 |
10*9=90 |
10*10=100 |
Student: Before I colored multiplication by two, there were 21 uncolored facts left. Now there are only 21-6=15 facts left that I may need to memorize.
 |
There are two numbers for which the following is true. You can multiply the number by itself or add the number to itself, and get the same exact result. What are these numbers? Why does it work for them? Why are there no more numbers of that sort? |
| © Copyright 1998 by Maria Droujkova and Dmitri Droujkov. All rights reserved. No part of these materials should ever be used in any situation that involves compulsory teaching. See also copyright notes and student rights. |