Multiplication: An Adventure in Number Sense

   

Times One for Free

Student: I am going to color another part that I do not have to memorize. But there are no more "twin facts"!

Mentor: Look at the table again and see if there are some yet uncolored facts that you get "for free," without any memorization:

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: Yeah! The first column! Any number times one is the same number! I will color it dark green.

Any number times one is the same number: a*1=a for any number a

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

Mentor: We had 55 facts before your turn to color. How many facts are left?

Student: I colored the whole column, and there are ten facts in each column. So only 45 facts are left. We are not done coloring, are we?

Mentor: Not at all! It's my turn to color.

What does it mean to multiply a number by 1? Why would people even want to do something like that? Try to find several possible reasons. Ask other people if they can suggest some reasons.  

   

     

© 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.