Multiplication: An Adventure in Number Sense

New! Natural Math� workshops in the Research Triangle Area, NC
March 7th "Multiplication adventure" report See pictures of fun activities, follow links to computer games and more!

Contents:

Why Would I Want to Play with This Stuff?

Introduction: Too Many Facts? The Facts You Do NOT Need to Memorize

Multiplication Applet (Java)

Coloring the Monster Table

Times Eleven and Arithmetic Progression

Twin Facts and Commutative Law

Times One for Free

Times Ten for Free

Times Nine Patterns

Times Nine "Tricks"

Times Five Pattern

Times Two

Off Diagonal

Summary of Patterns: No Need to Memorize...

More Patterns to Discover!

Printables and Reference:

Printable Grid

Facts You Do NOT Need to Memorize: The Hyperlinked Table

Printable Base 10 Multiplication Table (for coloring)

Printable Base 10 Multiplication Table (wallet size)

Base 16 Multiplication Table

The picture we use as a bullet is an ancient Egyptian symbol for number 1,000,000 (one million)

Why Would I Want to Read This Stuff?

The main reason why people read these materials is for fun. However, there are many "applied" uses for these pages:

• learn why you need to memorize only 13 multiplication facts (or less) in order to know the whole table
• learn a lot of useful tricks and patterns that will help in fast mental arithmetic and will develop your number sense
• follow suggested investigations to discover a lot of algebraic patterns (it is worth at least as much as taking the standard pre-algebra and algebra 1 courses)
• find getaways to advanced topics such as matrices or arithmetic progression

Each page in the unit consists of dialogs between a Student and a Mentor, as well as illustrations, summaries and suggestions for further explorations and activities. Users can skip dialogs if they wish, going directly for the summaries and activities.

Dialog Example

Student: There are too many multiplication facts to memorize.

Mentor: If you want to know the multiplication table from 1 to 10, you may want to memorize 13 facts, at most. There are very easy tricks that will let you get the rest of the facts as fast as if you remembered them.

Student: I think it is better when you are able to figure something out, rather than remembering it. It takes too much time to memorize things, and then I forget them so easily!

Mentor: Also, you learn a lot of useful stuff while you figure facts out.

Summary Example

To multiply a number by nine, multiply it by ten and subtract the number. 8*9 = 80 - 8 = 72

Suggestion Example

Find a multiplication fact you like. Try to find as many ways to express this fact as you can. Use graph paper, marbles, numbers, or anything else. How many ways have you found? Share them with somebody.

The more types of manipulatives students use, the more knowledge and enjoyment they can get from the unit. At the very least, students should have some kind of "counters" of several colors (e.g., marbles, poker chips, several kinds of beans), graph paper, and several pencils, markers or crayons. A page of graph paper can be printed out from here.

Pattern considered on these pages are only example. If people have a chance, they discover and develop their own unique patterns and personal relationships with numbers, facts and concepts. The more individual patterns each person can find, the better the person will feel about numbers and math ideas. Therefore, it may be more important for students to find their own patterns than to learn someone else's tricks and ideas.

Enjoy!