Month: January 2014

23 You Call That a Multiplication Table? THIS is a Multiplication Table

/ ivasallay / 4 Comments

A Discussion About the Multiplication Table:

Almost everyone is familiar with the traditional multiplication table:

Is this traditional way the best way for children to learn multiplication facts? Maybe not!

Beyondtraditionalmath published a post showing the Griddle’s creation of a different kind of multiplication table. This table can really help anyone visualize what multiplication means by relating any multiplication fact to its area. Every child learning to multiply should be exposed to this wonderful table. Even students who already know how to multiply would benefit from looking at it.

On the other hand, I hope it doesn’t completely replace the traditional multiplication table because that old, familiar table is the basis for my Find the Factor puzzles.

Factors of the Number 23:

  • 23 is a prime number.
  • Prime factorization: 23 is prime.
  • The exponent of prime number 23 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 23 has exactly 2 factors.
  • Factors of 23: 1, 23
  • Factor pairs: 23 = 1 x 23
  • 23 has no square factors that allow its square root to be simplified. √23 ≈ 4.79583

How do we know that 23 is a prime number? If 23 were not a prime number, then it would be divisible by at least one prime number less than or equal to √23 ≈ 4.8. Since 23 cannot be divided evenly by 2 or 3, we know that 23 is a prime number.

23 is never a clue in the FIND THE FACTORS puzzles.

More About the Number 23:

23 is the sum of three consecutive prime numbers:
5 + 7 + 11 = 23.

22 Factor Trees

/ ivasallay / Leave a comment

22 is a composite number. 22 = 1 x 22 or 2 x 11. Factors of 22: 1, 2, 11, 22. Prime factorization: 22 = 2 x 11.

When 22 is a clue in the FIND THE FACTORS 1 – 12 puzzles, use 2 and 11 as the factors.

‘Tis the season to use factor trees to find all the factors of a number. Here is a factor tree that shows all the prime factors of 560. Next to it is a factor tree for 324. Do you see all of their prime factors clearly?

560 green                           324 green

Because sometimes one can’t “see the factors for the trees,” I recommend circling the prime factors or doing something else to make them more distinct.  Here are the trees again with every prime factor clearly visible:

560 red                                    324 red

I make logic puzzles based on the multiplication table. The puzzles for today’s post could also be called factor trees because you have to factor the clues to find the solution, and the puzzles are shaped like evergreen trees in whole or in part. I’ve even included a tree hanging from the ceiling, of all places! It may seem like a modern novelty, but people have been hanging Christmas trees upside down in Eastern Europe for centuries. To solve the puzzles either cut and paste the puzzles into a document to print or click 12 Factors 2013-12-12.

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2013-12-12.5 2013-12-12.6

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