The Wonder Number Lessons

  1. Basic Counting
  2. Comparison
  3. Addition – Single Digit
  4. Addition – Double Digit
  5. Subtraction – Single Digit
  6. Subtraction – Double Digit
  7. Patterning
  8. Multiples and Factors
  9. Multiplication
  10. Primes and Composites
  11. Squares
  12. Division – No Remainder
  13. Division – With Remainder
  14. Simplifying Fractions
  15. Least Common Denominator
  16. Goldbach’s Conjecture

Lesson No. 8:  Multiples and Factors

The Wonder Number Board gives students a concrete illustration of what multiples and factors actually represent by color-coding them and consistently listing them on the board for easy viewing.  This visual reference leads to quicker and more thorough understanding.

Start the lesson by defining multiples and factors and then show exactly what they are.  A factor is any of the numbers multiplied to form a product.  A multiple is a number that is a product of two factors being multiplied together (factor x factor = product).

First, focus on the multiples of 3.  On the top row of the Wonder Number Board you will see 3 is colored red.  Any number throughout the rest of the board that is a multiple of 3 will have a small red 3 in the upper middle portion of its block.  Show this by placing viewers on the blocks containing numbers 57, 42, and 39. Now, find their factor pairs (see fig 41).  Point out that 3 x 19 = 27, 3 x 14 = 42, and 3 x 13 = 39.

Now look at multiples of 5. On the top row of the Wonder Number Board you will see 5 is colored green. Any number throughout the rest of the board that is a multiple of 5 will have a small green 5 in the upper right corner of its block. Place viewers on the blocks containing numbers 55, 40 and 75 (see fig 42). Point out that 5 x 11 = 55, 5 x 8 = 40 and 5 x 15 = 75.

Now focus on multiples of 9. On the top row of the Wonder Number Board you will see 9 is colored pink. Any number throughout the rest of the board that is a multiple of 9 will have a small pink 9 in the lower right portion of the block. Place viewers on the blocks containing numbers 27, 54 and 90 (see fig 43). Point out that 9 x 3 = 27, 9 x 6 = 54 and 9 x 10 = 90.

Finally, you can ask the student to find three multiples of all the basic numbers from 2 to10.

The small number pairs found on the top and bottom of each block are the factors of that number.  Let’s look at a few numbers and all their factors by placing viewers on them.  The first number is 20 (see fig 44).  The factors of 20, listed by pairs are 1 and 20, 2 and 10, 4 and 5, 5 and 4, and 10 and 2.  Multiplying any of these factor pairs gives the answer of 20.

The next number to place a viewer on is 44 (see fig 45).  The factors of 44 are 1 and 44, 2 and 22, and 4 and 11.  Multiplying any of these factor pairs gives the answer of 44.  

The next number to place a viewer on is 32 (see fig 46).  The factors of 32 are 1 and 32, 2 and 16, 4 and 8, and 8 and 4.  Multiplying any of these factor pairs gives the answer of 32.

Now ask the student to choose several different numbers and list all of their factors.  After they become familiar with this concept, it is useful to have them recite the relevant multiplication facts for each factor pair.  For example, 1 x 32 = 32, 2 x 16 = 32, 4 x 8 = 32, and 8 x 4 = 32.


© 2007 The Wonder Number Learning System, Patent No. 3975051 Dated 1976