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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. 9:  Multiplication

The color-coded Wonder Number Board makes multiplication facts easy to master. Multiplication is an operation that simplifies addition so instead of writing 2 + 2 + 2 + 2, you write 4 x 2 = 8.  This lesson will show three different ways to reach the same answer to each multiplication problem in a very visual and manipulative manner.

The first problem is 4 x 3.  Begin by using red chips to make four separate sets of three anywhere on the board below the first three rows.  Count these chips and identify them as four sets of three equaling 12.  Then push them together to form a rectangular array that is 4 chips by 3 chips.  Count the chips again, the answer is 12. 

A second way to obtain this same answer is to place a red chip on the first four multiples of 3, which are 3, 6, 9, and 12.  Again the answer is 12 (see fig 47).  Next you can place a viewer on 12 and look inside the 12 block to confirm the answer.  There is a factor pair of 4 and 3 which when multiplied together equal 12 (see fig 48).  Complete the problem by writing and saying 4 x 3 = 12.

Like addition, multiplication also has commutative properties.  For instance, 4 x 3 is the same as 3 x 4, as shown in the next example.

The second problem is 3 x 4.  Begin by using red chips to make three separate sets of four anywhere on the board below the first three rows.  Count these chips and identify them as three sets of four equaling 12.  Then push them together to form a rectangular array that is three chips by four chips.  Count the chips again, the answer is 12.  Complete the problem by  writing and saying 3 x 4 = 12.

A second way to obtain this same answer is to place a red chip on the first three multiples of 4, which are 4, 8, and 12.  Again the answer is 12 (see fig 49).  Next you can place a viewer on 12 and look inside the block to confirm the answer.  Inside the 12 block there is a factor pair of 3 and 4 which when multiplied together equals 12 (see fig 48).

The third problem is 2 x 7.  Begin by using red chips to make two separate sets of seven anywhere on the board below the first three rows.  Count these chips and identify them as two sets of 7 equaling 14. Then push them together to form a rectangular array that is two chips by seven chips.  Count the chips again, the answer is 14.  Complete the problem by writing and saying 2 x 7 = 14.

A second way to obtain this same answer is to place a red chip on the first two multiples of 7, which are 7 and 14.  Again the answer is 14 (see fig 50).  Next you can place a viewer on 14 and look inside the block to confirm the answer.  Inside 14 there is a factor pair of 2 and 7 which when multiplied together equals 14 (see fig 51).  Complete the problem by writing and saying 2 x 7 = 14.

The fourth problem is 7 x 2.  Begin by using red chips to make seven separate sets of two anywhere on the board below the first three rows.  Count these chips and identify them as seven sets of two equaling 14.  Then push them together to form a rectangular array that is seven chips by two chips.  Count the chips again, the answer is 14. Complete the problem by writing and saying 7 x 2 = 14.

A second way to obtain this same answer is to place a red chip on the first seven multiples of 2, which are 2, 4, 6, 8, 10, 12, and 14.  Again the answer is 14 (see fig 52).  Place a viewer on 14, look inside the block to confirm the answer.  Inside the 14 block there is a factor pair of 7 and 2 which when multiplied together equals 14 (see fig 51).  Complete the problem by writing and saying 7 x 2 = 14.



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