Multiplication With the Checkerboard


…box of numeral cards 1-9, gray and white
…box of bead bars 1-9, 55 of each

Propose a problem: 4357 x 23 =

a. 1st level
Form the multiplicand by using the white cards placed on the appropriate numerals
on the bottom edge of the board. (7 is placed on 1, 5 is placed on 10, etc.) Form the multiplier using the gray cards placed on the appropriate numerals on the right edge of the board.
Begin multiplying with the units. First we take 7 three times. Place 3 seven bars on the unit square.
5 x 3place 3 five bars on the tens square
3 x 3place 3 three bars on the hundreds square
4 x 3place 3 four bars on the thousands square
Keep a finger on the digit of the multiplicand to remember your place. Notice that there are three of each quantity in this row. Why? because the multiplier is 3. Since we have finished multiplying by the units, we can turn over the gray card. Continue multiplying by the tens noting the value of each square (this emphasis is important): tens multiplied by units give tens, tens multiplied by tens gives hundreds, etc. Notice that 2 dominates the row. Turn over the card.
Move the bead bars of the upper row along the diagonal to the bottom row. Beginning with units make changes to total the product, carrying over as necessary, i.e. the bead bars in the ten square total 3131 tens. How do we express 31 tens in conventional language? Three hundred ten. So, place a unit bead in the ten square, and a 3 bar in the hundred square.
Read the total and record the product.

Aim: to understand the process of multiplication using the board.

b. 2nd level-Small Multiplication
Propose a problem: 4357 x 423 = and set up the board with the numeral cards.
Begin multiplying with the units, but this time only put out the bead bars for the product.
7 x 3 = 21 put a unit bead in the unit square, 2-bar in tens
5 x 3 = 15 5-bar in tens square, unit in hundreds
3 x 3 = 9 9-bar in the hundred square
4 x 3 = 12 2-bar in thousands, unit in ten thousands
Turn over the gray card. Continue with the tens. Move the bead bars along the diagonal in the end.
Make the necessary changes and read the final product.

c. 3rd level-Partial Products (this passage can be skipped)
Multiply in the same way as before (2nd level). After everything in the multiplicand has been multiplied by the units, make the necessary changes in that row and record the partial product,
Continue with the tens, etc. After all of the partial products have been recorded, move the bead bars along the diagonal to the bottom row.
Make the changes and read the total product.

d. 4th level-Mental Carrying Over
The procedure is different from the 3rd level only in that the child carries mentally. 7 x 3 = 21 put the unit bead down, remember 2…5 x 3 = 15plus 2 = 17. etc. The partial product is read without making any changes.

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