LARGE BEAD FRAME – MULTIPLIERS OF 2 OR MORE DIGITS

a. The Whole Product

Materials:
…corresponding long form
…red and black pencils

Presentation:
Write a multiplication problem on the form

 8457 x   34 Decompose the multiplicand in the same way as before.

On the right side decompose the multiplicand as before. First decompose the number for multiplication by 4 units.

 7 30 400 8000 x 4

We must also multiply the multiplicand by 30; decompose the number a second time below the first. We know that we cannot multiply by such a large number on the bead frame. The rule is that we must always multiply by units. 7 x 30 is the same as 70 x 3. ( 7 x 30 = 7 x 3 x 10 = (commutative property) 7 x 10 x 3 = 70 x 3 ) So we can write this decomposition in a different way. For our work we will use the first and third decompositions.
Note: By decomposing the multiplicand we have reduced the problem to a series of small calculations at the level of memorization.

Begin multiplying

 7 x 4 = 28 28 units move forward 8 units, 2 tens 3 x 4 = 12 12 tens. move forward 2 tens and 1 hundred 4 x 4 = 16 16 hundreds. move forward 6 hundreds and 1 thousand 8 x 4 = 32 32 thousands move forward 2 thousands and 3 ten thousands

Continue with the second decomposition in the same way.

Read the final product and record it.

Note : This multiplication can be shown on an adding machine in the same way, though as a repeated addition. Calculators operate on the same principle of moving the multiplicand to the left and adding zeros.

The child may go on to do multiplication with multipliers of 3 or more digits as well. With a three-digit multiplier there will be 5 decompositions of which only the 1st, 3rd, 5th will be used for the multiplication on the frame.

b. Partial Products

Age: 7-8 years, or when the child is adding abstractly

Presentation: The child by this time should have reached a level of abstraction with column addition.
The procedure is exactly like the first, except that the child will stop after each multiplier and record the partial product, clearing the frame he begins multiplying with the next multiplier. When the child records all of the partial products, he adds them to find the total product.

 4387 x 245 21935 175480 877400 1074815

Here we can observe that the first partial product which was the result of multiplying the units has its first digit under the units column. The first digit (other than zero) of the second partial (which was the result of multiplying by the tens) is under the tens column, etc.