# Large Bead Frame: Multipliers of 2 or more digits

## Contents

7-8.

### Materials

• Corresponding long form
• Red and black pencils

### Presentation

The Whole Product:

1. Directress writes a multiplication problem on the form
2. 8457
x 34
3. Decompose the multiplicand in the same way as before.
4. On the right side decompose the multiplicand as before.
5. First decompose the number for multiplication by 4 units: 7  30  400  8000
6. We must also multiply the multiplicand by 30;
7. Decompose the number a second time below the first.
8. We know that we cannot multiply by such a large number on the bead frame.
9. The rule is that we must always multiply by units. <span id="fck_dom_range_temp_1246337190515_219" />
10. 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 )
11. So we can write this decomposition in a different way.
12. For our work we will use the first and third decompositions. By decomposing the multiplicand we have reduced the problem to a series of small calculations at the level of memorization.
13. Begin multiplying.
14. 7 x 4 = 28 28 units move forward 8 units, 2 tens
15. 3 x 4 = 12 12 tens. move forward 2 tens and 1 hundred
16. 4 x 4 = 16 16 hundreds. move forward 6 hundreds and 1 thousand
17. 8 x 4 = 32 32 thousands move forward 2 thousands and 3 ten thousands
18. Continue with the second decomposition in the same way.
19. Read the final product and record it.

Partial Products:</u

1. The child by this time should have reached a level of abstraction with column addition.
2. 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.
3. When the child records all of the partial products, he adds them to find the total product.
4. 4387
<u>x 245

21935
175480
877400
1074815

### Points Of Interest

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.

### Variation

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.