MULTIPLICATION BY 10, 100, 1000
(Note: This activity is a prerequisite for the small bead frame)
…decimal system materials
…black and red pencils
Direct Aim: ease of multiplying by powers of ten, and understanding of the characteristic patterns of such multiplication.
Indirect Aim: preparation for multiplication using the bead frames
The teacher isolates a 10-bar. How many units are there in 10? 10. The teacher isolates a hundred square. How many tens are there in 100? How many units? Isolate the cube. How many hundreds are there in 1000? How many units? tens?
We can say that 10 tens is the same as 100, 100 tens is the same as 1000 and so on. With the child draw relative conclusions of all the changes possible.
Aim: to be sure that the child has understood the concept of change
Write down a multiplication problem and ask the child to lay out the problem, using the golden bead material i.e. ( 21 x 10 =). The child, knowing the function of multiplication, combines these quantities and makes the necessary changes. With the answer – two hundreds, one ten, and the zero is written in red. 21×10 = 210 Observe that the product is simply 21 (the multiplicand) with a zero after it.
Do many examples of this type, including: 30 x 10 = 300
By one hundred
Write down a multiplication problem such as 23 x 100 = and ask the child to lay out the material.. We can’t put out 23 one hundred times, we would run out of beads! We can multiply each unit by 100. Isolate one bead from the 23.
1 x 100 = 100 Substitute the bead for a hundred square. Repeat for the other two units. Then 10 x 100 = 1000. Replace each ten bar with a thousand cube, and so on. Record the product. 23 x 100 = 2300. Notice that the product has the same number of zeros as the multiplier.
By one thousand
Write the problem 4 x 1000 =. As before, multiply each unit by 1000, replacing each bead with a thousand cube. Record the product 4 x 1000 = 4000. In this case we jumped from the units, past the tens, past the hundreds, to the thousands. For each hierarchy that we increased, one zero was added. Observe as before that the number of zeros in the product is the same as the number of zeros in the multiplier. The product is simply the number of zeros in the multiplier.