a. Multiplication By 10, 100, 1000

Materials:
…paper and pencil

Note: We are limited by the frame to having a multiplicand of only one digit when the multiplier is 1000 and vice versa.

Aims: to understand of the use of the small bead frame in performing multiplication
to reinforce the concepts of the relative positions of the hierarchies, and changing from one hierarchy to another

Presentation:
Write down the problem 2 x 10 =. Perform this on the frame by sliding forward groups of two beads, changing as necessary. Record the product 2 x 10 = 20. Repeat the process in the problem 20 x 10 =. Record the product 20 x 10 = 200. Try this problem
2 x 100 =. It would take all day and most of the night to bring forward 100 groups of two beads. Recall from the multiplication game-Multiplication by 10, 10, 1000 the simple way to do this. Slide forward the 2 beads to correspond to the multiplicand. We can multiply 1 x 100 and get 100-slide the one unit back, and slide one hundred forward. Repeat for the second unit. Record the product 2 x 100 = 200. We went from units to the hundreds. How many jumps did we have to take? 2 How many zero’s are in the product? 2 The two zero’s indicate that we have passed two hierarchies.
Do many other examples, i.e. 2 x 1000 = to be sure that the child is very comfortable and familiar with this process.

Note: We are limited by the frame to having a multiplicand of only one digit when the multiplier is 1000 and vice versa.

Aims: to understand of the use of the small bead frame in performing multiplication
to reinforce the concepts of the relative positions of the hierarchies, and changing from one hierarchy to another

b. Multiplication with a One-Digit Multiplier

Materials:
…small form

Note: Maria Montessori said, “When you go to the theater, you find that people are all sitting in different areas; some are in the balcony, some are in the boxes. Why? Each person has chosen a seat by buying a certain type of ticket. In the same way, these units must be in the top row of the bead frame. That is their fixed place.”

Age: 6-7 years

Aim: realization of the importance of the position of each digit

Presentation: To isolate the difficulty of decomposing the multiplicand, we begin with a static multiplication. From then on the child will work with dynamic problems.

 2321 x     3 Write the problem on the left side of the form.

The first thing we must do is to decompose the multiplicand. There are how many units? 1, we write 1 on the right side under units. All of this we must multiply by 3. On the bead frame, perform the multiplication. 1 x 3 = 3, move forward three units beads.
2 x 3=6, but 6 what? 6 tens! Move forward 6 ten beads, etc. (By this time the child should have memorized the combinations and should bring forward the product of the small multiplication) Read the product and record it on the left side of the form.

Try a dynamic multiplication

 2463 x     4 Decompose the multiplicand in the same way as before.

Perform the multiplication 3 x 4 = 12, 12 is 2 units and 1 ten…6 x 4 = 24, 24 what? 24 tens4 tens and 2 hundreds, etc.
Read the product on the frame and record it.

Experiment:
Try performing any one of these multiplications out of order, i.e. 6 x 4 = 24 tens,
2 x 4 = 8 thousands, 3 x 4 = 12 units and 4 x 4 = 16 hundreds. The product is still the same.