Direct Aim:
memorization of the multiplication tables
to bring the child to awareness of the functions of the multiplier and the multiplicand

Indirect Aims:
to understand that a number when multiplied by ten results in the same number of tens and zero units
to realize that a number multiplied by itself results in a square to give the concept of forming surfaces, starting with a line, progressing to rectangles

Materials:
…box containing colored bead bars 1-10, 55 of each
…Chart I (for control)

Presentation:
We are going to represent the table of a certain number with bead bars. The child is invited to choose a number, i.e., 8. We start with 8 taken one time. One 8 bar is lain horizontally 8 x 1 = ?8. The product is also represented by an 8 bar (lain vertically below the first) The child writes 8 x 1 = 8.
Now take 8 two times. The two 8 bars are lain horizontally 8 x 2 = ?16. A ten bar and a six bar to represent the product are lain vertically, thus making a double row, The child writes the equation in his notebook. This continues until 8 x 10 = 80. Observe the geometric figures which have been formed with the 8 bars: 8×1 is a line; 8×2 is a rectangle; and so on; 8×8 represents a square, etc.

NOTE: Notice the rectangles that come before the square have a base longer than the height. The rectangles that come after the square have a base which is shorter than the height. 8×8 produced a square, which is when the number was multiplied by itself.

Afterward the child does the other tables.

Direct Aims:
memorization of multiplication
independent realization of the fact stated previously: n x 10 = n0

Materials:
…same box of colored bead bars 1-10
…Chart I
…small white strips of paper
…black pen

Presentation:
The child is invited to take 10 bars of any color he wants. Lay them in a column, skip counting as you go. When he is finished and has found the total, lay out the corresponding number of 10 bars vertically in a row beneath the column (note the resulting rectangles should be congruent)
The number we took was 4 (place a label for 4 beneath the row of beads), 10 times. The result was 40. How do we write 40? The 4 will now indicate tens, and we put a zero for the units. (place a 0 label next to the 4 to make 40)
Repeat this with other numbers until the child realizes by himself that when you multiply a number by 10, the product will be the multiplicand with a zero tacked on in the units place.