Colored Bead Bars: Multiplication of a Sum

Age
6-9.

Materials

 * Box of colored bead bars 1-10
 * Box of signs for the operation
 * Chart I
 * Pieces of white paper
 * Pen

Presentation
Binomial Presentation:


 * 1) The directress writes on a strip ( 5 + 2 ) x 3 =, which is read, take 5 plus 2, 3 times.
 * 2) The directress says; "This is a multiplication problem".
 * 3) The problem is prepared as before with bead bars for the addends, signs, parentheses and the multiplier, written on a little card.
 * 4) Remind the child that the operation inside the parentheses is done first.
 * 5) The child places the 7-bar for the sum under the parentheses, places signs, multiplier and the product, represented in bead bars.
 * 6) The work is recorded on his journal.
 * 7) On a different day: Directress says to the child; "When you find a problem of this kind, you can also multiply one term at a time by the multiplier".
 * 8) The other way will be put aside for now.
 * 9) The equation in beads and cards: 7 x 3 = 21 is placed off to the side, leaving the slip of paper and the original layout of beads.
 * 10) First take 5, 3 times, 5 x 3 is written on a strip and 3 bars of 5 are placed below the original 5 bar plus (put out the sign) 2 taken 3 times, 2 x 3 is also written on a strip and 3 bars of 2 are lain out.
 * 11) Now we must find these products.
 * 12) The products are placed below the group in a perpendicular position.
 * 13) Add 15 + 6 and put out the result.
 * 14) The result is the same as the equation we put aside.
 * 15) The child writes in his journal:

( 5 + 2 ) x 3 = ( 5 x 3 ) + ( 2 x 3 ) = 15 + 6 = 21

Trinomial Presentation:


 * 1) The directress writes a problem on a strip: ( 5 + 2 + 3 ) x 4 =.
 * 2) The child lays out the corresponding beads for 5, 2, and 3, the signs, parentheses and a little card for 4.
 * 3) As before we must multiply each term by the multiplier.
 * 4) Then, for control, the child may add the addends within parentheses and multiply the sum by 4.
 * 5) When his work is written in his journal it should be:

( 5 + 2 + 3 ) x 4 = (__+__+__) x 4 = beads ( 5 x 4 ) + ( 2 x 4 ) + ( 3 x 4) = beads 20 + 8 + 12 = 40 beads

Points Of Interest
After the child has learned to multiply such a problem term by term, he should not go back to the first way of adding first, then multiplying. In this way the following aims will be achieved.

Purpose
Direct Aim:


 * To help on the memorization of multiplication.
 * To help understanding of the distributive property of multiplication over addition.

Indirect Aim:


 * Preparation for the square of the polynomial.