Colored Bead Bars: Multiplication of a Sum

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.