Colored Bead Bars: Multiplication of a Sum
- Box of colored bead bars 1-10
- Box of signs for the operation
- Chart I
- Pieces of white paper
- The directress writes on a strip ( 5 + 2 ) x 3 =, which is read, take 5 plus 2, 3 times.
- The directress says; "This is a multiplication problem".
- The problem is prepared as before with bead bars for the addends, signs, parentheses and the multiplier, written on a little card.
- Remind the child that the operation inside the parentheses is done first.
- The child places the 7-bar for the sum under the parentheses, places signs, multiplier and the product, represented in bead bars.
- The work is recorded on his journal.
- 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".
- The other way will be put aside for now.
- 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.
- 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.
- Now we must find these products.
- The products are placed below the group in a perpendicular position.
- Add 15 + 6 and put out the result.
- The result is the same as the equation we put aside.
- The child writes in his journal:
( 5 + 2 ) x 3 =
( 5 x 3 ) + ( 2 x 3 ) =
15 + 6 = 21
- The directress writes a problem on a strip: ( 5 + 2 + 3 ) x 4 =.
- The child lays out the corresponding beads for 5, 2, and 3, the signs, parentheses and a little card for 4.
- As before we must multiply each term by the multiplier.
- Then, for control, the child may add the addends within parentheses and multiply the sum by 4.
- 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
Control Of Error
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.
- To help on the memorization of multiplication.
- To help understanding of the distributive property of multiplication over addition.
- Preparation for the square of the polynomial.