Difference between revisions of "Colored Bead Bars: Multiplication of a Sum"
From wikisori
(New page: === Age === <br> === Materials === <br> === Preparation === <br> === Presentation === <br> === Control Of Error === <br> === Points Of Interest === <br> === Purpose...) |
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Line 1: | Line 1: | ||
=== Age === | === Age === | ||
− | <br> | + | 6-9.<br> |
=== Materials === | === Materials === | ||
− | <br> | + | *Box of colored bead bars 1-10 |
+ | *Box of signs for the operation | ||
+ | *Chart I | ||
+ | *Pieces of white paper | ||
+ | *Pen<br> | ||
=== Preparation === | === Preparation === | ||
− | <br> | + | <br> |
=== Presentation === | === Presentation === | ||
− | <br> | + | '''Binomial Presentation:''' |
+ | |||
+ | #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 =<br>( 5 x 3 ) + ( 2 x 3 ) =<br>15 + 6 = 21 | ||
+ | |||
+ | <br>'''Trinomial Presentation:''' | ||
+ | |||
+ | #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<br>( 5 x 4 ) + ( 2 x 4 ) + ( 3 x 4) = beads<br>20 + 8 + 12 = 40 beads<br> | ||
=== Control Of Error === | === Control Of Error === | ||
− | <br> | + | <br> |
=== Points Of Interest === | === Points Of Interest === | ||
− | <br> | + | 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.<br> |
=== Purpose === | === Purpose === | ||
− | <br> | + | '''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.<br> | ||
=== Variation === | === Variation === | ||
− | <br> | + | <br> |
=== Links === | === Links === | ||
− | <br> | + | <br> |
=== Handouts/Attachments === | === Handouts/Attachments === | ||
− | <br> | + | <br> |
[[Category:Mathematics]] | [[Category:Mathematics]] |
Revision as of 04:49, 1 July 2009
Contents
Age
6-9.
Materials
- Box of colored bead bars 1-10
- Box of signs for the operation
- Chart I
- Pieces of white paper
- Pen
Preparation
Presentation
Binomial Presentation:
- 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
Trinomial Presentation:
- 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.
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.
Variation
Links
Handouts/Attachments