Difference between revisions of "Checkerboard: Multiplication"
From wikisori
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=== Age === | === Age === | ||
| − | 6-9 | + | 6-9 |
=== Materials === | === Materials === | ||
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=== Preparation === | === Preparation === | ||
| − | Propose a problem: 4357 x 23 =<br> | + | Propose a problem: 4357 x 23 =<br> |
=== Presentation === | === Presentation === | ||
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#Form the multiplicand by using the white cards placed on the appropriate numerals on the bottom edge of the board. (7 is placed on 1, 5 is placed on 10, etc.) | #Form the multiplicand by using the white cards placed on the appropriate numerals on the bottom edge of the board. (7 is placed on 1, 5 is placed on 10, etc.) | ||
| − | #Form the multiplier using the gray cards placed on the appropriate numerals on the right edge of the board. | + | #Form the multiplier using the gray cards placed on the appropriate numerals on the right edge of the board. |
#Begin multiplying with the units. | #Begin multiplying with the units. | ||
| − | #First we take 7 three times. | + | #First we take 7 three times. |
| − | #Place 3 seven bars on the unit square. | + | #Place 3 seven bars on the unit square. |
| − | #5 x 3place 3 five bars on the tens square. | + | #5 x 3place 3 five bars on the tens square. |
| − | #3 x 3place 3 three bars on the hundreds square. | + | #3 x 3place 3 three bars on the hundreds square. |
| − | #4 x 3place 3 four bars on the thousands square. | + | #4 x 3place 3 four bars on the thousands square. |
| − | #Keep a finger on the digit of the multiplicand to remember your place. | + | #Keep a finger on the digit of the multiplicand to remember your place. |
#Notice that there are three of each quantity in this row. Why? because the multiplier is 3. | #Notice that there are three of each quantity in this row. Why? because the multiplier is 3. | ||
#Since we have finished multiplying by the units, we can turn over the gray card. | #Since we have finished multiplying by the units, we can turn over the gray card. | ||
#Continue multiplying by the tens noting the value of each square (this emphasis is important): tens multiplied by units give tens, tens multiplied by tens gives hundreds, etc. | #Continue multiplying by the tens noting the value of each square (this emphasis is important): tens multiplied by units give tens, tens multiplied by tens gives hundreds, etc. | ||
| − | #Notice that 2 dominates the row. Turn over the card. | + | #Notice that 2 dominates the row. Turn over the card. |
| − | # Move the bead bars of the upper row along the diagonal to the bottom row. | + | # Move the bead bars of the upper row along the diagonal to the bottom row. |
#Beginning with units make changes to total the product, carrying over as necessary, i.e. the bead bars in the ten square total 3131 tens. | #Beginning with units make changes to total the product, carrying over as necessary, i.e. the bead bars in the ten square total 3131 tens. | ||
| − | #How do we express 31 tens in conventional language? Three hundred ten. So, place a unit bead in the ten square, and a 3 bar in the hundred square. | + | #How do we express 31 tens in conventional language? Three hundred ten. So, place a unit bead in the ten square, and a 3 bar in the hundred square. |
#Read the total and record the product. | #Read the total and record the product. | ||
| − | '''2nd level-Small Multiplication''' | + | '''2nd level-Small Multiplication''' |
| − | #Set up the board with the numeral cards using the proposed problem. | + | #Set up the board with the numeral cards using the proposed problem. |
| − | #Begin multiplying with the units, but this time only put out the bead bars for the product. | + | #Begin multiplying with the units, but this time only put out the bead bars for the product. |
| − | #7 x 3 = 21 put a unit bead in the unit square, 2-bar in tens. | + | #7 x 3 = 21 put a unit bead in the unit square, 2-bar in tens. |
| − | #5 x 3 = 15 5-bar in tens square, unit in hundreds. | + | #5 x 3 = 15 5-bar in tens square, unit in hundreds. |
| − | #3 x 3 = 9 9-bar in the hundred square. | + | #3 x 3 = 9 9-bar in the hundred square. |
| − | #4 x 3 = 12 2-bar in thousands, unit in ten thousands. | + | #4 x 3 = 12 2-bar in thousands, unit in ten thousands. |
#Turn over the gray card. Continue with the tens. | #Turn over the gray card. Continue with the tens. | ||
| − | #Move the bead bars along the diagonal in the end. | + | #Move the bead bars along the diagonal in the end. |
#Make the necessary changes and read the final product. | #Make the necessary changes and read the final product. | ||
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#Multiply in the same way as before (2nd level). | #Multiply in the same way as before (2nd level). | ||
| − | #After everything in the multiplicand has been multiplied by the units, make the necessary changes in that row and record the partial product. | + | #After everything in the multiplicand has been multiplied by the units, make the necessary changes in that row and record the partial product. |
#Continue with the tens, etc. | #Continue with the tens, etc. | ||
| − | #After all of the partial products have been recorded, move the bead bars along the diagonal to the bottom row. | + | #After all of the partial products have been recorded, move the bead bars along the diagonal to the bottom row. |
#Make the changes and read the total product. | #Make the changes and read the total product. | ||
| − | '''4th level-Mental Carrying Over''' | + | '''4th level-Mental Carrying Over''' |
#The procedure is different from the 3rd level only in that the child carries mentally. | #The procedure is different from the 3rd level only in that the child carries mentally. | ||
| Line 63: | Line 67: | ||
=== Control Of Error === | === Control Of Error === | ||
| − | <br> | + | <br> |
=== Points Of Interest === | === Points Of Interest === | ||
| − | <br> | + | <br> |
=== Purpose === | === Purpose === | ||
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*To help the child understand the process of multiplication using the board.<br> | *To help the child understand the process of multiplication using the board.<br> | ||
| − | === Variation<br> === | + | === Variation<br> === |
=== Links === | === Links === | ||
| − | <br> | + | <br> |
=== Handouts/Attachments === | === Handouts/Attachments === | ||
| − | <br> | + | <br> |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 19:55, 29 June 2009
<videoflash>XqlD6P3ogJc</videoflash>
Contents
Age
6-9
Materials
- Checkerboard
- Box of numeral cards 1-9, gray and whit
- Box of bead bars 1-9, 55 of each
Preparation
Propose a problem: 4357 x 23 =
Presentation
1st level
- Form the multiplicand by using the white cards placed on the appropriate numerals on the bottom edge of the board. (7 is placed on 1, 5 is placed on 10, etc.)
- Form the multiplier using the gray cards placed on the appropriate numerals on the right edge of the board.
- Begin multiplying with the units.
- First we take 7 three times.
- Place 3 seven bars on the unit square.
- 5 x 3place 3 five bars on the tens square.
- 3 x 3place 3 three bars on the hundreds square.
- 4 x 3place 3 four bars on the thousands square.
- Keep a finger on the digit of the multiplicand to remember your place.
- Notice that there are three of each quantity in this row. Why? because the multiplier is 3.
- Since we have finished multiplying by the units, we can turn over the gray card.
- Continue multiplying by the tens noting the value of each square (this emphasis is important): tens multiplied by units give tens, tens multiplied by tens gives hundreds, etc.
- Notice that 2 dominates the row. Turn over the card.
- Move the bead bars of the upper row along the diagonal to the bottom row.
- Beginning with units make changes to total the product, carrying over as necessary, i.e. the bead bars in the ten square total 3131 tens.
- How do we express 31 tens in conventional language? Three hundred ten. So, place a unit bead in the ten square, and a 3 bar in the hundred square.
- Read the total and record the product.
2nd level-Small Multiplication
- Set up the board with the numeral cards using the proposed problem.
- Begin multiplying with the units, but this time only put out the bead bars for the product.
- 7 x 3 = 21 put a unit bead in the unit square, 2-bar in tens.
- 5 x 3 = 15 5-bar in tens square, unit in hundreds.
- 3 x 3 = 9 9-bar in the hundred square.
- 4 x 3 = 12 2-bar in thousands, unit in ten thousands.
- Turn over the gray card. Continue with the tens.
- Move the bead bars along the diagonal in the end.
- Make the necessary changes and read the final product.
3rd level-Partial Products
- Multiply in the same way as before (2nd level).
- After everything in the multiplicand has been multiplied by the units, make the necessary changes in that row and record the partial product.
- Continue with the tens, etc.
- After all of the partial products have been recorded, move the bead bars along the diagonal to the bottom row.
- Make the changes and read the total product.
4th level-Mental Carrying Over
- The procedure is different from the 3rd level only in that the child carries mentally.
- 7 x 3 = 21 put the unit bead down, remember 2...5 x 3 = 15plus 2 = 17. etc.
- The partial product is read without making any changes.
Control Of Error
Points Of Interest
Purpose
- To help the child understand the process of multiplication using the board.
Variation
Links
Handouts/Attachments
