The Division Boards

Material

  • 4 Boards; two with a green strip to represent units and thousands, one with a blue strip to represent tens, one with a red strip to represent hundreds. 
  • Green, Blue and Red beads.
  • Green, Blue and Red skittles.

Presentations

Start with the Unit Board: The child is first shown how to do division sums using the categories on the Unit Board. Only have the one unit board and leave the other boards in their home location.

  1. Take the sum 4,933÷ 4.  The divisor should be in the unit category hence no larger than 9. The number of digits in the divisor defines the number of boards used. And since 4 is only one digit, the unit digit, this is the reason why we will use just the unit board.
  2. Put the corresponding beads onto lids. They are colored green, red, blue and green, according to the category.
  3. Put out 4 green skittles at the top of the board starting on the left. 
  4. Starting with the thousands, divide out the beads.  Start on row 1, place a bead under the first skittle, then the second under the second, third under the third, and fourth under the fourth.  Make a mental note of this or put the share of one skittle aside. In this case, there is just the one row of beads under the skittles.
  5. Clear the board and put away those “thousands” beads.
  6. Next, set out the hundreds.  Again, there are four green skittles since that is the divisor.
  7. Since there are 9 red beads, each skittle gets two, hence completing two rows (under the four skittles). There is still one left, but since that does not complete a “4 skittle” row, it is a remainder, and must be exchanged in the next step.
  8. Bring forward the lid with 3 blue beads. Remember that we had a ‘100’ bead left, so now we need to change it for ten 10 beads (blue).  This will make a count of 13 blue beads in the lid.
  9. We now give out the tens, and discover that each skittle gets three with one left over.
  10. Continue with unit beads in the same way.
  11. Conclusion:4933÷ 4 = 1233, remainder 1.
  12. Discuss with the child.

Use all three boards

  1. Take the sum of 7836÷672.  There are three digits in 672, so we will use three boards, the hundreds, tens, and units boards.
  2. The boards are placed with the hundreds on the left.
  3. Put the corresponding numbers of beads onto their lids.
  4. Put out 6 red skittles on the hundred board, 7 blue skittles on the ten board, and 2 green skittles on the unit board.
  5. ‘If the “hundred” skittles get the 1000 beads, what are the “ten” skittles going to get? 100, etc.
  6. Place the lid containing the ‘1000’ beads beside the hundred board, the lid containing the ‘100’ beads beside the tens board, the lid containing the ’10’ beads beside the units board, and leave the unit lid to one side for the moment.
  7. Moving one row at a time across all three boards, start by placing the 1000 beads on the first row under the skittles on the hundreds board.  If there are not enough to complete the row, then exchange these for ‘100’ beads and put these into the ‘100’ beads lid, then move to the tens board and place the beads from the ‘100’ beads lid under the 7 skittles on the tens board.  Then place beads from the ’10’ beads lid under the skittles in the units board.  If there are not enough, then borrow one, if one exists, from the ‘100’ beads lid and exchange it for 10 ’10’ beads and add these to the ’10’ beads lid.  Continue down the rows until there are no beads left in the ‘1000’ beads lid.  Set it aside and clear the beads off of all three boards placing these into the matching colored bowls.  Then move the lids up one step, so the ‘100’ bead lid will go to the one hundreds board, the ’10’ bead lid will go to the tens board, and now you can start using the ‘1’ beads lid moving it next to the unit board.  Now repeat the step again, starting with the ‘100’ bead lid, place beads from it under the skittles of the 100s board.  If there are enough, then move to the first row of the tens board, and add beads from the ’10’ bead lid.  If there are not enough, then take one of the beads from the ‘100’ beads lid and exchange it for 10 ‘ten’ beads and place these in the ’10’ bead lid.  Then complete the row under the skittles in the tens board.  Now go to the unit board and fill out its first row with beads from the ‘1’ beads lid.  If there are not enough, borrow a bead from the ’10’ bead lid, exchange it for 10 unit beads, and place these in the ‘1’ bead lid.  Then complete the row under the skittles on the unit board.  Then move back to the 100s board with the ‘100’ bead lid, and fill out the next row under the skittles.  If there are not enough, then skip this, and go to the tens board, and set out the beads from the ’10’ bead lid.  If there are not enough to complete the row, then grab a bead from the ‘100’ bead lid, and exchange it for 10 tens beads and place these in the ’10’ beads lid.  Complete the row on the ten board under the skittles, then move to the units board.  Repeat this process until the beads in the lid on the hundreds board are gone, then remove it, and count the remainders.  
  8. As the thousands are completely finished with, when you have changed the remaining one for ten hundreds, add that bead to the dish, and move these out of the way. 
  9. Move the remaining lids to the next board, bringing in the units. Deal out in the same way.
  10. When no more hundreds can be divided out equally, the categories cannot be further subdivided, so the remaining beads are left as the remainder.
  11. The answer is the share of one unit or skittle 7,836÷672=11, remainder 444.