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Unit Division Board

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Material

A wooden board with 81 shallow holes arranged 9 by 9.
At top, a green border with9 indentations for the skittles.
At left, a vertical row of numbers 1 to 9.
9 green skittles in a small container (divisor).
81 green beads in a small container (dividend).
A small container or bowl.
Packets of 81 sheets for recording division combinations.
Division Chart 1.
Pencil holder and a pencil.

Presentation

Introduction
  1. Invite the child to the lesson.
  2. Introduce the unit division board.
  3. Ask the child to bring the materials to a table.
  4. Bring two papers, underlays, and pencils on a tray.
  5. “Do you remember what division is? Yes, that’s right, division is sharing a number out.”
  6. Point out the features of the board.
  7. “Up here we have the numbers that we’ll be sharing out to, the divisor.”
  8. “Over here on the side, we have the numbers that will give us the answer.”
  9. “We have these skittles, they are like people that we can share the number out to. Let’s share out to three skittles. Can you place three skittles up here?”
  10. “Let’s share twenty-seven beads to three skittles. Can you count twenty-seven beads, one at a time, and put them in this bowl?”
  11. Wait for the child to count 27 beads into the bowl.
  12. “Alright, let’s see what twenty-seven shared three times is!”
  13. Place on bead in the indentions under each skittle.
  14. Place another bead in the indentions under each skittle, so that you have two beads in each skittle’s column.
  15. Ask the child to finish sharing out the beads.
  16. “In division, the answer is always how much one gets. So here, the answer is what? Right, it’s nine!”
  17. “I’ll show you how to write it.”
  18. Place paper horizontally.
  19. Write 27 ÷ 3 = 9 and read it aloud.
  20. Ask the child to write it and to read it too.
  21. Do another problem with the child, but this time a problem that results in an answer with a remainder, such as 29 ÷ 3 = 9 r.2
  22. Show the child how to solve it, write it, and then read the problem with the answer aloud.
Presentation
  1. Continue the presentation where you left off with the introduction.
  2. Bring the “Booklet of 81.”
  3. Ask the child to count aloud 81 beads into the cup.
  4. Turn to the first page of the booklet, the table of 81.
  5. Write 81 at the top of the page.
  6. Write an 81 in all the blanks on the left.
  7. Read the first problem “81 shared 9 times.”
  8. “Well, we need 9 skittles.”
  9. Place 9 skittles at the top of the board.
  10. “Now we need to share out these 81 beads 9 times! You can do that.”
  11. Wait for the child to share them out.
  12. “What did each skittle get? Right, 9! And you know, that’s the answer!”
  13. Write a 9 in the first blank on the right.
  14. Read the next problem, “81 shared 8 times.”
  15. “Oh, we only need to share out to 8 skittles. Let’s put this last skittle back in the box.”
  16. Put all beads back in the cup.
  17. Ask the child to share out the beads to the 8 skittles.
  18. “Oh, there isn’t any space on the board for the rest of the beads.”
  19. “How many are left over? 9. I’ll show you how to write it.”
  20. Write in the answer blank on the right: 9 r. 9
  21. “Our remainder is 9. It’s bigger than our divisor 8. Whenever our remainder is bigger than our divisor, we are done with the page!”
  22. “I’ll show you what to do.”
  23. Draw a line through the problem that has a remainder larger than its divisor.
  24. Draw a diagonal line through the dividend of the strikethrough problem, down to the last remainder spot on the page.
  25. Turn the page of the booklet, and write 80 at the top.
  26. Write 80 in all the blank dividend spots.
  27. “We only need 80 beads this time, so let’s take away one bead and put it back in the bead box.”
  28. Read the first problem.
  29. “Oh, we need 9 skittles again.”
  30. Place the 9th skittle back on the board.
  31. Repeat the process the same as with 81; continue working on the table of 80 until you arrive at a problem that has an answer with a remainder larger than the divisor, and then strike through it.
  32. Draw the diagonal line and turn to the next page.
  33. Write a 79 at the top of the page and a 79 in all the dividend spots.
  34. Take away one bead and place it back in its box so that you have 79 beads.
  35. Let the child work independently, repeating the process now with 79.
Finding Combinations with no Remainder
  1. Invite the child to the lesson.
  2. Bring a red pencil and a red ruler, along with a long grid paper and underlay on a tray.
  3. Bring the child’s unit division booklet that he has already worked on. (He does not need to have finished from 81 down to 1, he just needs to understand the purpose.)
  4. “We’re going to find the problems that do not have any remainder!”
  5. Start with the first page, the page of 81.
  6. Place the ruler right below the first problem that doesn’t have a remainder, and underline the problem with the red pencil, using the ruler as a straight edge.
  7. Ask the child to look for all the problems that he’s done that do not have a remainder, and to underline them with the red pencil.
  8. “Once you’ve found them all, come get me!”
  9. Wait for the child to finish and to invite you back to the table.
  10. Look through the booklet.
  11. “It would be great to have all these underlined problems in one spot!”
  12. Write the first underlined problem on the long grid paper.
  13. Ask the child to go through the booklet and write all the underlined problems onto the grid paper.
Connection with Multiplication
  1. Invite the child to the lesson.
  2. Ask the child to bring the unit division board.
  3. Bring the box of beads and the yellow underlay.
  4. Bring the long grid paper, pencil, and underlay on a tray.
  5. Write a problem such as 12 ÷ 4 =
  6. Ask the child to solve the problem with the unit division board.
  7. Write the answer: 3.
  8. Open the box of beads.
  9. Take out four 3 bead bars and place them vertically on the underlay.
  10. To the right of the first problem, write the opposite of it in multiplication, such as 3 x 4 = 12.
  11. Place four 3 bead bars vertically on the underlay, again, this time for the multiplication problem.
  12. Talk about, and point out, the similarities of the two problems.
  13. “12 divided by 4 equals 3, looks the same as 3 taken 4 times equals 12! They look just alike.”
  14. Do another division problem such as 12 ÷ 3 = 4, and then its corresponding multiplication problem 4 x 3 = 12
  15. Show the similarities using the bead bars.
  16. Continue giving the child problems to solve. (Numbers 12, 18, and 24 work very well for this presentation)

Exercises

Child works independently.

Purpose

Memorization of division facts.

Control of Error

None.

Age

5 1/2 to 6 1/2

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