Unit Division Board
Materials:
A wooden board with holes for 9 skittles across the top and the numerals 1 - 9: holes for beads; numerals 1 - 9 down the left side by each row. It is painted green across the top to indicate that the divisor is units
Container with 9 small green skittles
Box with 81 green beads
Small tray
81 printed papers
Pencil, red pencil, small ruler
Squared papers
Purposes:
To memorize the essential division combinations.
To show that not every number is evenly divisible, and some are divisible only by a few numbers.
Age: 5 – 6
Preparation: Division Stamp Game (single-digit divisors)
Presentation 1: Introduction to the Materials
Invite the child, they will bring the tray and the board to the table.
Introduce the board, the spaces for the skittles, the skittles.
Count 18 beads to the dish with the child’s help.
The child will help place nine skittles across the board.
Explain you will share the 18 beads among the nine skittles.
Share across so each skittle gets one (“One for you, one for you…”), transfer to the child after the first few.
After all are shared, remind that the answer is in the last unit skittle.
“18,” point to the end of the last filled row, “divided by nine,” point to the nine skittle, “equals two.” Slide your finger under the last full bead row and point to the two on the left side of the board.
Help the child remove the beads one at a time to the dish.
Remove three skittles and repeat with the 18 beads (dividing evenly), after sharing verbally summarize, remove the beads.
Remove three more skittles and repeat.
Remove one more skittle to show the child the short-cut: to redistribute the line without a skittle to the remaining skittles by moving beads to the end of the columns.
Move beads to the dish and move to Presentation 2.
Presentation 2: Experimentation
Present the stack of papers to the child and tell them they have a big work to do.
Explain that they will use all the beads and have the child count them.
Write 81 on the paper.
Tell the child to put all the skittles along the top and place all the beads on the board.
The child may count them as they place them or after they are all placed.
Read the board for the child by pointing 81÷9=9.
Have the child write the answer, note that there is no remainder and have the child underline it in red.
Child reads the next divisor ÷8 and removes a skittle.
Try to redistribute the beads. Tap the place on the board where a bead would go but there is no divot/space. The child sees there is no room to redistribute. Draw a diagonal line with a ruler across the rest of the problems on the paper.
Set the paper aside and take a new one.
Remove a bead from the bottom row on the lower right and place it in the dish.
Replace the skittle so there are nine.
Write 80 in the first equation.
Redistribute under the nine skittle.
Point to the numbers and running finger under last full row pointing to remainder 80÷9=8 r8.
Child writes.
Remove a skittle and redistribute for the column without a skittle to the first open row.
Continue until there is no room to continue on the board, line out the rest of the equations with a ruler.
Take a new page, remove a bead to make79, replace skittles, redistribute the bottom row (redistributed beads) to the nine skittle top to bottom.
Sit with the child until they get to 72 beads.
Encourage the child to do this for as long as they can. They can always pick up where they left off the next day.
When the child is done with the 81 papers, they may use the Division Control Chart and check the ones that are underlined in red.
Presentation 3: Extracting the Tables
The child will need the completed 81 papers.
Bring nine grid papers.
Explain the important combinations are underlined.
Place the stack upside down on the table for 1÷1 is at the top and 81÷9 is at the bottom.
Write all equations underlined in red that are ÷1.
The child will write and say them aloud.
Flip the turned pages back on the stack upside down. Take a new grid paper and find the underlined problems ÷2. Repeat as before.
Repeat though ÷9
Have the child check with the control chart when they are done.
Encourage the child to make a lovely book out of the 9 papers (special cover with decorations).
Control of Error: Division Control Chart
Pedagogical Notes:
The divisor must be between 1-9 and the answer, quotient, must be between 1-9 for it to be an essential combination.
The child will sort through all the possible combinations to locate the few essential combinations that they actually need to memorize.
Second plane children like BIG work that takes time. This is the child who will be getting this lesson.
Dr. Montessori would bundle the 81 pages with a ribbon and give it to the child like a gift, a moment of arrival.