Operations of the Decimal System: Division
Materials:
Large quantity of golden bead material
Large number cards 1 - 9000
Several sets of small number cards 1 – 3000
Set of unit cards 1-9
Trays with bead cups
Small tray with bead cup for making exchanges
A large tray with bead cup
Tables or Underlay Mats for laying out the small cards
2 rugs
Purposes: To show the child the process of division as the sharing of a quantity into a certain number of equal parts, sometimes leaving a remainder that can’t be shared.
Age: 4 ½ – 5 ½
Preparation: The child understands multiplication.
The child has been doing the operations of addition, subtraction, and multiplication with the golden beads.
Presentation 1: Static Division
Lay-Out
Invite three children for the lesson. They will need to help set up:
Two rugs, one horizontal and one vertical.
Each will need a small mat to lay out on a table, a small box of cards set up on their mats, and a math tray.
Lay out the large cards on the vertical rug.
The guide will gather a quantity (divisor) from the store (evenly divisible by three) and get the large cards to match.
Operational Process
Tell the children you have a large quantity that you will share it all with them. Tell the children there will be two rules. 1. You will share the largest quantity and 2. that everyone will get the same.
Pass out the thousands one by one to each child and ask if everyone has the same.
Share the other quantities (hundreds, tens, then units) and ask if they all have the same.
Place the large cards at the top left corner of the rug (child’s view).
Calculation
Ask child 1 to count what they have.
Ask child 2 to count what they have.
Ask child 3 to count what they have.
Ask each child to get the small cards to match what they have on the tray and to place them on the tray
Story Summary of the Operation
“I started with a large quantity, and I shared it with each of you equally. Child 1’s share was XXXX (place the cards to the right of the large number), child 2’s share was XXXX (place the cards below the other small cards), and child 3’s share was XXXX (place the cards under the other small cards).
“We started with a large quantity, and we shared the same amount three times, (stack the quotients so only one is showing saying one share, two shares, three shares) we only need to say it once, we use this 3 (place a 3-unit card for the divisor in-between the dividend and the quotient)
When you start with a large quantity, and you make smaller equal shares you have done division!”
Presentation 2: Dynamic Division
Layout
Invite three children to set up as in static division.
Guide gets a quantity and large cards to match on the tray. Example: 7542
Operational Process
Remind the children of the two rules for division. You will share the largest quantity and that everyone will get the same.
Share the thousands, so not all will have the same. Ask if they all have the same. They will not.
Explain that an exchange is needed. Take the extra thousand and exchange it for 10 hundreds.
Share the hundreds. What isn’t shared evenly is exchanged for 10’s.
Share the tens. What isn’t shared evenly is exchanged for units.
Share the units.
If there are too few to change, tell them we cannot exchange it and we will leave it on the tray.
Calculation
Have each child count their quantity and get the number from their small cards and return to the rug.
Story Summary of the Operation
Use the same story as in Static Division.
Note: If your example did not end in a remainder, do an example with one.
Control of Error: None, accuracy of the result is not the purpose of this exercise.
Pedagogical Notes:
Allow the children to work with and truly understand the operation of addition, subtraction, and multiplication for several weeks or months before introducing division. This allows the children to internalize, always starting with the units. Division offers the opposite pattern by starting with the thousands.
If the children are working on their own and reverse the operation starting with the units, allow them to do so. Let them explore and experience what happens.