Operations of the Decimal System: Long Division with Bows
Materials:
Large quantity of golden bead material
Large number cards 1 - 9000
Small number cards 1 – 3000
Trays with bead cups
Small tray with bead cup for making exchanges
A large tray with bead cup
9 green ribbons for units, 9 blue ribbons for tens, and 9 red ribbons for hundreds in a box or basket
10 extra small trays with cups
2 rugs
Purposes: A realization of how quantities are distributed in long division, but that in the end the result is the same – the answer in division is the amount that one unit of the divisor receives. It is sufficient for the child to sensorially experience this.
Age: 5 - 6
Preparation: The child is comfortable with division with the golden bead material.
Presentation: 1
Layout
Invite three children for the lesson. They will need to help set up:
Two rugs, one horizontal and one vertical
One small mat to lay out on a table, one small box of cards set up out and each needs a math tray.
The exchange tray, ribbons, and the 10 small trays will need to be brought.
Lay out the large cards on the vertical rug
The guide will gather a quantity (divisor) from the store (evenly divisible by 12, or other two digits) and get the large cards to match.
Tell the children you want to make many shares.
Pass out the ribbons. Give one child a blue ribbon and the other children green ribbons (hence the #12, one ten and two units)
Explain that the child with the blue ribbon will be the “tens representative” and will be collecting enough quantity to share with the others in the community.
The child with the blue ribbon keeps a small individual tray and passes out the remaining 9 trays amongst 9 children in the room.
Each helper friend that gets a small tray can just set it on the table next to their work
Operational Process
Review the rules of division with the children but remind them that the child with the blue ribbon will get a higher category because that child is collecting for ten people.
Distribute the quantity. Child one (blue ribbon) gets 1000, child 2 get 100, child 3 gets 100.
Repeat this process with the rest of the categories, always giving the child with the blue ribbon a larger category.
After distributing all the quantities, ask each child to count what they have. The child with the blue ribbon has much more but now they need to distribute it to their helper friends.
Starting with the largest category, they exchange and then distribute amongst all the children with individual trays. The child will keep one share on their own small individual tray.
Calculation
Gather all the small trays from around the room and line them up on the rug.
Have the children count what is on each tray. They will see they are all the same.
Count how many equal shares there are.
Have one child retrieve the small card that represents the answer.
Story Summary of the Operation
“We started out with a large quantity of 1452 in the tray. And then we made 12 equal shares and each share was 121”. (The divisor can be represented by laying the ribbons where the 12 would be)
“When we make this large number of shares, more than 9, that’s called long division. But look, we had our answer with us all along because our unit representatives, the children with the green ribbons, had the answer. So, we didn’t have to actually share with our 10 friends. Let’s do this again and we will know the answer is in the tray of the unit representatives.”
Control of Error: None
Pedagogical Notes:
Do not rush the work with the golden beads. It is critical that the children physically manipulate quantity to understand the operational processes.