Operations of the Decimal System: Subtraction

Materials:

Purposes:

To show the operations of subtraction as a larger quantity dispensed into two or more smaller quantities
To show that 1 of any category is equal to 10 of the next lower category

Age: 4 – 5 ½

Preparation: The child has done Dynamic Addition with the golden beads

Presentation 1: Static Subtraction

Layout

Invite one child for the lesson. They will need to help set up:
- Two rugs, one horizontal and one vertical.
- 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.
- Lay out a set of small cards (up to 9,000) below the large cards.
Guide will gather a large quantity of bead material onto the large tray, take it to the horizontal rug, and get the large cards to match.
Meet the child at their cards and tell them a number to place on their tray. They will bring their tray to the rug.

Operational Process

Say the minuend conventionally and place the cards at the top left (from the child’s view) of the rug. Tell the child you are going to give them some of the quantity.
Ask the child to read their number and then invite them to take that much from the large tray. Prompt the child for each category, “How many units will you take?” Repeat for all categories.

Calculation

Invite the child to count how many beads you have left.
The child will count each category and the guide gets the small card from the large cards rug to match each quantity and places the card on the tray.
The child’s subtrahend is placed below the minuend on the rug.

Story Summary of the Operation

Example:” I had a really large quantity (say the number name). And you took (say the child’s number). And then I had (say the number name and place the difference below the subtrahend) left. When you have a large quantity and you take a small quantity away, you have done subtraction. You did subtraction!”

Presentation 2: Dynamic Subtraction

Layout

Set up in the same manner as in Static Subtraction, but you will have two children-each with a set of cards and an exchange tray is needed.
The guide gathers a large quantity from the store on the tray, brings it to the rug, and gets the corresponding large cards to put on the tray.
The guide tells each child a number to bring from their cards on their math tray.

Operational Process

The operational process is the same. Have one child take their quantity from the large tray.

Have the children take turns counting what is left on the large tray, getting the large card to match and placing it on the large tray.
Point to the cards for the minuend and explain that you don’t have that much anymore. Turn the cards over and place the new number cards onto them. State the new number.
Repeat for the next child. When there is not enough of a quantity for the child to take: Explain that when there is not enough that you need to make an exchange. You take one from the category larger and exchange it for 10 of the category you need.
The child makes an exchange, places it back to the large tray and then keeps taking from the tray and exchanging as needed using the script above.

Calculation

After child #2 is done, have the children take turns counting what is left on your tray and get the small cards to match.
Place the new number on the tray assembled.

Story Summary of the Operation

Turn over the large cards so the original amount is facing up. “I started out with a really large quantity (name number) But then Child #1 took XXXX” and lay it below the first minuend. “And Child #2 took XXXX” lay below the other. “And now all I am left with is (say difference)” and lay at the bottom of the rest. “We started with a large quantity, and we took small quantities away from it and we are left with a smaller quantity. That’s subtraction!

Control of Error: None, the accuracy of the result is not the purpose.

Pedagogical Notes:

Do not use the term “share”. Sharing refers to division.
Let the children take the thousands away first if you see them doing this on their own. If they do it, they will soon discover why this is challenging.
If at some point the child/ren become concerned with the “correctness” of their calculation, you can invite them to put their quantities back together again to see if they get their original quantity.
Using small answer cards reflects a smaller amount and also gives the impression that this small quantity is not any more important than the small quantities the children took.
The small number cards the children use go to 3000 because we cannot exchange the 1000’s. This helps them stay in the 9000 or under.

Operations of the Decimal System: Addition