Stamp Game
Materials:
Box divided into compartments
Green squares with 1 written on them to represent units
Blue squares with 10 written on them to represent tens
Red squares with 100 written on them to represent hundreds
Green squares with 1000 written on them to represent thousands
Paper, pencil, red pencil
Colored pencils in a container
For division only: 10 green, 9 blue, and 9 red skittles
1 green skittle 3 times the size of the small skittles, for the 1000 divisor
Green, blue, and red colored circles, the size of the bottom of the skittles, used to represent zeroes in the divisors
For introduction only: Decimal beads introduction tray
Purposes:
To give the child an opportunity to continue sensorial work individually with each operation
To offer a more symbolic experience with the operations
To begin to write complex numbers
To introduce the signs for the operations
Age: 4½ and up
Preparation: Operations of the decimal system addition, subtraction, and multiplication.
Note: Don’t go on to the stamp game too quickly.
1. Children don’t want to go back to the golden beads after they have “moved on” from them. This is in part because they see this as the next step forward for older children and the Stamp Game is much simpler and more efficient (it is all in one box on the table). The five-year-old has a need to be efficient, this is much less the case for a four-year-old.
2. If we move the child on too soon, we can rob them of the concrete sensorial experience the golden beads offer.
Presentation 1: Introduction to the Stamp Game
Invite the child for the lesson, model how to carry the box and ask them to take it to the table. The Guide brings the decimal beads introduction tray.
Open box lid keeping it underneath.
Compare
Introduce each category of the Stamp Game by linking it to its corresponding category golden bead. Have the child feel the differences, note the color and zeros.
Offer a Three-period lesson with the four stamps.
Return the decimal intro tray to the shelf.
Recording
Model how to use the stamps to build a number and slide them off the table into your hand.
Verbally offer the child some quantities to build. Recite the number when the child is complete.
Show the child how to write the number that was constructed in the stamps on the paper.
Recite the number, clear the table and write a number for the child to build.
Recite the number and have the child build it.
If they are confident, suggest the child make their own numbers and write them as long as they like.
Presentation 2: Static Addition
Layout
The child will bring the stamp game and the writing tray.
Tell the child you will be doing addition. Write a number and have the child read it.
Ask the child to build the number.
Write another number under the first addend for the child to read.
Model building the second addend below the first with space between. Build the units and transfer to the child.
Use a red pencil and add a plus sign to the paper and explain what it represents. Ask the child if they remember what addition is.
Use a red pencil and straightedge to draw the line under the problem and explain what it represents.
Operational Process
Slide up the second addend up to meet the first.
Calculation
Show the child to start at the bottom and count upward.
Write the answer after counting units.
Repeat for all categories allowing the child to help. Have the child reads the answer.
Show the child how to read the entire equation.
Point out the and give language for the addends and the sum.
Invite the child to draw a design with crayon under the sum and the guide write another equation.
Clear away the stamps and do another.
Note: As long as the child is working at this level, they are dependent on the teacher to write problems. As soon as they are confident with the process, move onto dynamic addition. This way they may become independent in writing their own problems.
Presentation 3: Dynamic Addition
Layout
Set up in the same way as static but write a problem that requires exchanges.
Operational Process
Child slides up the bottom addend.
Calculation
Remind the child what they did with the golden beads for a quantity of ten in a category.
Let them count to 10, pulling down the stamps slightly and say, “Stop”.
Model the exchange: Slide the stamps into your hand, place in the box, remove one ten and set it to the right of the top ten stamp.
Child finishes counting the units and records.
Repeat for the rest with the child making the exchanges.
Have the child read the whole equation.
Presentation 4: Static Subtraction
Layout
Write a minuend, ask the child to read the number, and build it with the stamps.
Write the subtrahend. Child will read it.
In red write the minus sign, explain what it is and ask the child if they remember what subtraction is.
Use the straight edge to draw the equal line.
Operational Process
Model how to pull down the units in the subtrahend to the bottom edge of the table. Prompt the child as they go, let them do the rest.
Calculation
Explain the answer is what is left at the box.
Have the child count each category and record.
Read the equation to the child. Explain the minuend and the subtrahend and the difference.
Note: As long as the child is working at this level, they are dependent on the teacher to write problems. As soon as they are confident with the process, move onto dynamic addition. This way they may become independent in writing their own problems.
Presentation 5: Dynamic Subtraction
Layout
Set up in the same way as static but write a problem that requires exchanges.
Operational Process and Calculation
Remind the child what they did with the golden beads when they made exchanges for subtraction.
Model the exchange: Set one stamp balanced on the lower edge of the box in front of its compartment.
Remove 10 of the category lower and line them up downward to the right of the stamps that are already there.
Then bump the balancing stamp into the box.
Take away as before to the bottom edge of the table. Have the child count what is left and record.
Repeat for the other categories with the child working the stamps.
Have the child read the entire equation.
Presentation 6: Dynamic Multiplication
Layout
Move the chair to the long end of the table so you have room for the stamps.
Write the child a number, have them read it.
Write the times symbol in red, explain what it is and ask the child if they remember what multiplication is. Write the multiplier and explain what it is.
Have the child build the first number.
Lay the ruler/straight edge under the stamps.
Ask the child to build the number again below the ruler, butting the top of the first stamp against it.
Repeat this for as many times as the multiplier indicates.
Operational Process
Slide up the stamps.
Calculation
Have the child count and record the units then other categories. Verbalize the exchange (Ex: “What do 10 hundreds exchange for?”)
Read the equation.
Explain the multiplicand, multiplier, and the product.
Note: Dynamic multiplication is the same process as dynamic addition. So we do not have to bother with a static presentation.
Presentation 7: Static Division
Layout
Turn the grid paper horizontal and starting at the left side, write a number that is evenly divisible.
Have the child build it with the stamps.
Write the division sign in red, explain what it is and ask the child if they remember what division is. Write the divisor and explain what it is. Write an equal sign in red and explain it is.
Remind the child of the 2 rules of division.
Remove 2 green skittles and explain that we don’t have friends to share with so we will use these and line up vertically at the left edge of the table.
Operational Process
Share the thousand stamps equally to the skittles one by one.
Transfer the distribution to the child.
Calculation
Show the child to find the answer in one of the units.
Ask the child to record starting with the thousands and then read the equation.
Explain the dividend, the divisor, the quotient.
Presentation 8: Dynamic Division
Layout
Set up as you would for static division with a problem that requires exchanges with a single-digit divisor.
Have child read it and build it.
Child sets up the skittles on the left side of the table.
Operational Process
Remind the child of the rules.
The child shares until they cannot share equally.
Model the exchange: Set the stamp on the edge of its compartment and remove ten the next lower category. Bump the stamp into the box.
Continue sharing and exchanging as needed.
Calculation
Ask the child to count and record the answer. With the red pencil show the child to make a ‘r’ in cursive for the remainder and write the remainder number in red (ex: r3)
Read the equation.
Note: If the equation does not have a remainder, do another problem with one to show them how to record.
Presentation 9a: Long Division with a Two-Digit Divisor
Layout
Write the child the problem Ex: 127 ÷ 21 =
Have the child read and build the dividend.
Remind the child of the Long Division with Bows and the children that wore different colored ribbons and what that represented.
Remove two blue skittles and one green, lined up vertically on the left-blue on the top.
Operational Process
Remind the child of the rules of division.
Try and share the 100.
The child can exchange it for 10 tens and line them up to the right of the tens already on the table.
Share the tens to the ten skittles and a unit to the unit skittle.
Invite the child to continue the sharing.
Leave the one unit remaining at the box because it cannot be shared equally.
Calculation
Ask where the answer is found, have them count the stamps at the green skittle, write the answer and remainder.
Read the equation with the child.
Presentation 9b: Division with a Three-Digit Divisor
Layout
In the same manner above using a three-digit divisor.
Explain that the red gets a category higher than the blue and the blue gets a category higher than the green.
Operational Process
Share one stamp for each and then transfer to the child, exchanging as needed.
Calculation
Ask where the answer is found. Have the child count the stamps at the green skittle.
Read the equation with the child.
Presentation 10: Long Division with Zero in the Divisor
Layout
Begin as before.
Example problem 1421 ÷ 203 =
Have the child read and build the dividend.
Have the child get the skittles and line up on the left side of the table.
Show that a blue disc is for the zero and place it below the hundred skittles.
Operational Process
Ask the child to tell you the rules for division.
Explain that the red gets a category higher than the blue, but it is a zero so it gets nothing, and that the green gets a category smaller than what the blue would have gotten.
Distribute stamps exchanging as needed. As you share, the disc will move along each time it should be shared with, so it is even with the ends of the shared stamps.
Calculation
Find the answer in the unit and have the child write it and then read the equation.
Presentation 11: Long Division with a Zero in the Units Place of the Divisor
Layout
Begin as before.
Example problem 920 ÷ 230 =
Have the child read and build the dividend.
Have the child get the skittles and line up on the left side of the table. There will be a disc used for the units.
Operational Process
Ask the child to tell you the rules for division.
Share as in Presentation 11 in regard to the disc.
When the sharing is complete, the child will see there are no stamps at the unit to get the answer. Explain you will need to make unit skittles.
Exchange one ten skittle for 10-unit skittles and line them up across the table.
Line up 10-unit skittles down the center of the table.
Exchange the ten skittle’s stamps one by one and share to the new unit skittles.
Ask the child to find the answer, record it, and read the equation.
Control of Error: None, accuracy is not the result
Pedagogical Notes:
The child needs concrete experience with the decimal materials because as they progress through this area, their experience becomes more and more abstract. The beads offered the child visual and tactile input (think weight of the categories of beads) The only input they receive from this material is visual. This is more abstract for the child.
Move from static to dynamic as soon as the child is confident so that they can work independently.
Stamp Game and the Decimal System operation work should be included in parent education. Parents focus on correct answers when the process of the operation is what is important.
Originally, the stamps were paper run through a sewing machine to make perforated lines forming squares. Stamps were special and you had to be careful tearing them. This was special and caused the children excitement in the children to work with the material.