Formation of Numbers
Materials:
A Tray of Nine which contains 9 units, 9 tens, 9 hundreds, and 1 thousand
2 rugs
A tray with a bead cup
A set of large number cards from 1-1000 in a container
Purposes:
To associate the categories of the decimal system with their names and symbols
To familiarize the child with the creating and reading numbers that have more than one category
To show that only nine of any category are needed to make any number
To show that zero indicates an empty category
To show that the position of the digit in a number gives it its value
Age: 4 – 5
Preparation: The child has a good understanding of the categories of the decimal system through much practice with the introduction activities with both the beads and the cards
Parallel Work: The Teen Beads and Boards and the Tens Boards
Presentation 1: Tray of Nine Layout (the association of quantity and symbol)
Invite the child for the lesson and to lay out two rugs with some distance between them.
Bring the Tray of Nine and the box of cards to the rugs.
Lay out the beads:
Place a unit bead at the top right edge of the rug and count the bead (one unit).
Set the second below the first with the length of a ten bar between them and count the bead (two units).
Repeat in this way for the third unit bead.
Invite the child to place the rest of the unit beads while counting them aloud.
Place the first ten bar vertically to the left of the first unit, aligning the top beads, and count aloud (one ten).
Place the next below the first, aligning the bar in the same way as the previous, counting aloud (two tens).
Repeat in this way for one more.
Invite the child to finish laying the ten bars while counting them aloud.
Place the first hundred to the left of the ten bar, aligning the top beads and count aloud (one hundred).
Place the next below the first, aligning the hundred in the same way as the previous, counting aloud (two hundreds).
Repeat in this way for one more.
Invite the child to finish laying the hundreds while counting them aloud.
Place the thousand cube to the left of the hundreds aligning the top beads and count it aloud (one thousand).
Lay out the cards:
Remove each category stack and place them at the top of the rug so they reflect the order of the beads. The units will be on the right and the thousand on the left.
Beginning with the units, count aloud (one unit, two units…) while laying each card down along the right edge of the rug leaving a little space between. Do a few and transfer it to the child.
Allow the child to count aloud and lay the cards after three units.
Offer the tens, hundreds, and thousand in the same way.
Explain that you are going to put a quantity on their tray and they will get the cards to match. Gather the quantity from the top of the rug downward.
Place a quantity of units onto the tray, ask the child the count and to get the card to match.
When the child returns, count the quantity with them and ask them to identify the card they brought. Do two or three and then reverse to offer the card first and the child matches the beads.
Repeat in this manner with various quantities from each of the categories one at a time.
Presentation 2: The Formation of Complex Numbers
Invite the child (can also be a small group) to lay-out the beads and the cards in the same manner as Presentation 1.
Place a bead quantity that incorporates more than one category on the child’s tray.
Depending on the child, start with four categories or build up from two.
Ask the child to get the cards to match the cards on their tray.
When the child returns, verify the quantity to the card by counting with the child
Explain that you are going to show them a new way to read the number.
Stack all the cards aligned at the left. Holding the top and bottom of the stack with the fingers of the left hand, push the cards to the other side to reveal the complete number. (Magic Slide)
Read the number conventionally.
Invite the child to replace the cards and the quantity.
Repeat with another number.
Note: At some point you will use a number that incorporates a zero. Over time use numbers with more than one zero. The child will gain the impression that zero is a placeholder.
Note: Do not say, “and” for the zero Example for 1,207: one thousand two hundred seven
Control of Error: In the ability of the child to count the beads and read the number symbols.
Following Exercises:
Verbal Commands: Verbally have the child build with beads and cards quantities with 2 categories, then three, then four (2 tens and five units).
The child can work from a full set of cards 1 to 9,000 and they can work directly from the store.
Pedagogical Notes:
This is the exercise the child MUST have before the Tens Board: Renaming the Tens exercise. This is where the children begin to read these numbers conventionally.
Mastery of this activity is considered a “key” to numeration: a method or process of numbering, and counting
Take the beads from the top of the rug so the child has the visual impression of beads and cards will always be the same.
“It is the possibility to reach large numbers soon, or better, to begin with large numbers, that arouses intense interest, to compose and to analyze, to move objects, encourages the repetition of a fascinating exercise” (Montessori, 2016, Psychoarthmetic, p. 20).