Wooden Hierarchy Material
Materials:
A geometric representation of the hierarchies for 1 to 1 million:
1 green cube .5 cm3 which represents l
1 blue bar .5 cm2 x 5 cm marked with green divisions, which represents 10
1 red square prism 5 cm2 x .5 cm marked with blue bars, which represents 100
1 green cube 5 cm3 with red lines that mark squares on four sides, which represents 1,000
1 blue bar 5 cm2 x 50 cm marked in green, which represents 10,000
1 red square prism 50 cm2 x 5 cm marked in blue, which represents 100,000
1 green cube 50 cm3 marked in red, which represents 1,000,000.
Small number cards with the corresponding numerals
Purposes: To bring awareness of the decimal system hierarchies up to one million through concrete quantity and number symbol.
Age: 6
Preparation: The child has done addition and subtraction on the Small Bead Frame.
Note: The child must have concrete experience with larger numbers to continue progressing with the Passage to Abstraction materials. This material allows the child to sensorially experience quantities up through 1,000,000.
Presentation 1: Concrete Quantity
Invite the child/ren (small groups do well with this lesson) to lay two rugs end to end.
Bring the tray of quantity up to 1,000, and place on the right side of the rug according to the child’s view.
Invite a child/ren to bring the 10,000 bar, 100,000 square and the 1,000,000 cube and lay them in category order to the left of the tray (child’s view). It takes two children to carry the 100,000 and the 1,000,000.
Bring the decimal bead introduction tray to the rug to compare the familiar beads to the wooden material for unit, ten, and thousand.
Count the wooden unit. Count the wooden ten bar with the unit top to bottom. Count the wooden hundred with the wooden ten left to right. Count the wooden thousand with the wooden hundred top to bottom.
Introduce the 10,000 bar and pass it around for the children to feel. Use the 1,000 cube to count it (one 1,000, two 1,000…).
Introduce the 100,000 square and pass it around for the children to feel. Use the 10,000 to count along it (one 10,000’s, two 10,000’s…).
Introduce million, children stand up to feel it. Invite a child to help hold the 100,000 to count the cube (one 1000,000’s, two 1000,000’s…).
Start a Three-period lesson with all of the materials giving commands to all of the children (point to, stand by, hold your hand over, hand me).
Invite the children to explore them for as long as they like-remind them they need to use two people to carry the million and the hundred thousand.
Presentation 2: The Symbol (The next day)
Invite one child to bring the tray of cards.
Review the cards of the numbers the child knows, reference color and zeros and turn them upside down at top right corner of table.
Show 10,000, cover the three zeros with your and-ask what the number is then uncover the zeros and explain the zeros make it ten thousand. Ask for the color and how many zeros.
Show 100,000 and 1,000,000 in the same way.
Proceed with a Three-period lesson with the three new cards.
Presentation 3: Association of Quantity and Symbol
Help the child lay out the wooden hierarchical material on two rugs.
Bring the number cards to a table.
Mix up the cards upside down. Have the child pick a card and match it to the quantity.
When the child is done, they can mix up the cards and repeat.
Control of Error: In the child’s knowledge of the numbers and quantity.
Pedagogical Notes:
This material can be borrowed from an elementary classroom if you so not have it.
All following Passage to Abstraction work depends on this presentation.
Offers a good visual of the green unit being the start of the categories and the repetitive nature of the categories and they become large.
Not only is this material scientifically precise but offers the child a visual support to link the categories. The line that are drawn on the materials are the color of the category that makes up the category.