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# Wooden Hierarchical Material

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4. Passage to Abstraction
5. Wooden Hierarchical Material

#### Material

Seven wooden solids representing the following hierarchical values:
1: a green cube of 1/2 cm x 1/2 cm x 1/2 cm

10: a blue prism of 1/2 cm x 1/2 cm x 5 cm, divided into equal parts by free lines to that each section represents the preceding value (one)

100: a red prism of 1/2 cm x 5 cm x 5 cm, divided into equal parts by blue lines so that each section represents the preceding value (ten)

1,000: a green cube of 5 cm x 5 cm x 5 cm divided into equal parts by red lines so that each section represents the preceding value (hundred)

10,000: a blue prism of 5 cm x 5 cm x 50 cm divided into equal parts by green lines so that each section represents the preceding value (unit of thousand)

100,000: a red prism of 5 cm x 50 cm x 50 cm divided into equal parts by blue lines so that each section represents the preceding value (ten of thousand)

1,000,000: a green cube of 50 cm x 50 cm x 50 cm divided into equal parts by red lines so that each section represents the preceding value (hundred of thousand)

#### Presentation

##### Quantity
1. Invite the child to the lesson.
2. Ask the child to lay 2 large rugs next to each other, forming a large square.
3. Show the child the Wooden Hierarchical Material.
4. Ask the child to say “wooden hierarchical material.”
5. Bring the small tray of Wooden Hierarchical Material to the rug.
6. Bring the golden bead introduction tray.
7. Pick up the unit bead.
8. Ask the child “What is this? Right, a unit!”
9. Place the small green cube next to the unit bead.
10. “This is also a unit.”
11. Repeat this process, comparing the blue prism with the 10 bar, the red prism with the 100 square, and the larger green cube with the 1000 cube.
12. After all the beads are compared, return the golden beads to the shelf.
13. Count the unit cube and say “One. This is one.”
14. “Let’s see how many ones go into this.”
15. Slide and count the unit cube next to the blue prism.
16. “One, two, three…nine, ten. This is ten.”
17. “Let’s see how many tens go into this.”
18. Slide and count the ten-prism next to the red prism.
19. “Ten, twenty, thirty…ninety, one hundred. This is one hundred.”
20. “Let’s see how many one hundreds go into this.”
21. Lift the one hundred prism and compare it to each row of the cube.
22. “One hundred, two hundred, three hundred…one thousand. This is one thousand.”
23. Perform a 3 period lesson with the wooden hierarchical materials that are on the rug.
24. Once the child is secure with this knowledge, invite the child to see the large Wooden Hierarchical Material.
25. Show the child how to hold the large blue prism and ask him to bring it to the rug.
28. Repeat this process the same as before, comparing 1000 cube to blue prism.
29. “One thousand, two thousand, three thousand…ten thousand. This is ten thousand.”
30. Repeat this process for the rest of the prisms.
31. Do another three-period lesson with all seven of the prisms.
32. After the three-period lesson, group the material by color: 1 with 1,000 and 1,000,000; 10 with 10,000; and 100 with 100,000.
33. Help the child clean up the material.
##### Symbol
1. On another day, invite the child to the lesson.
2. Take the box of white cards to the table.
3. Open the box and take the cards out.
4. Place the cards into a stack.
5. Ask the child what the first card says:
“Right, one!”
6. Move the card to the side of the stack, revealing the next card in the stack.
7. “What is this? Yes, ten!”
8. Move the card to the side.
9. “What is this? Right, one hundred!”
10. Move the card to the side.
11. “What is this? Yes, one thousand! What does this comma mean? The comma just separates the family.”
12. Repeat this process for 10,000 and 100,000 and 1,000,000; emphasizing the comma, such as: “This is one hundred” pause and point at the comma “thousand. One hundred thousand!”
13. Proceed with a three-period lesson.
14. Ask the child how many zeroes are in the numbers.
##### Quantity and Symbol
1. On another day, invite the child to the lesson.
2. “Let’s get out the wooden hierarchical material, and bring the cards to the rug too!”
3. Randomize the wooden hierarchical material on the rug.
4. Ask the child to place the cards with the corresponding prisms.
5. Admire the child’s work once all cards are placed.
6. Remove the cards and order the wooden hierarchical material based on family.
7. Ask the child to place the cards back with their prisms again.
8. With the child, think about what even larger quantities would look like.

#### Exercises

Child works independently.

#### Purpose

To give familiarity with categories above 1000 and give practice in reading, including commas.
To reinforce the idea of families, such as hundreds, thousands, and millions.

None.

5 1/2 to 6 1/2