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# Large Bead Frame

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3. Mathematics
4. Passage to Abstraction
5. Large Bead Frame

#### Material

A large bead frame similar to the small bead frame, but with seven horizontal wires representing categories up to units of millions.

Notation paper similar to the small bead frame, but this paper has vertical lines from units up to units of millions.

#### Presentation

##### Introduction
1. Invite the child to the lesson.
2. Ask the child to set up the wooden hierarchical material.
3. Introduce the large bead frame.
4. As you go over the categories of the large bead frame, ask the child to touch each wooden hierarchical prism that corresponds to the categories on the large bead frame.
##### Frame and Notation Paper
1. Count the beads just as you did with the small bead frame:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
10 unit beads is the same as one 10 bead; all the way to ten 100,000 beads being the same as one 1,000,000 bead.
2. Write on the notation paper the same as with the small bead frame;
just the numbers themselves on the wires, then the numbers on the wires followed by 0’s accordingly.
3. Show the child how to make numbers, just as with the small bead frame.
4. Ask the child to make numbers, such as:
“Can you make 18?” and “Can you make twenty-five 10’s? How much is twenty-five 10’s? Right, 250!”
5. Ask the child to write the numbers down on the notation paper.
6. Separate each number with designs that go across the whole row.
7. Continue verbally giving the child random numbers to make; increase the difficulty of the numbers such as one hundred twenty-two 10,000’s: “How much is that? You made it, so let’s count and see. Wow! It is one million, two hundred, twenty thousand!”
##### Addition and Subtraction
1. The child may do addition and subtraction the same way as with the small bead frame, only this time he can use and make much larger numbers.
##### Static Multiplication
1. Invite the child to the lesson.
2. Write a problem on your own notation papers, such as:
31232
x 3
3. Start with units. “What is 2 units taken 3 times? You know that! Right, it’s six, six units.”
4. Slide six unit beads to the right.
5. Go to the next category.
6. “What is 3 tens taken 3 times? Yes, 9 tens.”
7. Slide 9 ten beads to the right.
8. Repeat this process for each category.
9. Record the answer on your paper starting with the units category; make sure the child writes it on his notation paper too.
10. Read the answer; give the child more problems to do.
11. Separate each problem with designs that go across the whole row.
##### Dynamic Multiplication
1. delete this after
2. Write a number such as:
382644
x 4
3. “4 units taken 4 times is what? Right, 16 units. How do you make 16 units?”
4. Count the units and slide them to the right:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
5. Elongate the 10 “teeeeeeeeeeeeeeen.”
6. Slide one 10 bead to the right, then slide all the unit beads back to the left.
7. Continue counting where you left off:
11, 12, 13, 14, 15, 16.
8. “4 tens taken 4 times is what? Yes, 16 tens.”
9. Repeat this process for all the categories, making exchanges the same way.
10. Once all categories are accounted for, record the answer.
11. Give the child more problems.
12. Separate each problem with designs that go across the whole row.

#### Exercises

Child works independently.

#### Purpose

To lead the child to add, subtract, and multiply without using the material.

5 1/2 to 6 1/2