How to Teach Division With Exchanging Using Montessori Golden Beads
Montessori golden beads are used in a wide variety of counting and math related lessons. They are particularly useful for helping children visualize how mathematical operations like division actually work, since you can demonstrate with golden beads using actual quantities that can be exchanged for one another, manipulated through the process and handled at every point in the proceedings.
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Things You'll Need
- Large green mat
- As many trays as the number you are going to divide by
- Large number cards
- Small number cards
- Golden beads
Instructions
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Select a problem that will require exchanging. For example, you might use 3,432 divided by 2. The answer will be 1716.
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Build the dividend on the mat using the large number cards and the golden beads. For this problem, you should have the 2 card on top of the 30 card on top of the 400 card on top of the 3000 card. Below the cards you should have three thousand cubes, four hundred squares, three ten bars and two unit beads.
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Explain what you are about to do. Say, "I have 3,432 and I am going to divide it evenly between two children." As you say this, assign two children their own trays.
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Divide up the golden beads, exchanging when necessary. First, you will give each child a thousand cube. Then, since there are not enough thousand cubes left to give each child another, explain that you will exchange the left over thousand cube for ten hundred squares. This will give you 14 hundred squares, and each child can have seven. Then, you will give each child one ten bar. Point out that you cannot divide the last ten bar evenly, so you will exchange it for ten unit beads. This will give you twelve unit beads, and each child can have six.
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Have the children assign small number cards to the amount in their trays. They should each have 1,716 golden beads, which means that they will have a 6 card on top of a ten card on top of a 700 card on top of a 1000 card.
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Place the small number cards from one tray above the large number card dividend. In this case, you will have 1716 over 3432. As you do so, say, "I had 3,432 and I divided it equally between two children. They each got 1,716."
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Work more problems in the same way. As the children become more comfortable with the division and exchanging processes, they will start participating more aggressively and calling out directions. This is okay as long as they do not disturb their classmates who are not taking part in the lesson.
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Resources
- Photo Credit http://www.mymontessorihouse.com/images/golden_beads.jpg
