*The second of three blog posts about the Montessori Small Bead Frame.
The Small Bead Frame is an arithmetic material which helps a child move toward an abstract understanding of mathematical operations. Addition, subtraction and multiplication equations are solved using this material.
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| The Small Bead Frame |
The Small Bead Frame is introduced at either the end of the Montessori casa program (ages 3 to 6 years) or at the beginning of the Montessori lower elementary program (ages 6 to 9 years). Work with the Golden Beads Decimal System material
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| Solving an Addition Equation with the Golden Bead Decimal Material |
and the Stamp Game precede this work.
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| Solving an Addition Equation with the Stamp Game |
How is the Small Bead Frame used to solve subtraction equations?
Subtraction - Static
Let's solve a static (no borrowing) subtraction equation.
4,693 - 3,251 =
Form the minuend by sliding 3 unit beads, 9 ten beads, 6 hundred beads and 4 thousand beads to the right.
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| The minuend - 4,693 - is on the right of the Small Bead Frame. |
Have the child subtract the subtrahend by sliding the beads to the left. Slide 1 unit bead to the left. What is the difference? Write 2 on the Small Bead Frame paper. Do the same for the tens, hundreds and thousands.
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| The difference of the equation - 1,442 - is on the right. |
The difference is on the right. The difference is 1,442.
4,693 - 3,251 = 1,442
Subtraction - Dynamic
Let's solve a dynamic subtraction equation. Dynamic subtraction equations involve borrowing.
7,963 - 3,428 =
Form the minuend by sliding 3 unit beads, 6 ten beads, 9 hundred beads and 7 thousand beads to the right.
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| The minuend - 7,963 - is on the right. |
Subtract the subtrahend by sliding the beads to the left. For the units, begin sliding the unit beads to the left. We have 3 unit beads and must subtract 8. Slide the 3 unit beads to the left.
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| Three unit beads have been slid over to the left. We will borrow one ten by sliding a ten bead from the right to the left. This will give us ten units which will be slid to the right. Continue subtracting. |
We need more unit beads. Where can we find them? We can borrow 1 ten bead from the tens row by sliding it over to the left. Slide the ten fresh units over to the right and continue subtracting the minuend. Your answer is 5 unit beads. Write the answer on the Small Bead Frame paper.
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| Continue subtracting the subtrahend. |
Continue sliding the beads of the subtrahend to the left.
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| The difference is 4,535 (on the right). |
The difference is on the right. The difference is 4,535.
7,963 - 3,428 = 4.535
Note: This material is introduced to children at 5 1/2 + in a Montessori program (SK - grade 1). Numbers to the thousands are introduced to children in grade 4 of the Ontario Math Curriculum. The addition and subtraction of numbers to 1000 is expected by the end of grade 3 of the Ontario Math Curriculum.
