Math Materials ~ The Small Bead Frame ~ Operations ~ Subtraction

*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.  

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 

Solving an Addition Equation with the Golden Bead Decimal Material

and the Stamp Game precede this work.

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.

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.

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.

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. 

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.

Continue subtracting the subtrahend.

Continue sliding the beads of the subtrahend to the left.

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

A Blog Post explaining multiplication with the Small Bead Frame will follow.

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.