Math Materials ~ The Small Bead Frame ~ Operations ~ Addition

* The first 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 toward 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) and the Stamp Game precede this work.

The Small Bead Frame

The Small Bead Frame consists of four wires strung with ten beads each. 

The top wire - 10 green unit beads

The second wire - 10 blue ten beads

The third wire - 10 red hundred beads

The fourth wire - 10 green thousand beads

(Note that the colour coding for units, tens, hundreds and thousands is consistent across the majority of the Montessori math materials.)

The Simple Family - units, tens, hundreds - is in white.

The Of Thousands Family - 1000 - is in grey.

The units, tens and hundreds form the simple family.  The thousand is part of the of thousands family.  There is a gap between the two families.  When writing large numbers, a comma represents the space between families.

(Note:  As the child progresses through the Montessori Lower Elementary (ages 6 to 9 years), they will be introduced to numbers into the millions.  The Large Bead Frame (among other materials) follows that introduction.  The Large Bead Frame consists of the simple, of thousands and of millions families.)

How is the Small Bead Frame used to solve addition equations?

Addition - Static

Let's solve a static (without exchanging) addition equation.  

1,423 + 4, 562 =

Small Bead Frame Paper

Begin by forming the first addend 1,423.  Slide 3 unit beads, 2 ten beads, 4 hundred beads and 1 thousand bead to the right.  

The first addend - 1,423 -  is on the right of the Small Bead Frame.

Now begin to add the second addend.  Slide 2 units to right to join the beads already there.  How many units do we have in total?  Write five on the Small Bead Frame paper.

The units of the second addend - 2 units - have been slid over.

Do the same for the tens, hundreds and thousands.

The sum is 5,985.

The sum of the addition equation - 5,985 - is on the right side.

Addition - Dynamic

Let's solve a dynamic addition equation.  Dynamic addition equations involve exchanging.  

2,649 + 4,326 =

Begin by forming the first addend.  Slide 9 unit beads, 4 ten beads, 6 hundred beads and 2 thousand beads to the right.

2,649 on the right side of the Small Bead Frame

Now add the second addend.  Begin by sliding 6 unit beads to the 9 already there.  It cannot be done without exchanging.  Slide the last remaining unit bead over.  

We must add 6 units to the nine already there.
Slide the remaining unit bead to the right.
We have made one ten.

What have you made?  You have made one ten.  Slide a ten bead over to the right and slide all your unit beads over to the left.  

Continue sliding unit beads over to the right until you have slid 6 unit beads in total.  Your answer is 5 unit beads.  Write the answer on the Small Bead Frame paper.

Continue sliding beads to the right for the tens, hundreds and thousands.

The sum is 6,975.

The sum is 6,975.

Blog Posts explaining subtraction and 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.