Large abacus

The Montessori arithmetic framework enables school children to calculate with numbers in the millions. The pearls are moved depending on the calculation and the result can already be read.

For example, the child gets a task like 123.112 + 97.394. By simply moving and exchanging the beads in the respective value, you add up. In addition to addition and subtraction tasks, multiplications can also be easily displayed.

Application, advantages, areas of application for this Montessori material:

Practice additions, plus problems up to a result of 9,000,000

Learn subtractions, minus problems within 9,000,000

Understand multiplications, painting tasks on the arithmetic frame up to 9,000,000

Simply explain place values ​​using the typical Montessori place value colors

Montessori material for elementary school and children from 5 years

Scope of Montessori material:

Wooden frame with metal rods and wooden balls, approx. 34 x 26 x 7 cm

Instructions for the large Montessori calculating frame

The adult places the calculating frame on the table in front of him.

The beads of the rake frame are on the left. Now he pushes a green one bead to the right side and says: That's one. Then he takes a ten bead, pushes it to the right as well and says: That's ten. The rest of the place values ​​are introduced in the same way (hundreds, thousands...)

To better illustrate this exercise, the Token Game or the Golden Beads material can be added. Here the adult pushes the one-bead of the counting frame to the right side, then places the ones tile from the token game or a one-bead made of the bead material on the table and says: That's one. Likewise with everyone else.

Now that the calculation frame has been introduced, the next exercise can begin.

The adult starts with the one-pearls. He slides bead by bead from left to right and counts out loud (one, two, thirteen...ten). Now we swap into the next place value: We swap ten ones into a ten Now the ten ones are pushed back to the left and a ten bead to the right. The ten beads are counted in increments of ten (ten, twenty...hundred - exchange ten tens for one hundred bead). The remaining beads are also counted.

Just as in the token game, arithmetic problems can be solved (231 + 924 – one bead of one, three beads of ten and two beads of hundreds are pushed to the right 231 plus 924 now four ones, two tens and nine beads of hundreds are added. In this task, the place value can change immediately be practiced by exchanging the ten hundred bead for a thousand bead.

Subtraction using the Montessori framework

The abacus is on the table, the beads are on the left edge. A task is selected, e.g. 2526 - 1234.

For the number 2526, 6 green ones beads (top row), 2 blue tens beads (second row from the top), 5 red hundreds beads and 2 green thousands beads are pushed to the right.

The number 1234 is subtracted. To do this, 4 beads are pushed back from the ones on the right to the left edge (minus 4). Since 3 cannot be subtracted from 2 tens, the calculation must be made in increments (minus 2 and minus 1). First, the two existing beads are subtracted (shifted to the left). Now a hundred is exchanged for 10 tens. A hundred bead is shifted to the left, while 10 tens are shifted to the right.

Now the second partial calculation (minus 1) can be done. A ten-bead is pushed back to the left edge.

In the hundreds row, 2 pearls are subtracted from the four remaining pearls (to the left) and in the thousands row, 1 pearl is subtracted (also to the left).

The result can be read on the right edge: 1292.

2526 – 1234 = 1292

Multiplication without swapping

The pearls of the calculating frame are on the left edge.

There the respective place value is printed for each row of beads (ones, tens, hundreds...)

A task is chosen, e.g. 216574 x 2 =

Now it is calculated in the head. First the ones (here 4), then the tens (here 7), the hundreds (here 5), thousands (here 6), the tens of thousands (here 1) and finally the hundreds of thousands (here 2) are multiplied by 2.

4 x 2 = 8 (8 green one-pearls are pushed to the right)

7 x 2 = 14 (14 tens are 1 hundred and 4 tens - 4 blue tens and one red hundred bead

are shifted to the right)

5 x 2 = 10 (10 hundreds is 1 thousands – 1 green thousands bead is pushed to the right)

6 x 2 = 12 (12 thousands are 2 thousands and 1 ten thousands – 2 green thousands and 1 blue

ten thousand pearls are shifted to the right)

1 x 2 = 2 (2 blue tens of thousands are shifted to the right)

2 x 2 = 4 (4 red hundreds of thousands are shifted to the right)

From top to bottom, the following beads are now on the right edge of the calculation frame:

8 green ones

4 blue tens

1 red hundred

3 green thousands

3 blue ten-thousanders

4 red hundreds of thousands

The result can therefore be read from bottom to top: 433148

Multiplication with exchange

Some tasks require swapping beads to the next number category, e.g.

23978 x 4 =

8 x 4 = 32 (to be shifted to the right: 2 green ones, 3 blue tens)

7 x 4 = 28 (shoved to the right: 8 blue tens – not possible, since there are only ten beads each

row are available and three have already been pushed to the right. Now you push

first the remaining seven to the right, then the 10 tens become a hundred

exchanged, i.e. a hundred bead to the right, the ten tens to the left again.

Finally, the missing tens are pushed to the right edge (another one

pearl) and two red hundreds pearls)

9 x 4 = 36 (to be shifted to the right: 6 red hundreds, 3 green thousands)

3 x 4 = 12 (to be shifted to the right: 2 green thousands, 1 blue tens of thousands)

2 x 4 = 8 (to be pushed to the right: 8 blue ten-thousanders)

The result can now be read from bottom to top: 95912