Children in Montessori kindergarten can learn about the concept of carrying and exchanging in addition by using the golden bead material in dynamic addition.
Definition of Terms and Materials
The golden beads used by Montessori are similar to the base ten blocks used in other programs. The thousand cube has 1,000 beads. The hundred square has 100 beads. The ten bar has 10 beads. The unit bead is one independent bead.
Dynamic addition means when two quantities are added, there will have to be some exchanging or carrying, as certain places may have a sum greater than 10.
Purpose of Dynamic Addition
Montessori math introduces concepts at an early age, by using concrete means. Later math work with pencil and paper and memorization can be built upon this foundation.
Dynamic addition introduces the concept of "carrying the one" by children literally carrying beads to be exchanged.
Prior Learning Required
The child receiving the presentation for dynamic addition needs to be familiar with the numeral cards and golden bead materials as they are used in the bank game, creating quantities, and forty-five layout. He should also have worked with static addition.
- Large work rug.
- Two wooden trays for carrying quantities between shelf and rug.
- Set of golden beads, ideally consisting of 45 of each.
- Two sets of small numeral cards, 1-9, 10-90, 100-900, 1,000-9,000.
- One set of large numeral cards, numbered same as above.
- Small signs depicting + and =
The Montessori Presentation of Dynamic Addition
- Invite the children to come to a lesson on dynamic addition. Give two children different quantities to retrieve from the golden bead bank. Make sure some carrying will be involved, such as when adding 5,716 and 3,478.
- When the children return to the rug, have them gently pour out the beads onto the rug. Put the corresponding small numeral cards onto their trays.
- Sort out the golden beads, putting thousands on the left and units on the right. Say you're going to begin counting with the units. When you reach 10, say "Oh, when I have 10 units, it is the same as a ten bar, so I am going to exchange them!" Have the children follow you as you carry the ten loose beads on the tray to the bank to exchange for a ten bar.
- Upon returning to the rug, place the new ten bar with the others, and continue counting the units. When you are finished counting the units, place the corresponding large card underneath, in this case four.
- Continue counting with the tens, then the hundreds, and finally the thousands. Any time you need to exchange, in this case when counting hundreds, send a child to do the exchanging, after asking them what to do. Label each final count with the corresponding large card.
- Demonstrate laying out the small cards for the quantities, complete with the + and = signs, followed by the large cards as the answer, just as in the static addition demonstration.
Independent Follow-Up Work
The child is free to make up her own problems, now that she knows what to do with ten or more beads. Encourage writing out problems on paper with a grid to ensure proper spacing. Create a small booklet of addition problems.
When the child becomes comfortable with the process, she can practice with smaller quantities, such as 532 + 186, or those with a 0, such as 5,302 + 2,868, just like in static addition.