How to Teach Addition With Exchanging Using Montessori Golden Beads

Golden beads are designed to help children visualize quantities.

Golden beads are a counting tool used in most Montessori classrooms to do everything from introduce numbers of varying quantities to demonstrating the actions behind basic math. You can use golden beads, which come in hierarchies of units (tens, hundreds and thousands), to build and perform any type of math operation with components and a result of less than 9,999. This lesson is used to demonstrate "carrying" or "exchanging" numbers in addition problems.

Things You'll Need

• Set of golden beads
• Large number cards
• Small number cards
• 2 felt-lined trays
• Large green floor mat

Instructions

1. Use the small numbers to create two numbers to add together. One number should be in each tray. If you wish, you can place a child in charge of the small number cards and have them create the numbers. This involves more children in the exercise and gives them additional practice making numbers with the cards. For example, one tray might have the number 1, 298 and the other might have 2, 673.

2. Give a tray to each child and have them build the number in their tray with golden beads. They should use all of the hierarchies, if necessary. Using the example from Step 1, one child would return with 1 thousand cube, 2 hundred squares, 9 ten bars and 8 unit beads. The other child would return with 2 thousand cubes, 6 hundred squares, 7 ten bars and 3 unit beads. Do not check the quantities, as you should assume that the children have brought the correct amount for now.

3. Line up the addends (the numbers being added together) on the mat. Take the first tray and place the small number cards on the mat with the associated golden beads a little way beneath them. Say, "You have brought 1,298." Place the second addend cards directly below the first while saying, "You have brought 2,673." The second addend beads should be placed slightly below the first addend beads. The numbers you say will change based on the problem that you assigned. At this point, you should have the number cards reading 1,298 and 2,673 directly on top of each other, and all the associated beads below.

4. Summarize what you are about to do. Indicate the piled golden beads and the associated number cards. Say, "Here we have 1,298 (point to this number) and 2,673. We will add them together and see how much we have all together." Physically move all the golden beads together, keeping the hierarchies slightly separate from each other so that the cubes are grouped together, as are the squares, ten bars and unit beads.

5. Count the new pile of golden beads. You can do this yourself as a demonstration the first time, or allow a child to help you. Have a child count all of the unit beads first. Point out that each time he reaches ten, he can exchange those ten beads for an additional ten bar. This ten bar should be placed slightly above the rest of the ten bars to indicate that it arrived separately. Do the same for the tens, exchanging for hundred squares when necessary, and for the hundreds, exchanging for thousand cubes when necessary. As you complete a hierarchy and any exchanges, number cards should be placed next to the beads to show the results. For example, in this case, the unit beads will have one bead left after exchanging, so you will place a 1 card next to the beads.

6. Superimpose the number cards to get the final sum. As you do so, repeat the problem. Say, "We had 1,298 and 2,673. We added them together. We got 3,971." You should repeat this multiple times until everyone seems comfortable with the adding process.

Tips & Warnings

• If you wish, demonstrate the parts of the problem by pointing to the two numbers that you added together and saying, "addend" and then pointing to the final result and saying, "sum." You can test the children's recall by doing this with each problem.