The Montessori Multiplication Checkerboard math material is one of my Top Ten math materials for elementary. It is a 9×4 grid on a board or cloth mat consisting of 36 squares; nine horizontally across the bottom and 4 vertically up the side. The squares repeat a green, red, blue pattern visually representing the place value and numbery hierarchy. It can be used to do multi-digit multiplication and can result in products in the billions. Along the bottom of the board from right to left are the numerals:
1
10
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
Along the right, vertical side of the board are the numerals:
1
10
100
1,000
Each square is the intersection of a row numeral (a multiplicand) and a column numeral (a multiplier) and is colored green, blue, or red depending on its place value.
To Purchase the Montessori Multiplication Checkerboard math material click HERE.
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Preceding Materials
The Montessori Multiplication Checkerboard math material is preceded by the Multiplication Bead Bars, Golden Beads, Stamp Game, Bead Frames, and Multiplication Bead Board.
The Lessons
Build Numbers and Make Exchanges
One-digit Multiplier
Two-digit Multiplier
Partial Product Recording
Three and Four-digit Multipliers
Build Numbers and Make Exchanges
Introduce the Montessori Multiplication Checkerboard math material to children by allowing them to build and read numbers with the Montessori Colored Bead Bars.
Take a Bead Bar from the box and place it on a square along the bottom edge of the board. For example, a child may take the 5-bead bar and place it on a square. If the child places the 5-bead bar on the first green square to the right, it represents the numeral 5. If it is moved one place to the left on the blue square, the value of the bead is now 50. Moving it to the left on the red square the value is now 500, and so on. The bead bar tells us the quantity and the square tells us the place value.
Next, provide an opportunity to make exchanges from one place value to the next. The rule of the checkerboard is that only one bead bar may be in each square. Otherwise, they must be combined and exchanged. Place a 6-bead bar and a 4-bead bar in the unit square. The child must combine 6+4 (10) and exchange the 6 and 4 bead bars for a red 1-bead, placing it in the blue square (the tens place). Allow the child to practice building numbers and making exchanges.
Start With One-Digit Multiplication
Since this is a new material, have the child start with a 1-digit multiplication equation to gain confidence with the process. For example, 3,231 x 3. The number 3,231 is built in white numeral tiles along the bottom of the board to represent the number being taken (the multiplicand) and the numeral 3 is built in a grey tile along the right side to represent how many times to take the number (the multiplier).
Beginning in the right green square (the unit’s place), the child takes three 1-bead bars and places them in the square to represent 1×3. He continues the process for each place value category.
To find the product, the child must combine the beads in each square beginning with the unit’s place. If the child is not familiar with the multiplication facts, he can simply count the beads to find the product. In the unit’s place, he counts the three 1-bead bars resulting in 3 so he will exchange the three 1-bead bars for a 3-bead bar in the unit’s place. He continues combining in each place value category.
As children become proficient with their multiplication facts, they will begin to place the bead bar(s) that represent the fact instead of multiples of the bead. For example, instead of laying out three 2-bead bars, counting 6, and exchanging them for a 6-bead bar, they will simply lay out a 6-bead bar because they know that 2×3 is 6.
Subsequent lessons with the Montessori Multiplication Checkerboard math material will include exchanges and zeros in the multiplicand.
Two-Digit Multiplication
If, for example, the equation was 3,231×23 the child will put a grey tile with a numeral 2 along the side of the board next to the second row from the bottom. After finding the first product, the child will then move up to the second row from the bottom and multiply each digit in the multiplicand (3,231) by 2 (tens).
Once the product is achieved (64,620) the child will begin in the second row and slide the bead bars diagonally down to the bottom keeping the bead bars in their correct place value category. He will then add the beads together in each square exchanging them for the final product.
Partial Product Recording
When a child is comfortable with the process of 2-digit multiplication, he can begin recording the first partial product and the second partial product on paper. Here it is a matter of discovery that we begin the second product in the tens place (represented by a blue square) and so we must write a zero in the unit’s place and begin recording in the ten’s place. The material is self-correcting in that the place value on the board and the place value recorded on the paper should match. If it does not, the child needs to investigate as to why.
These equations take some time to complete and require much concentration. The emphasis is placed on understanding and internalizing the process of multiplication. If the child does not get the correct answer, we encourage continued work with the material. His accuracy will improve as he becomes more proficient with the process and the multiplication facts.
Three and Four-Digit Multipliers
Once a child is proficient with a 2-digit multiplier, you can introduce a 3-digit multiplier following the same process. Next, introduce a 4-digit multiplier. Encourage exploration by asking the child what they think is the largest number they could multiply and let them play around with large multiplicands and multipliers.
To purchase the Montessori Multiplication Checkerboard math materiak click HERE.