Multiplication on the Cranmer Abacus

1. Multiplication on the Cranmer Abacus Sara Larkin Math Consultant Iowa Educational Services for the Blind and Visually Impaired Resource used: Millaway, S. M. (2002). Abacus basic competency: A counting method. American Printing House for the Blind.

2. Prerequisites • The student must know the multiplication tables • The student should be aware of terms used in multiplication such as multiplicand, multiplier, factors, and product

3. Abacus Skills • The student must be able to set numbers on the abacus • The student must be able to read numbers on the abacus • The student must be able to demonstrate an understanding and proficiency in the use of the Rules for addition on the abacus

4. Multiplication on the Abacus • More areas of the abacus are used • The product will be written on the right side of the abacus • The multiplicand, or initial number in the problem, is set on the extreme left • The multiplier is placed towards the right, but not all the way to the right and is based on the number of digits in the problem • The abacus is not used for multiplying a single digit by a single digit since multiplication facts are used anyway

5. Setting the Multiplier • With the right hand moving from right to left, repeat the problem while the right index finger touches a rod for each digit and for the word times. • When the finger touches the last number of the multiplier, that is where the student begins to set the first digit of the multiplier

6. Practice Setting • 243 x 6 • 12 x 7 • 32 x 25 • 2000 x 400

7. Multiplying • Begin multiplying the units digit of the multiplier by the first digit of the multiplicand, extreme left. Continue multiplying each digit of the multiplicand by the units digit of the multiplier • When multiplying a number, think in terms of two digit answers. For instance 2 x 8 is 16, but think one-six and 2 x 3 is 6, but think zero-six. The first digit is added to the current rod and the next digit is added to the following rod • When you finish with the units digit of the multiplier, clear it and begin using the next digit of the multiplier if one exists until no digits are left in the multiplier • The result after the last digit of the multiplier is cleared is the product

8. Practice Multiplying • Group A • 200 x 40 = 8000 • 82 x 4= 328 • 50 x 7 = 350 • 34 x 2 = 68 • Group B • 26 x 2 = 52 • 78 x 3 = 234 • 503 x 9 = 4527

9. More Practice • Group C • 28 x 8 = 224 • 68 x 6 = 408 • 576 x 9 = 5184 • Group D • 38 x 12 = 456 • 54 x 53 = 2862 • 132 x 241 = 31,812