Use of the Cranmer Abacus

Use of the Cranmer Abacus (2nd Ed.)

by Rita Livingston, Ph.D.
© TSBVI 1997 - 153 pages ($15.00) Order # 59420CAP (16 oz.)
Note: This curriculum is sold unbound and printed on 3-hole punched 8 1/2 x 11 paper ready for a ring binder.

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This guide gives step by step instructions using two methods for basic math operations.

TSBVI Method - Adding, subtracting, multiplying, dividing, decimals, percent, fractions, ratios
Counting Method - Adding, subtracting, multiplying, dividing, similar to finger math ("Chismbop")
Includes the Elementary Math Skills Continuum

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Contents of Use of the Cranmer Abacus

by Rita Livingston, Ph.D.

The Parts of an Abacus

The TSBVI Method

Addition of Whole Numbers
- Skills Needed
- Definition of Terms
- Teacher Tip
- Sample Addition Problems
  - 1-digit addends less than 5
  - 1-digit addends less than 10
  - 2-digit addends, multiples of 10
  - 3-digit addends, multiples of 100
  - a 2-digit and a 1-digit addend
  - 2-digit addends
  - 3-digit addends less than 500
  - 1-digit addends
  - 2-digit addends
  - 1-digit addends
  - 2-digit addends
  - 2-digit addends, multiples of 10
  - 2-digit addends
  - 2-digit addends
  - 1-digit addends
  - 2-digit addends
  - 2-digit addends with 3-digit sum
  - Three or more addends
  - Addends greater than 100
- Teacher Tip
Subtraction of Whole Numbers
- Skills Needed
- Definition of Terms
- Teacher Tip
- Sample Subtraction Problems
  - 1-digit numbers less than 5
  - 1-digit numbers less than 10
  - 2-digit numbers, multiples of 10
  - 3-digit numbers, multiples of 100
  - 1-digit subtrahend from a 2-digit minuend
  - 2-digit subtrahend from 2-digit minuend
  - 3-digit subtrahend from a 3-digit minuend
  - 1-digit numbers
  - 2-digit subtrahend from a 2-digit minuend
  - 2-digit subtrahend from a 2-digit minuend, multiples of 10
  - 2-digit subtrahend from 2-digit minuend
  - 1-digit subtrahend from 2-digit minuend
  - 2-digit subtrahend from 2-digit minuend
  - 2-digit subtrahend from 3-digit minuend
  - 2-digit subtrahend from 3-digit minuend
  - 2-digit subtrahend from 2-digit minuend
  - 1-digit subtrahend from 2-digit minuend
  - 2-digit subtrahend from 2-digit minuend
  - 2-digit subtrahend from 3-digit minuend
  - Subtrahend and minuend > 100
Multiplication
- Skills Needed
- Definition of Terms
- Method
- Teacher Tip
- Sample Multiplication Problems
  - 1-digit multiplicand by a 1-digit multiplier
  - 2-digit multiplicand by a 1-digit multiplier
  - 3-digit multiplicand by a 1-digit multiplier
  - 2-digit multiplicand by a 2-digit multiplier
  - 2-digit multiplicand by a 3-digit multiplier
  - 3-digit multiplicand by a 3-digit multiplier
- Teacher Tip
Division
- Skills Needed
- Definition of Terms
- Method
- Teacher Tip
- Sample Division Problems
  - 1-digit dividend by a 1-digit divisor
  - 2- or more digit dividend by a 1-digit divisor
  - 2-digit or more divisor
- Alternate Method of Division
  - 1-digit dividend by a 1-digit divisor
  - 2- or more digit dividend by a 1-digit divisor
  - 2- or more digit divisor
Decimals and Money
- Definition of Term
- Adding and Subtracting
- Teacher Tip
- Setting Decimals
- Sample Addition Problem
- Sample Subtraction Problem
- Multiplication
  - Sample Multiplication Problem
- Division
  - Decimal number by a whole number
  - Dividend with a decimal fraction by a divisor with a decimal fraction and rounding to the nearest 100s
- Teacher Tip
Fractions
- Definition of Terms
- Teacher Tip
- Addition and Subtraction
- Sample Fraction Problems
  - Adding fractions with a common denominator
  - Adding fractions with unlike denominators
  - Adding mixed numbers
  - Mixed numbers, three or more addends, unlike denominators
- Sample Subtraction Problems
  - Simple fractions with common denominator
  - Mixed numbers - the fraction in minuend less than the fraction in the subtrahend
  - Fractions, unlike denominators
- Multiplication and Division of Fractions
- Sample Multiplication Problems
  - Multiplication of simple fractions
  - Multiplication of simple fractions factoring
  - Changing mixed numbers to improper fractions.
  - Multiplication of mixed numbers
- Division How-Tos
  - Division of fractions
  - fraction by a whole number
  - Division of mixed numbers
Ratios, Percent, and Square Roots
- Definition of Terms
- Ratios
- Percent
- Square Roots
- Examples of Square Roots
- Teacher Tip

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Counting Method on the Abacus

Definition of Terms
- Teacher Tip
Exchanges for Addition and Multiplication
- 4/5 Exchange
- 9/10 Exchange
- 49/50 Exchange
- 99/100 Exchange
- Teacher Tip
Addition
- Prerequisites
- Definition of Terms
- Sample Addition Problems
  - 1-digit addends
  - 2-digit addends, multiples of 10
  - 3-digit addends, multiples of 100
  - 1-digit addends
  - 1-digit addends
  - 2-digit and a 1-digit addend
  - 2-digit and a 1-digit addend
  - 3-digit numbers less than 500
  - 2-digit addends
  - 2-digit addends resulting in a 3-digit sum
  - Addends greater than 100
  - 3 or more addends
Multiplication
- Prerequisites
- Definition of Terms
- Sample Multiplication Problems
  - 1-digit multiplicand by a 1-digit multiplier
  - 2-digit multiplicand by a 2-digit multiplier
  - 3-digit multiplicand by a 1-digit multiplier
  - 3-digit multiplicand by a 2-digit multiplier
  - 3-digit multiplicand by a 3-digit multiplier
Exchanges for Subtraction and Division
- 4/5 Exchange
- 9/10 Exchange
- 49/50 Exchange
- 99/100 Exchange
Subtraction
- Definition of Terms
- Sample Subtraction Problems
  - 1-digit numbers less than 10
  - 1-digit numbers less than 10
  - 2-digit subtrahend from 2-digit minuend
  - 1-digit subtrahend from a 2-digit minuend
  - 1-digit subtrahend from a 2-digit minuend
  - 1-digit subtrahend from a 3-digit minuend
  - 2-digit subtrahend from a 2-digit minuend resulting in a 2-digit difference
  - Subtraction with subtrahend and minuend greater than 100
Division
- Prerequisites
- Definition of Terms
- Sample Division Problems
  - 1-digit dividend by a 1-digit divisor
  - 2-digit dividend by a 1-digit divisor
  - 2- or more digit dividend by a 1-digit divisor
  - 2-digit or more divisor
  - Quotients with Remainders

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Appendix

Bibliography
Math Skills Continuum

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Last Revision: March 8, 2006