# Information on the Abacus

This article discusses general information on the abacus and its uses.

Types:

- Beginner’s
- A counting frame for reinforcing beginning mathematical concepts such as one-to-one correspondence, counting, place value, addition and subtraction.
- Introduces basic abacus terms such as “set” and “clear.”
- Consists of a black rectangular frame with 2 rods. Rods have 9 large white beads that slide against a red felt backing. Frame measures 2 1/2 x 5 1/2 x 1.

- Expanded Beginner’s
- The Expanded Beginner's Abacus introduces visually impaired students to early math concepts and number operations, as well as abacus terminology. It supports concepts and skills such as one-to-one correspondence, number meaning, addition, and subtraction. It also lends itself to preparing a young student for the Cranmer Abacus.
- The abacus consists of a black frame with 3 rods. Each rod has 9 white beads that slide against a red felt backing. The red felt background provides a sharp visual contrast and prevents beads from slipping.
- The simple design of the Expanded Beginner's Abacus allows for direct representation of a given value and enhanced readability for “little fingers”. Measures 5.37 x 3.25 x 0.75 inches.
- Hook/loop strips are provided for connecting multiple abacuses together, in order for students to complete computations that involve amounts of money or numbers too large for the EBA.

- Cranmer
- 13-rod abacus. Frame measures 6 1/8 x 3 1/4 inches. White beads have a diameter of 3/8 inch. Red felt backing prevents beads from slipping.
- An optional metal coupler is available for linking two abacuses together.
- Recommended ages: 5 years and up.

- Large Bead Cranmer
- Young students and those without fine motor skills can benefit from this large 13-rod abacus. Frame measures 8 1/4 x 4 1/2 inches and the bead diameter is 1/2 inch.
- White beads slide against a red felt backing.
- Recommended ages: 5 years and up.

- EZeeCOUNT
- Designed with two-textured beads and a large frame to accommodate needs of students who are blind and visually impaired.
- This abacus consists of a 10 x 10 grid of flat beads. The beads can be flipped and distinguished by color and/or texture. The red beads are wavy/rough and the yellow beads are smooth. Each row of beads slides along an elastic band from left to right. The reverse side is a dry-erase board.
- The included instruction booklet provides examples of how the EZeeCOUNT Abacus can be used in a variety of ways.
- Activities:

- Counting
- Addition
- Subtraction
- Number Combinations
- Multiplication
- Fractions
- Patterns
- Graphs
- Place Value
- Games

- Before using the EZeeCOUNT Abacus for any of the activities in the Instruction Booklet, allow the student to practice:
- Flipping the beads from one side to the other.
- Recognizing and describing the texture difference between the beads.
- Sliding the beads from left to right while practicing abacus terminology. For example, when the beads are moved to the right side they are “set” and when they are moved to the left side they are “cleared.”
- Counting the number of rows and columns of beads.

Methods:

- Counting method - This method has the student count each bead as it is added or subtracted, moving from the unit beads to the 5 beads (but counting only 1 for all beads). There are also specific rules regarding certain numbers and operations, but fewer than the full set of secrets. (S. Millaway)
- More information available in the book Abacus Basic Competency: A Counting Method By Susan M. Millaway

- Logic or Partner Method - This method focuses on understanding the “what” and “why” of the steps in solving a problem on the abacus. It requires that the student know the partners or complements of the numbers up to ten (5=2+3, 5=1+4). This method uses synthesis when beads cannot be set directly. Verbalizing the steps and the reasons for each movement made on the abacus is an important feature of this approach. (R. Livingston)
- Cranmer (Secrets, sometimes called indirect) method - This method focuses on the process of moving the abacus beads in a particular sequence, following a specific set of rules for different numbers and operations. It does not emphasize the understanding of that process, rather the rote memory of the bead movements. (M. Davidow)
- Paper-compatible (sometimes called indirect) method - This method has the user complete problems in the same way an individual completes them using paper and pencil. The standard math facts are used, not the secrets or a series of questions. (D. Willoughby)
- More information available in the Handbook for Itinerant and Resource Teachers of Blind and Visually Impaired Students (1989) by Doris M Willoughby and Sharon L. Duffy

Skills:

- Setting/clearing
- Adding
- Subtracting
- Multiplying
- Dividing
- Money
- Decimals
- Use of a coupler APH item# 1-03160-00

Useful Sites:

- Abacus Position Paper
- Information on the counting method http://www.tsbvi.edu/abacus/74-abacus/3284-using-an-abacus-and-the-counting-method-
- Information on the abacus by Susan Osterhaus http://www.tsbvi.edu/mathproject/ch5-sec3.asp
- Basics plus prime factorization videos http://www.teachingvisuallyimpaired.com/cranmer-abacus-instruction.html
- Indo on abacus goals http://www.teachingvisuallyimpaired.com/abacus-goals.html

Useful Books:

- Abacus Basic Competency: A Counting Method, print edition APH item# 7-00219-00, braille edition APH item# 5-00219-00
- Abacus Made Easy Second Edition Simplified Manual for Teaching the Cranmer Abacus, large print APH item # 4-00100-00, volume one, braille edition http://www.aph.org/files/manuals/5-00220-V1.brf, volume two, braille edition http://www.aph.org/files/manuals/5-00220-V2.brf
- Beginner's Abacus Guidebook, print edition http://www.aph.org/files/manuals/7-03180-00.pdf, braille edition http://www.aph.org/files/manuals/5-03180-00.brf
- Expanded Beginner's Abacus Guidebook, print APH item# 7-03181-00, braille APH item# 5-03181-00
- EZeeCOUNT Abacus Instruction Booklet, print edition APH item # 61-078-022, braille edition http://www.aph.org/files/manuals/5-03185-00.brf
- Using the Cranmer Abacus for the Blind, large print edition http://www.aph.org/files/manuals/4-27110-00.pdf, braille edition http://www.aph.org/files/manuals/6-50100-V1.brf

Useful videos:

- Hands‑On Experience with the Cranmer Abacus APH item# 1-30004-DVD
- The Cranmer Abacus: Unit One - An Introduction, Unit Two - The Counting Method of Addition & Subtraction, Unit Three - The Indirect Method of Addition & Subtraction, Unit Four: Fractions & Decimals
- APH Cranmer Abacus with Susan Osterhaus
- Abacus Chapter 1: Introduction, Abacus Chapter 7: Subtraction No Exchange, Abacus Chapter 8: Subtraction 4-5 Exchange, Abacus Chapter 9: Subtraction Intro to 9/10 Exchange, Abacus Chapter 10: Subtraction Intro to 49/50 Exchange, Abacus Chapter 11: Subtraction Intro to 99/100 Exchange