Abacus Level 1

Abacus Level 1: The Foundation of Mental Arithmetic

Level 1 is the most crucial stage in Abacus training. Students transition from direct counting to using logical formulas. This level focuses on mastering the “Friend” concepts, which allow students to perform addition and subtraction when there aren’t enough beads available on a single rod.

1. Small Friends (Concept of 5)

Small Friends are used when we need to add or subtract numbers, but the lower beads are unavailable and the “5” (upper bead) is free. In this concept, 5 is the Best Friend.

• Addition Formulas:

  • +1 = +5 – 4

  • +2 = +5 – 3

  • +3 = +5 – 2

  • +4 = +5 – 1

• Subtraction Formulas:

  • -1 = -5 + 4

  • -2 = -5 + 3

  • -3 = -5 + 2

  • -4 = -5 + 1

2. Big Friends (Concept of 10)

Big Friends are used when a rod is full (reaching its capacity of 9) and we need to move to the next rod (the tens place). In this concept, 10 is the Best Friend.

• Positive Big Friends (+): Used when you don’t have enough beads to add.

  • Example: +9 = -1 + 10 | +8 = -2 + 10 | +7 = -3 + 10 … up to +1.

• Negative Big Friends (-): Used when you don’t have enough beads to subtract.

  • Example: -9 = +1 – 10 | -8 = +2 – 10 | -7 = +3 – 10 … up to -1.

3. Combination Formulas (The Family Concept)

Combination formulas are a mix of both Small Friends and Big Friends. These are used specifically for the numbers 6, 7, 8, and 9 when neither the Small Friend nor the Big Friend formula can be applied directly. It involves the “Mama, Papa, and Babies” movement (5, 10, and the specific digits).

• Addition Combinations:

  • +6 = +11 – 5 (or +1 – 5 + 10)

  • +7 = +12 – 5 (or +2 – 5 + 10)

  • +8 = +13 – 5 (or +3 – 5 + 10)

  • +9 = +14 – 5 (or +4 – 5 + 10)

• Subtraction Combinations:

  • -6 = -11 + 5

  • -7 = -12 + 5

  • -8 = -13 + 5

  • -9 = -14 + 5

Learning Outcomes for Level 1:

• Finger Technique: Mastering the use of the thumb and index finger for speed.

• Mental Theory: Introduction to visualizing the Abacus (Mental Math).

• Accuracy: Solving 1-digit and 2-digit addition and subtraction with 100% precision.