Racks and Tubes — Long Division

Long division is elementary's toughest algorithm; Racks and Tubes make it sensorial. Each category has its rack; each divisor gets a skittle. The child distributes beads one category at a time. Indirect aim: abstract long division, remainders, decimal division.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Division
• Level: Ages 8-10

Objectives

• Perform multi-digit division with divisors up to three digits
• Use green (units) and blue (thousands) hierarchical racks
• Exchange across categories when dividend is insufficient
• Bridge to abstract long division on paper

Materials

• Racks and Tubes set (bead tubes in hierarchical colors)
• Division boards in green and blue families
• Peg skittles for each category
• Problem slips and recording paper
• Control chart of worked examples

Instructions

1. Present the problem: 8,762 ÷ 34. 2. Set the thousands bead tubes (8), hundreds (7), tens (6), units (2) on their racks. 3. Set 34 as divisor: 3 red skittles (tens), 4 green (units). 4. Distribute thousands to each skittle set (the full 34) — can 8 thousands be divided 34 ways? No — exchange thousands to hundreds. 5. Now 87 hundreds. Distribute: 2 per skittle set, using 68 hundreds, remainder 19 hundreds. 6. Record 2 in the hundreds place of the quotient. 7. Continue with the tens and units, exchanging where needed. 8. Final quotient and remainder recorded; verify with abstract long division.

Educator tip

Children often conflate divisor and dividend. The skittles keep them apart. Once the pattern is sensorial, paper division becomes a compressed shorthand of the same process.

Assessment

Observe correct exchange, systematic distribution, and accurate transfer to paper.

More from Mathematics

• Large Bead Frame — Up to 1,000,000
• Stamp Game — Long Multiplication Extension
• Fraction Insets — Equivalencies
• Decimal Fraction Board — First Introduction
• Squaring Chain — Passage from Linear to Squared
• Cubing Chain of 5 — Linear to Cube
• Pythagorean Theorem — Sensorial Proof
• Algebraic Peg Board — Solving Linear Equations