Decanomial Bead Bar Layout (Short Form)

The short decanomial replaces each row of identical bead bars with a single bead tile. The 10×10 grid of tiles shows the complete multiplication table at a glance. The squares along the diagonal are especially beautiful.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Multiplication
• Level: Ages 7-8

Objectives

• Lay out the short decanomial using square bead tiles
• Discover the commutative property sensorially
• Compute all products 1×1 through 10×10
• Link squares along the diagonal to squared numbers

Materials

• Bead cabinet
• Felt mat (1m × 1m)
• Square bead tiles for each number 1-10

Instructions

1. Bring tiles and mat out. 2. Lay the 1×1 tile at top left. 3. Beside it: 1×2, 1×3… 1×10. 4. Next row: 2×1, 2×2, 2×3… 2×10. 5. Continue through 10 rows. 6. Notice the diagonal: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 — the squares. 7. Note pairs of tiles reflecting across the diagonal: 2×3 and 3×2 are equal. 8. Record observations. 9. Compare with the long decanomial (bead bars).

Educator tip

The layout is beautiful; let children admire it before disassembly. Photograph the finished grid for the classroom album.

Assessment

Note accurate layout, recognition of commutativity, and identification of squares.

More from Mathematics

• Introduction to Negative Numbers
• Area of a Rectangle — Formula from Counting
• Area of a Triangle — Half the Rectangle
• Circumference and Pi — Measuring the Circle
• Percent Cards — Hundredths as Percentages
• The Coordinate Plane — Plotting Points
• Checkerboard Multiplication — Multi-Digit Products
• Racks and Tubes — Long Division