Fractions to Decimal Fractions

Decimal fractions extend the decimal system into the infinitely small. The child who built thousands with golden beads now builds thousandths with green beads. The material reveals that 0.1 is to 1 as 1 is to 10 — a profound symmetry. A misplaced bead on the wrong column breaks place value immediately.

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

Objectives

• Convert common fractions to decimal fractions
• Recognize that 1/10 = 0.1, 1/100 = 0.01, etc.
• Use the decimal fraction board
• Extend place value beyond the decimal point

Materials

• Decimal Fraction Board (green wooden board with columns for tenths, hundredths, thousandths)
• Green bead bars for tenths, hundredths, thousandths
• Fraction insets (for comparison)
• Paper and pencil

Instructions

1. Show 0.1 as one tenth — one bead in the tenths column. 2. Show 0.01 as one hundredth. 3. Show 0.001 as one thousandth. 4. Compare to 1/10 fraction inset: same quantity, different notation. 5. Write 0.25 and build it: 2 tenths + 5 hundredths. 6. Convert a fraction: 1/4 = 0.25 (divide 100 by 4). 7. Practice conversions both directions. 8. Record results. 9. Note that some fractions (1/3) produce repeating decimals.

Educator tip

The green bead color echoes the unit (green). Emphasize that 0.1 is one-tenth of one, not ten. The color link makes this clear.

Assessment

Note accurate conversion, correct place-value placement, and recognition of terminating vs. repeating decimals.

More from Mathematics

• Pythagoras Plates — Sensorial Proof of the Theorem
• Algebraic Peg Board — Equations and Signed Numbers
• Word Problems with Materials
• Short Chains — Squaring Visualized
• Ratio and Proportion
• Volume — Measuring Three Dimensions
• Factor Trees and Prime Factorization
• Addition Snake Game