Introduction to Fractions — The Fraction Circles

Fractions are introduced through the eye and hand: ten red circles, each cut a different way, showing the whole and its parts. The child feels 1/4 as a piece, 3/4 as three pieces, and 4/4 as the whole returned.

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

Objectives

• Identify fractions from 1/1 to 1/10 using the fraction insets
• Name numerator and denominator
• Compose wholes from fractional parts
• Discover equivalences (2/4 = 1/2)

Materials

• Set of ten fraction insets — red metal circles divided into 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 equal parts
• Small knob for each piece
• Control chart

Instructions

1. Present three insets: whole, halves, thirds. 2. Remove the pieces and set them beside the frames. 3. Name the whole: 'one.' 4. Name the halves: 'one-half' each, 'two halves make a whole.' 5. Name the thirds: 'one-third, one-third, one-third, three thirds make a whole.' 6. Use a three-period lesson to name them. 7. Over lessons, introduce all ten insets. 8. Explore compositions: 1/2 + 1/4 + 1/4 = 1. 9. Discover equivalents: 2/4 = 1/2, 3/6 = 1/2.

Educator tip

Introduce only a few insets at a time. The geometric fit is the sensorial control — pieces must return exactly.

Assessment

Note naming accuracy, compositions, and discovered equivalents.

More from Mathematics

• Addition and Subtraction of Fractions
• Multiplication Short and Long Chains (Squaring and Cubing)
• Small Bead Frame
• Binomial Square — Algebraic Pattern
• Geometry — Study of Lines
• Geometry — Study of Angles
• Fractions to Decimal Fractions
• Pythagoras Plates — Sensorial Proof of the Theorem