Addition and Subtraction of Fractions

Once the child knows the fraction names, operations follow naturally with the insets. Adding 1/4 + 2/4 is visibly 3/4. For unlike denominators, the child discovers the need to find equivalents, experiencing the rule before naming it.

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

Objectives

• Add and subtract fractions with like denominators
• Convert fractions to equivalents with like denominators for addition with unlike denominators
• Record fractions with numerator over denominator
• Develop concrete understanding before abstract rules

Materials

• Fraction circles
• Recording paper
• Small chalkboard for working

Instructions

1. Start with like denominators: 1/4 + 2/4. 2. Place 1/4 and 2/4 on the work area. 3. Count the quarters: 3. 4. Record '1/4 + 2/4 = 3/4.' 5. Move to subtraction: 3/4 - 1/4 = 2/4. 6. Try unlike denominators: 1/2 + 1/4. 7. Discover that 1/2 = 2/4, so 2/4 + 1/4 = 3/4. 8. Record the conversion explicitly. 9. Explore many operations.

Educator tip

Let the child discover that unlike denominators require equivalents. This insight is the whole lesson.

Assessment

Note the child's use of insets, correct recording, and the moment of discovering equivalents.

More from Mathematics

• 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
• Algebraic Peg Board — Equations and Signed Numbers