Fractions — Addition with Unlike Denominators

Unlike denominators can't be added directly — 1/2 + 1/3 is not 2/5. The insets show why: 1/2 and 1/3 are different-sized pieces. Common denominator makes them same-sized. Indirect aim: abstract fraction arithmetic, preparation for algebraic fractions.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Fractions
• Level: Ages 7-9

Objectives

• Find a common denominator for two fractions
• Convert each to the common form
• Add the numerators
• Simplify if possible

Materials

• Fraction Insets
• Equivalencies chart
• Recording paper
• Worked example chart

Instructions

1. Write: 1/2 + 1/3. 2. Take 1/2 inset; find sixths that fill it: 3/6. 3. Take 1/3 inset; find sixths: 2/6. 4. Now both are sixths. 5. Add: 3/6 + 2/6 = 5/6. 6. Record: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. 7. Repeat with 1/4 + 1/3 using 12ths. 8. Generalize: multiply denominators for common form.

Educator tip

The insets physicalize common denominators. Don't move to abstract rule until the child has done several with the material.

Assessment

Observe correct common-denominator finding, accurate conversion, and correct sum.

More from Mathematics

• Fractions — Multiplication
• Fractions — Division
• Decimal Multiplication
• Decimal Division
• Perimeter — Various Polygons
• Angles and Protractor Use
• Ratio and Proportion
• Integer Operations — Signed Number Arithmetic