About This Lesson
Why Half Plus a Third Isn't Two Fifths — Making Fractions Mean Something
Topic: Fractions as quantities, not rituals. Students who can shade 3/4 of a circle still add denominators a week later — this lesson attacks the "fraction = two whole numbers" misconception head-on with fair-share situations, paper folding, and number-line placement.
Target learning outcomes — by the end, students can:
- Place 1/2, 1/3, 2/3 and 3/4 on a number line and defend the placement
- Explain with a folded strip why 1/2 + 1/3 cannot be 2/5
- Decide which of two fractions is bigger using a strategy other than "bigger denominator"
Audience: Grades 3–5 (ages 8–10), 26 students, mixed ability. Fractions anxiety is real in this room — several students already say "I'm bad at math."
Materials: paper strips, scissors, rulers, whiteboard. No tablets.
Constraints: One 45-minute in-person lesson. Needs a quick exit check that shows me who still adds denominators.
