Fractions: Halves, Thirds, and Quarters
Warm-up
I have a chocolate bar (draw a rectangle). I want to share it equally with my friend. How should I cut it? Students suggest. If I cut it unevenly, is this fair? Why not? The intuition of fairness motivates the mathematical requirement of equal parts.
Explore
Paper folding: fold a piece of paper into halves in 3 different ways. Are all the ways valid halves? (Yes, if the two parts are equal.) Fold into quarters in 2 different ways. Are all valid quarters? Now try thirds: harder to fold evenly. How do you check if thirds are equal?
Consolidate
Practice
Students fold paper into halves, thirds, and quarters in multiple ways, verifying equality each time. Solve 4 fair-sharing problems and draw the fraction model. Exit ticket: draw a rectangle divided into thirds and shade two thirds.
Exit ticket
Students fold paper into halves, thirds, and quarters in multiple ways, verifying equality each time. Solve 4 fair-sharing problems and draw the fraction model. Exit ticket: draw a rectangle divided into thirds and shade two thirds.
Quarters means 4 equal parts. Check: are all 4 parts the same size? Fold the paper in half one way, then the other way, crossing in the middle. All 4 parts should be equal. The name quarter only works when the parts are truly equal.
No: one half always means one of two equal parts, but the SIZE of those parts depends on the size of the whole. This is the fraction-as-relative-quantity idea: the same fraction of different wholes gives different amounts. The whole matters.