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Can 1/3 Be Bigger Than 1/2? Grid Shading Discovery
Lesson
A frequent slip at this stage is treating fraction symbols as fixed amounts independent of the whole — students may insist 1/3 is always smaller than 1/2. Ground each comparison in the specific grid being used, and return to the opening puzzle to confirm that 1/3 of a large chocolate can exceed 1/2 of a small one. Having physical grid sheets for every student, rather than one shared display, gives each child a concrete referent.
0–8Open with the puzzle: can 1/3 of one chocolate be bigger than 1/2 of another? Invite a quick show of hands — who thinks yes, who thinks no — then hold the answer and let curiosity carry the unit forward.
8–30Playing with a Grid, p.17 ("shade 1/8 red, 1/6 blue, 1/12 yellow...."). Distribute grid sheets. Students shade each fraction, then mark 1/3 on a grid of their choice. Pairs compare their shaded regions and discuss which coloured region looks largest and why.
30–40Whole-class share-out: display two grids of different sizes. Ask — if we shade 1/3 of this small grid and 1/3 of that large grid, which shaded piece is bigger? Draw out the idea that a fraction names a part of its own whole, so the same fraction name can represent different amounts when the wholes differ.
Playing with a Grid, p.17 — Shade 1/8 of Grid A in red, 1/6 of Grid B in blue, 1/12 of Grid C in yellow; mark 1/3 in any grid.
Here are two rectangles. Rectangle P has 8 equal parts. Rectangle Q has 12 equal parts. Shade 1/8 of Rectangle P and 1/12 of Rectangle Q. Which shaded part is bigger? Write one sentence to explain your answer.
1/8 of Rectangle P is bigger than 1/12 of Rectangle Q, because Rectangle P's parts are larger — even though both fractions are one part of their own whole.
Also saved as 5 periods.
- 2Fitting Pieces: Discovering Equivalent Fractions With the Kit
Lesson - 3From Fitting Pieces to the Multiply Rule
Lesson - 4Same Pieces, Same Slices: Two Comparison Strategies
Lesson - 5Beyond One Whole: Parathas, Improper Fractions, and the Number Line
Lesson - 6Is It More or Less Than One Whole? The Benchmark 1 Strategy
Lesson - 7Above or Below Half? The Benchmark 1/2 Strategy
Lesson - 8The Fraction Challenge: Choose Your Strategy, Justify Your Answer
Lesson
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