Normally you cut a tray of brownies with straight lines to make squares or rectangles. But this cake-cutter by Matthias Wandel makes hexagons instead! There are only 3 shapes with all equal sides and angles that can fit together with no gaps or overlaps: hexagons, squares…and can you think of the last one? Triangles. Try cutting your brownies that way, too!
Wee ones: A hexagon has 6 sides and a square has 4 sides. Which shape has fewer sides?
Little kids: If you eat a hexagon brownie and then a normal square one, how many edges do they have all together? Bonus: If you cut 2 straight lines across a square cake and then 2 straight lines from back to front, how many pieces will you have?
Big kids: If you cut your brownies into 6 rows of 4 hexagons plus 6 half-hexagons, how many total hexagons do you have? Bonus: If you can fit 36 squares instead, how many more brownies do you have by cutting squares?
The sky’s the limit: By what fraction is each of 27 hexagons bigger than one of the 36 squares from the same size tray?
Answers:
Wee ones: The square, because 4 is less than 6.
Little kids: 10 edges, since the square has 4. Bonus: 9 pieces — imagine a tic tac toe board.
Big kids: 27 hexagons, since the 6 halves give you 3 more. Bonus: 9 more brownies.
The sky’s the limit: 1/3 bigger than a square. Each hexagon is 4/3 of a brownie, since you can cut only 3/4 as many of them. If you carve out 3/3 for the square brownie, you’re left with 1/3 extra.
