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Talking math with your kids

Which fits where? A three-dimensional challenge

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Here’s a fun game to play. Which of the solids on the right (sphere, cylinder, cube, cone, pyramid) fits into which holes on the left?

On the left an array of 9 two-dimensional cutouts (two triangles, two circles, a parabola, a half ellipse, two rectangles and a trapezoid); on the right, five solids with a common width and height (sphere, cylinder, cube, cone, and pyramid)

Each hole fits at least one solid, and each solid fits in at least one hole.

What does it mean to fit? That’s open to interpretation—make your own rules if you like! Generally, either passing through without a gap, or sitting nicely at some sort of angle without gaps between the cutouts and the solids is pretty satisfying. You CAN drop the sphere through the square hole, but I’m not counting it—that’s a different game.

Here are additional views of the frame and solids.

  • Five solids with a common height and width—cube, sphere, cylinder, cone, and pyramid
  • Wooden frame with cutouts labeled by letters. A: equilateral triangle, B: half ellipse, C: small circle, D: rectangle (taller than it is wide), E: parabola, F: square, G: tall skinny isosceles trapezoid, H: isosceles triangle, I: large circle

I’ll post some solution images in the coming weeks. In the meantime, play along at home, and/or on social media (Twitter and Instagram links are at the bottom of the page.)

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