The Power of Perspective: Seeing Math Through Different Eyes

Hold your thumb up to the sky and “cover” a faraway tree. Did your thumb really get bigger — or did your view change?
That’s perspective — the math of how we see the world.

Last week, we played with scale, shrinking and stretching things to make sense of size.
This week, let’s explore perspective — how where you stand (or sit, or crouch!) changes what you see.

If you are thinking, “great, another activity just for the little ones,” here’s your friendly reminder about SUMM’s favorite idea: low floor, high ceiling.
That means there are lots of ways to explore the same idea — from quick, playful noticing to deep, creative discovery.

In this case, a low floor might be to…
Take a silly photo! Hold a toy dinosaur close to the camera so it looks like it’s eating your sibling. Line up your hand so it looks like you’re pinching the Space Needle.

And you can use those same skills all the way to the high ceiling of…
Sketch a street or hallway using perspective lines, or explore how photographers and artists use geometry to guide the eye toward a vanishing point.

Kids are natural experts at noticing perspective. They crouch down to see under tables, lie on the floor to look up, or tilt their heads until the world makes sense.
All we have to do is name the math that’s already there.

Try this together:

• Go on a “perspective walk.” Take turns crouching, standing, and stepping to one side. What things look different from each spot? What stays the same?

• Use your phone or camera and take three photos of the same object from three different distances. Which looks “real”? Which looks “funny”? Why?

• Draw a road or hallway disappearing into the distance. Ask, “Why do the sides look like they meet?” (Spoiler: they don’t — your brain is doing the math.)

For older kids, take it further. Artists use vanishing points — places where parallel lines seem to meet. Architects and video game designers use projection — math rules that turn 3D objects into 2D images that make sense to our eyes. Even street chalk artists use perspective tricks to make flat drawings look like holes or towers!

You can connect this to maps and models from last week, too.
Maps show things from above — a “bird’s-eye” perspective.
Models usually show things from the side — a “human” perspective.
And your imagination can switch between them instantly.

Perspective is also about empathy and imagination. When we change where we stand — literally or figuratively — we learn to see the world differently. And that’s one of the best math skills there is.

This week, take a few minutes to play with point of view.
Lay on the floor. Look up. Step outside. Hold your thumb over the moon.
Ask your kids (and yourself):
What do you notice?
What changes when I move?
What stays the same?

Math helps us measure the world, but it also helps us see it — from every angle.