Teaching Dilations with Precision: Scaling Figures in the Coordinate Plane
Let’s talk about one of the most underrated transformations in the coordinate plane: dilations. They don’t flip, slide, or spin like the others, but what they do is arguably cooler—they grow and shrink figures with mathematical precision. And what better way to teach this than with… flies?
Yes, flies. Giant ones. Tiny ones. Just imagine your classroom buzzing with ideas (not actual insects, hopefully).
🪰 The Fly-Sized Magic of Scale Factor
At the heart of every dilation is the scale factor—a little number with big power. The scale factor determines whether your figure grows (scale factor > 1) or shrinks (scale factor between 0 and 1).
So here’s the setup: Picture a normal fly, minding its business on a 5x5 grid. Then—boom! A math student hits it with a “scale factor of 3.” Suddenly, that fly’s wingspan is 3 times longer, its eyes are bugging out, and it’s covering 9 times the area. Say hello to the giant fly!
On the flip side, if another student uses a scale factor of ½, now you’ve got a mini fly barely visible on the graph. Same shape, same proportions, just cuter and less terrifying.
🧠 Why Dilations Help Students Build Math Muscles
Dilations help students:
Understand proportional reasoning
See how distance from the center of dilation impacts the outcome
Apply scale factors in real-world contexts (maps, blueprints, models, and yes—giant insects)
Let your students draw a square and then use the center of dilation (typically the origin) to plot every transformed point. Encourage colored pencils to track pre-image and image.
🎲 A Silly Lesson Idea: The Fly Swat Challenge
Draw a regular fly (pre-image) on the coordinate plane. Then, call out scale factors at random and have them quickly create the image. You can even throw in a silly story:
“This fly just fell into a radioactive soda. Scale factor: 2.5!”
“This one flew into a shrinking machine. Scale factor: 0.3!”
Let the fun begin!
📏 Final Buzz
Teaching dilations doesn’t have to be dry or complicated. With a little creativity—and some imaginary mutant flies—your students will grasp the power of scale factor in no time. Remember: they’re not just drawing bigger or smaller shapes. They’re learning how precision and proportionality scale up in math and in life.
So break out the graph paper, unleash the flies, and let the dilation fun begin. 🪰
Bonus Tip: For students who struggle, keep a simple checklist:
Multiply each coordinate by the scale factor
Plot and label the new points
Check that the shape stayed proportional
Starting with dilations around the origin and some basic polygons will build student confidence. I love using colored pencils to help students identify the original and the image. Students will be more engaged and it will help them visualize the concept.
