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Media Path · Lens 1: Math
The
Math
of Media
The opening question
Every video you've ever scrolled past is secretly a giant pile of numbers. Who picked those numbers, and what are they doing?
Why are movies wide but phone videos tall? How does slow motion actually work? Why can a chart tell the truth and still lie? This module hands you the math to find out, and then you get to make something with it.
Inside this module
- 00First Principlesp.2
- 01Screen shapes: aspect ratiosp.4
- 02Frame rates & slow motionp.5
- 03Thirds, φ & compositionp.6
- 04Pixels & file sizesp.7
- 05Numbers that liep.8
- 06Algorithms are mathp.9
- ✦Self-check · Make it · 5 Questions · Side Questp.10
How this works
CoreThe main path. Everyone does this part. All you need is multiplication and division.
Level UpOptional, harder challenges if you want to push further.
Try ItHands-on. Put the pencil (or phone) to work.
You'll need: pencil, calculator (a phone is fine), a phone or camera, a ruler, a few sticky notes.
Media Path · Unizon01/13
Media Path · Lens 1: Math00 · Start here
Before anything else
First
Principles
Principles
A first principle is a basic truth you can build on, something that doesn't depend on anything else. Thinkers have used this idea for more than 2,000 years: strip a big topic down to its building blocks, then build back up. Three questions. Be honest; nobody's grading this.
1
What do I already know?
Dump it all out. Half-sure counts.
What do you already know about how screens, cameras or videos work?
Where do you already use math when you watch, make or share media (even without noticing)?
Circle every word you could explain to a friend right now. Underline the ones you've heard but couldn't explain.
ratiopixelframefpsresolutionmegabytepercentaveragealgorithmcomposition
2
What is necessary?
The building blocks you need before going further
Everything in this module is built from four math bricks. Rate yourself on each one, then check the example to see if your rating holds up.
RatioComparing two amounts. 16:9 means 16 wide for every 9 tall
Got itKindaNot yet
RateHow much per one of something. 30 frames per second
Got itKindaNot yet
PercentA part out of 100. 25 out of 200 = 12.5%
Got itKindaNot yet
VariableA letter standing in for a number. if L = likes, 2 × L doubles them
Got itKindaNot yet
Is anything else necessary? What else do you think you'd need to know or have to really get this topic?
The Math of Media02/13
Media Path · Lens 1: Math00 · Start here
3
What is the objective?
What am I trying to understand or be able to do by the end?
The module's objective
By the end, you'll be able to look at any piece of media and see the numbers behind it.
- 01Simplify a screen size into an aspect ratio, and explain why phones and cinemas use different ones.
- 02Calculate frames in a clip and how much slow motion stretches time.
- 03Use thirds (and the golden ratio) to compose a stronger shot.
- 04Estimate pixels and file sizes, and explain why compression matters.
- 05Spot a misleading graph or percentage, and fix it.
- 06Explain how a simple ranking formula decides what shows up first.
My objective
The list on the left is ours. Now make it yours. What do you want out of this?
By the end, I want to be able to
The part I'm most curious about is
I'll know I've got there when
Knowledge meter
How much do you know about the math of media right now? Shade the boxes in pencil. You'll come back at the end (p.10) and shade it again in pen.
NothingCould teach it
Why start this way? When you know what you already have (1), what you need (2) and where you're going (3), you learn faster and you notice the gaps. Every module on the Media Path starts with these same three questions, so it becomes a habit.
Your route through this module
00
First Principles
01
Ratios
02
Frames
03
Thirds
04
Pixels
05
Lies
06
Feeds
✓
Check
▶
Make
?
5 Qs
★
Quest
The Math of Media03/13
Media Path · Lens 1: Math01 · Aspect ratios
01
Screen shapes
Why is TikTok tall?
An aspect ratio is a screen's width compared to its height, written width:height. It's the shape of the window you're looking through.
Why tall? You hold your phone upright, so a 9:16 video fills the whole screen. Movies and TVs are wide partly by tradition and technology, and it's often said our side-by-side eyes see more across than up-and-down. Same content, different window.
Worked example
A YouTube video is 1920 × 1080 pixels. What's its ratio?
1Find the biggest number that divides into both. 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9
2So 1920 × 1080 simplifies to 16:9. Turn the phone upright and it's 1080 × 1920, which is 9:16.
Can't spot the big divisor? Keep dividing both by small numbers (2, 3, 5) until you can't anymore.
Try it
Simplify these real sizes
a) 1080 × 1350 (Instagram portrait)
b) 1080 × 1080
c) 4032 × 3024 (a common 12 MP phone photo)
Answers: a) 4:5 (÷270) · b) 1:1 · c) 4:3 (÷1008)
Level Up
The letterbox problem
You play a 16:9 video on a vertical 1080 × 1920 phone without zooming. It shrinks to fit the width, so it's 1080 pixels wide. How tall is it? What percent of the screen does it actually use? Then: many cinema films are about 2.39:1. Is that wider or narrower than 16:9 (≈ 1.78:1)?
1080 × 9 ÷ 16 = 607.5 px tall · 607.5 ÷ 1920 ≈ 31.6% of the screen · 2.39 > 1.78, so wider
The Math of Media04/13
Media Path · Lens 1: Math02 · Frame rates
02
Frames & time
Video is a flipbook
Video doesn't really move. It's a stack of still pictures, called frames, shown so fast your brain blends them into motion. Frame rate is how many frames show each second: fps.
| fps | Where you see it |
|---|---|
| 24 | Movies. The film standard since sound films took over in the late 1920s. |
| 30 | Lots of phone and online video. (North American TV is really 29.97!) |
| 60 | Sports, gaming, anything that needs to look extra smooth. |
Worked example
How many frames in a 15-second clip at 30 fps?
frames = seconds × fps
15 × 30 = 450 frames
That's 450 separate pictures in just 15 seconds.
The slow-mo trick
Many phones can record at 120 or 240 fps. Slow motion happens when you play those frames back at a normal speed like 30 fps.
240 ÷ 30 = 8 → everything moves 8× slower. One real second of a skateboard trick becomes 1 × 8 = 8 seconds on screen.
Try it
The sticky-note flipbook
Draw a ball bouncing across 12 sticky notes, moving it a little each time. Stack them and flip through in about one second: that's roughly 12 fps. Now, how many frames would a 15-second clip need at:
24 fps? 60 fps? 12 fps?
Answers: 360 · 900 · 180
Level Up
Time per frame
At 60 fps, each frame is on screen for 1 ÷ 60 of a second. How many milliseconds is that? (1 s = 1000 ms.) What about at 24 fps?
1000 ÷ 60 ≈ 16.7 ms · 1000 ÷ 24 ≈ 41.7 ms
Animating "on twos"
Hand-drawn animators often hold each drawing for 2 frames. A 3-minute music video at 24 fps has how many frames? How many drawings on twos?
180 s × 24 = 4320 frames · 4320 ÷ 2 = 2160 drawings
The Math of Media05/13
Media Path · Lens 1: Math03 · Composition
03
Where to put stuff
Thirds, φ & the frame
rule-of-thirds lines
golden-ratio lines
Dots mark the four "sweet spots" where thirds lines cross. Our subject sits on one.
Split any frame into a 3 × 3 grid. Put your subject on a line or where two lines cross, instead of dead centre. That's the rule of thirds, and it's just division.
Worked example
Where are the thirds lines on a 1080 × 1920 phone video?
1Width: 1080 ÷ 3 = 360, so lines at 360 and 720 px from the left.
2Height: 1920 ÷ 3 = 640, so lines at 640 and 1280 px from the top.
Meet φ (phi), the golden ratio ≈ 1.618
Start with 1, 1, then add the last two numbers each time: 1, 1, 2, 3, 5, 8, 13, 21… (the Fibonacci sequence). Divide each number by the one before it and watch what happens:
5÷3 ≈ 1.667 · 8÷5 = 1.6 · 13÷8 = 1.625 · 21÷13 ≈ 1.615 → 1.618…
Watch out
You'll see claims online that the golden ratio is hidden in every famous painting, logo and face. Many of those claims are stretched or simply not true. Treat φ as one useful tool, not a magic law.
Try it · phone camera
Three shots, one object
Turn on your camera's grid (iPhone: Settings → Camera → Grid; on Android, look for "grid lines" in the camera app's settings). Photograph the same object three ways:
A dead centre B on a thirds line C on a sweet spot
Which feels most interesting? Why do you think so?
Level Up
Golden lines vs thirds
On a 1080-wide frame, the golden lines sit at 1080 ÷ 1.618 ≈ 667 px and 1080 − 667 = 413 px. Are they closer to the centre than the thirds lines (360 and 720)?
Now find the golden lines for the 1920 height.
Yes, closer to centre · 1920 ÷ 1.618 ≈ 1187 px and 1920 − 1187 = 733 px
The Math of Media06/13
Media Path · Lens 1: Math04 · Pixels & file sizes
04
Zoom all the way in
Every image is a grid
Zoom into any photo far enough and you hit tiny squares of single colours called pixels. Resolution is how many there are: width × height. One million pixels is a megapixel (MP).
Worked example
How many pixels in HD vs 4K?
1HD: 1920 × 1080 = 2,073,600 ≈ 2.1 MP
24K: 3840 × 2160 = 8,294,400 ≈ 8.3 MP
34K is twice as wide and twice as tall, so it has 2 × 2 = 4 times the pixels. Not double. Quadruple.
Why videos are HUGE
Each pixel stores 3 numbers (red, green, blue), each from 0 to 255. A number that size fits in 1 byte, so one pixel = 3 bytes. One uncompressed HD frame:
2,073,600 × 3 = 6,220,800 bytes ≈ 6.2 MB
A 15-second clip at 30 fps is 450 frames (remember p.5?):
450 × 6.2208 MB ≈ 2,799 MB ≈ 2.8 GB for 15 seconds! Your phone shrinks this with compression: math that trims detail and mostly stores what changes between frames.
Try it
Your own photo
Open a photo on a phone and look at its info or details. Find its width × height, then multiply. How many megapixels is it?
× =
Check: is your answer close to what the phone says (like "12 MP")?
Level Up
How much does compression save?
Say (example number) a phone saves video at 8 megabits per second. There are 8 bits in a byte. How many megabytes is the 15-second clip? About how many times smaller than 2,799 MB is that?
8 × 15 = 120 megabits · 120 ÷ 8 = 15 MB · 2,799 ÷ 15 ≈ 187 times smaller
Pixel ladder · drawn to scale
| 720p · 1280 × 720 | 921,600 ≈ 0.9 MP |
| HD · 1920 × 1080 | 2,073,600 ≈ 2.1 MP |
| 4K · 3840 × 2160 | 8,294,400 ≈ 8.3 MP |
| Photo · 4032 × 3024 | 12,192,768 ≈ 12.2 MP |
Here 1 MB = 1,000,000 bytes (some computers use 1,048,576 instead).
The Math of Media07/13
Media Path · Lens 1: Math05 · Numbers that lie
05
True numbers, fake stories
Numbers that lie
A chart can use 100% real numbers and still fool you. Two channels, example numbers: Channel A got 9,800 views and Channel B got 10,200. Same data, two charts.
Worked example
How much bigger is B, really?
1Difference: 10,200 − 9,800 = 400 views
2Compare to A: 400 ÷ 9,800 ≈ 0.041 → about 4% more
In the hype chart, B's bar rises 500 views above the axis and A's only 100, so B looks 5× bigger. Chopping the axis is trick #1.
Trick #2: big percentages, tiny numbers
"Views up 200%!" sounds huge. But going from 3 views to 9 views is a 200% increase: (9 − 3) ÷ 3 = 2 = 200%. Always ask: percent of what?
Trick #3: percent vs percentage points
If engagement goes from 2% to 3%, it rose 1 percentage point, or rose 50% (1 ÷ 2). Both true. Guess which one ends up in the ad?
Try it · stat detective
Find one chart or stat this week (an ad, a news story, an app, a video). Ask it three questions:
1. Where does the axis start? 2. Compared to what? 3. How big is the real number?
Level Up
One common way to define engagement rate is interactions ÷ views × 100 (platforms and marketers define it differently). Example numbers: Post X has 5,000 interactions on 100,000 views; Post Y has 50 on 200. Calculate both. Which is "more successful"? Argue both sides.
X: 5,000 ÷ 100,000 = 5% · Y: 50 ÷ 200 = 25%
The Math of Media08/13
Media Path · Lens 1: Math06 · Algorithms
06
Who goes first?
Your feed is a formula
An algorithm is a set of steps for solving a problem. A ranking algorithm turns numbers about posts into an order: who shows up first in your feed. Real platforms use far more signals and much more complex systems, and they don't publish all the details. But the core idea is math you can do. Here's a made-up toy formula:
Score = ( L + 3×C + 5×S ) ÷ ( H + 2 )
L = likesC = comments (worth 3)S = shares (worth 5)H = hours since posted
Dividing by H + 2 makes older posts sink. The "+2" means a brand-new post (H = 0) never divides by zero, and gets a head start without rocketing off the chart.
| Post (example numbers) | L | C | S | H | Score |
|---|---|---|---|---|---|
| A · Cat falls off couch | 120 | 10 | 6 | 4 | 30 |
| B · How to fix a bike chain | 60 | 20 | 12 | 1 | |
| C · Classic meme repost | 400 | 8 | 16 | 22 |
Worked example · Post A
1Top: 120 + 3×10 + 5×6
= 120 + 30 + 30 = 180
= 120 + 30 + 30 = 180
2Bottom: 4 + 2 = 6
3Score: 180 ÷ 6 = 30
Order of operations: multiply first, then add, then divide.
Try it
Score posts B and C in the table and rank all three. Then: what if the platform stopped caring how old posts are? Remove the "÷ (H + 2)" part and re-rank.
B = 180 ÷ 3 = 60 · C = 504 ÷ 24 = 21 → B, A, C · Without time: A 180, B 180, C 504 → C jumps to first
Notice: the post with the most likes came last. Whoever picks the weights picks what wins. That's a human choice, hiding inside the math.
Level Up
Design your own feed
Write a formula for a feed that rewards something you value (learning? local creators? friends?). Pick your variables and weights. Then play the villain: how could someone game your formula?
The Math of Media09/13
Media Path · Lens 1: MathSelf-check
✓
No pressure, just proof
Quick self-check
Six questions, one from each stop. Show your work. Answers are upside down at the bottom; no peeking till you're done.
1 · Simplify 1280 × 720 into an aspect ratio.
2 · How many frames in a 10-second clip at 60 fps?
3 · You record at 120 fps and play at 30 fps. How long do 2 seconds of real action last on screen?
4 · A 1080 × 1080 square post: where are the two vertical thirds lines?
5 · Your likes go from 40 to 50. What's the percent increase?
6 · Using the toy formula, score a post with L = 20, C = 0, S = 2, H = 0.
1) 16:9 (÷80) · 2) 600 frames · 3) 120 ÷ 30 = 4× slower → 8 seconds · 4) 360 px and 720 px · 5) 10 ÷ 40 = 25% · 6) (20 + 0 + 10) ÷ 2 = 15
Back to First Principles
Re-shade your knowledge meter
Flip back to p.3 and shade the meter again, this time in pen (or shade this one). Then look at the four bricks on p.2. Did any move from "Not yet" to "Got it"?
NothingCould teach it
Did I hit my objective? What's my evidence?
The idea that surprised me most:
The Math of Media10/13
Media Path · Lens 1: MathMini challenge · Make it
Mini challenge · Execution
The 15-second explainer
Make a vertical video (or, if you don't have a camera, a storyboard) that teaches one idea from this module to someone who's new to it, in exactly 15 seconds. Use the math to plan it like a pro.
1 · Run the numbers
My idea:
Aspect ratio: fps:
Total frames (15 × fps):
5 equal shots = s each = frames each
(Check: at 30 fps that's 450 frames total, and 3 s or 90 frames per shot.)
2 · Your must-haves
- At least one shot uses the rule of thirds
- One real number, shown honestly (no chopped axes!)
- Text on screen big enough to read on a phone
- Exactly 15 seconds (time it)
- Show one person: can they explain the idea back to you?
3 · Storyboard Sketch each shot in the 9:16 frames. Thirds grid included.
Shot 23–6 s
Shot 36–9 s
Shot 49–12 s
Shot 512–15 s
Before you film or post: ask anyone who appears in your video for permission. If you're under 18, check with a parent or guardian before sharing anything online. Keeping it on your device is totally fine.
The Math of Media11/13
Media Path · Lens 1: Math5 Questions I Still Have
The best part of learning is what's next
5 Questions
I Still Have
This module didn't answer everything. Good. Write 5 new questions it didn't answer, one of each type below. There are no wrong questions, only ones nobody's asked yet.
1
How does it work?
Pick something you use and wonder about the inside of. e.g. "How does my phone decide what to throw away when it compresses a video?"
2
Why?
Ask about a reason or a cause. e.g. "Why did 24 fps become the movie standard, and not 20 or 30?"
3
What if?
Change one thing and imagine the result. e.g. "What if every screen in the world were round?"
4
Connect it
Link this to another lens (science, psychology, technology, history, language & storytelling, art & design, execution) or another subject. e.g. "Do people really prefer the golden ratio, or is that a myth?"
5
My life & community
Bring it home: your feed, your friends, your Edmonton. e.g. "What do local Edmonton creators say actually helps their videos get seen?"
★ Star the one question you'd most like answered. You'll need it on the next page.
The Math of Media12/13
Media Path · Lens 1: MathSide Quest · Optional
My quest question:
1What I'll find out
Break your big question into 2 or 3 smaller ones you could actually answer.
2Where I'll look
A library (Edmonton Public Library counts!)Someone who does it for a jobAn experiment I run myselfTrustworthy websites (who wrote it? when?)A book or documentary
3How I'll share it
A one-page zineA 15-second explainer (you know how now)A poster or infographicA 2-minute talkSomething else
Who I'll share it with:
Done by:
Next on the Media Path
Lens 2 · Science asks a new question about the same screens: how does a camera turn light into all those numbers?
The Math of Media13/13