Math4ML Lesson 2: From Numbers to Pictures

This lesson shows how graphs turn data into pictures—so patterns become easier to spot and easier to predict.

Watch: Sam’s Slime Shop

Watch this 2-minute story before the lesson. Join Evie and Mark to turn Sam’s weekly slime sales into a graph, one point at a time.

Watch, pause, and try: Pause at 0:58 to plot week three’s seven jars. At 1:47, discuss whether an upward trend guarantees more sales next week. Then explore the graphing activities below.

Open the video in its own player

The Secret Behind the Slime Sales

Meet Sam, a 12-year-old who started selling homemade slime at school. Each week, Sam writes down how many jars were sold:

Week	Jars Sold
1	2
2	5
3	7
4	10
5	14

At first, it’s just numbers.
But when Sam plots them on a graph, something amazing happens — the numbers turn into a picture.
A line that goes up! 📈

“Wow,” Sam says, “I can actually see my business growing!”

That’s the power of graphs:

• Tables help you store data.
• Graphs help you see patterns and tell a story quickly.

Turning Data into Pictures

A graph is basically a map from input → output.

• x-axis (horizontal): the input (often time, week number, or something you control)
• y-axis (vertical): the output (the result you measure)
• point (x, y): one real observation (one “data example”)

For Sam’s slime:

• x = week number
• y = jars sold
• (3, 7) means “week 3, sold 7 jars.”

Two kinds of graphs you’ll use a lot

1) Line graph (connect the dots)
Good for tracking change over time: steps per day, temperature each hour, slime sales per week.

2) Scatter plot (don’t connect the dots)
Good for comparing two measurements: height vs arm span, practice time vs score.

Reading a graph like a detective

When you look at a graph, ask:

1. Direction: Are we going up, down, or flat?
2. Speed: Is it rising fast or slowly?
3. Smooth vs messy: Are the points close to a path (predictable) or scattered (noisy)?
4. Outliers: Is there a point that doesn’t fit the rest?

That “smooth vs messy” idea matters a lot later—because noise makes prediction harder.

Activity 1 — Graph Your Own Story

Choose something you can measure for a week:

• Hours you sleep each night
• Minutes spent gaming
• Temperature outside
• Steps walked

Pick something you can measure for 7 days (same choices you already have):

• hours of sleep
• minutes spent gaming
• temperature outside
• steps walked

Do this

1. Record the numbers in a table.
2. Make a line graph (paper or a digital tool like Desmos).
3. Answer:
   • What day was highest? Lowest?
   • Is your trend up/down/flat?
   • Predict Day 8. (Explain your reasoning.)

Compute “average change per day”:

$$\text{average change}=\frac{\text{last value} – \text{first value}}{\text{number of days}}$$

Activity 2 — Guess the Graph

Draw (or print):

• Increasing
• Decreasing
• Flat
• Noisy zig-zag

Now ask:

• Which one is hardest to predict—and why?
• Which could be “improving running time”?
• Which could be “plant growing”?
• Which could be “pizza left over time”?

Activity 3 — Make Graph Art

Who says math can’t be creative?

• Use coordinates (x, y) to draw a shape or pixel art picture.
• Try making a heart, star, or smiley face using points.
• You can use grid paper or Desmos for this.

This shows that even art has math hiding inside it!

NEW Activity 4: Feature → Outcome Scatter Plot

Machine learning usually learns from many examples that look like points.

Pick two measurements (real or made-up data):

• hours slept → quiz score
• minutes practiced → shots made
• height → arm span (classic)

Make a scatter plot. Then answer:

• Do you see a trend?
• Would a straight line be a reasonable “model”?
• Are there outliers?

This sets up Lesson 3 perfectly.

How This Connects to Machine Learning

When computers learn, they don’t “see stories.” They see data points.

• Each dot = one example
• The axes = features (measurable inputs)
• A model is a rule that tries to predict an output from inputs

If the points make a clear pattern, prediction is easier.
If the points are scattered, prediction is harder (more noise).

That’s why graphing isn’t just math—it’s a basic tool for data science.

Takeaway Message

Graphs turn math into pictures — and pictures make patterns visible.
Every time you make or read a graph, you’re taking the first step into data science.

Additional Resources

Activities

• Create bar graphs comparing favorite snacks or sports.
• Introduce scatter plots (two related measurements, like height vs. arm span).
• Use Google Sheets to visualize real-world data. Example: ShallWeLearn M4ML Lesson 2 Resource

Bar Graph

Scatter Plot