Week 9: Why Numbers Go Up and Down (What Happens When Demand Exceeds Supply)

Unit 3: Limits and Patterns

This Week's Big Question

Why do some numbers shoot up, level off, or crash?

This week begins with a pattern children can picture: rabbits increase, wolves follow later, and both lines wiggle over time. The lesson stays visual and hands-on before introducing any formal graph labels.

Kid Version in One Sentence

Numbers in a system often go up and down because the parts affect each other.

You'll Discover

• how systems can grow fast, level off, or go too far and crash
• how one population can affect another
• how simple feedback loops can make a change smaller or bigger

Grown-up Note

• Start with rabbits and wolves, birds at a feeder, or cafeteria lines, not formal graph names.
• Use stickers, tokens, or dots before using neat pencil curves.
• Sessions are designed for about 20 minutes. Use the Short Path when you only have 15-20 minutes. Extra Challenge options can stretch closer to 25-30 minutes.

Common Kid Misconceptions

• Misconception: "If a number is rising, that means everything is going well." Response: "A rise can be healthy or it can be a warning, depending on the rest of the system."
• Misconception: "Crashes happen for only one reason." Response: "Usually several connected parts are involved."
• Misconception: "Graphs cause the pattern." Response: "Graphs are just pictures of what the system is doing."

Week at a Glance

Session length	About 20 minutes
Prep time	About 10 minutes
Materials	Stickers or counters, graph paper or plain paper, pencil, Systems Log
Safety	No special safety needs for the main path
Core vocabulary	pattern, loop, rocket curve, leveling-off curve, crash
Older learner words	exponential growth, J-curve, S-curve, overshoot, feedback loop

Core Vocabulary

Word	Kid-friendly meaning
pattern	A shape or behavior that repeats
loop	A change that comes back and affects the system again
rocket curve	A line that shoots upward fast
leveling-off curve	A line that rises and then flattens
crash	A fast drop after a system goes too far

Short Path for Younger Learners

• Build one simple graph with stickers or counters.
• Name three shapes: rocket, leveling-off, and up-too-far-and-crash.
• Draw rabbit and wolf lines as waves.
• End with a Systems Log entry and one spoken explanation.

Success looks like: the child can match a curve shape to a story about what the system is doing.

Extra Challenge for Older Learners

• Compare rabbit and wolf timing on a simple graph.
• Explain balancing loops and amplifying loops in plain language.
• Connect a local pattern, such as birds at a feeder or a cafeteria line, to one of the curve shapes.

Read-Aloud Opening

"Today we are looking at number stories. Sometimes a system grows like a rocket. Sometimes it rises and then levels off. Sometimes it goes too far and crashes. We are going to use animals, stickers, and simple shapes to see why."

Guided Session 1: Build the Shape With Tokens

Time: 20-25 minutes

Materials: counters or stickers, paper

Setup: Make three blank spaces labeled rocket, leveling-off, and crash.

Activity steps:

1. Add more and more counters quickly to show a rocket pattern.
2. Slow the increase and flatten it for a leveling-off pattern.
3. Push the pattern too far and then remove many counters for a crash.
4. Match each shape to a simple story.

What to ask:

• Which shape feels stable?
• Which shape looks risky?
• What might make a number stop rising?

Draw It: Draw the three curve shapes with kid-friendly names.

Talk About It:

• Where have you seen something fill up and then level off?
• What might make a system overshoot its limit?
• Why is a fast rise not always good news?

What success looks like: The child can connect a shape to a system story.

Guided Session 2: Rabbits and Wolves

Time: 20-25 minutes

Materials: paper, markers, Systems Log

Setup: Draw a simple time line and two blank lines.

Activity steps:

1. Start with rabbit numbers rising.
2. Let wolf numbers rise a little later.
3. Show rabbits dropping after wolves increase.
4. Show wolves dropping later when rabbits are scarce.
5. Repeat the wave pattern once more.

What to ask:

• Why don't the two lines rise and fall at exactly the same time?
• Which line changes first?
• What is pulling the system back toward balance?

Draw It: Draw rabbit and wolf lines as waves.

Talk About It:

• What is a balancing loop in this story?
• What would an amplifying loop look like in another system?
• Can you think of a people system that also goes up and down this way?

What success looks like: The child can explain why the two lines take turns rising and falling.

Systems Log

Use this simple entry:

What I noticed:
What moved:
Where it came from:
Where it went:
My drawing:
One question I still have:

Helpful prompts for this week:

• What I noticed: "The line changed shape when..."
• What moved: "The rabbit or wolf number moved..."
• Where it went: "The pattern later went..."
• My drawing: three curve shapes or rabbit and wolf waves

Systems Thinking Move

An environmental system is made of connected parts. When one part changes, other parts may change too. Some changes are quick. Some changes take time. Some effects are easy to see, and some are hidden.

Learner questions:

• What parts are in this system?
• What changes over time?
• What causes what?
• What happens next?
• What feedback loop might make the change stronger or weaker?

Environmental Data Check

• What do these lines or counters measure?
• When does one line change first?
• What labels or axes help me read the pattern?
• What might this graph not show about a real ecosystem?
• Is another source showing a similar pattern?

Engineer Corner

Older learners and facilitators can add the formal labels here.

• Rocket curve can be called a J-curve or exponential growth.
• Leveling-off curve can be called an S-curve.
• Up-too-far-and-crash is often called overshoot and collapse.
• Lotka-Volterra math and more formal feedback analysis belong here, not in the main path.