Pie Charts and Travel Graphs

Lesson 1 of 4: Data Handling

In this lesson:

• Construct and interpret pie charts
• Read and interpret distance-time (travel) graphs
• Solve problems using both types of graph

What You Will Learn Today

1. Construct a pie chart — sector angle = fraction × 360°
2. Interpret a pie chart — recover quantity or percentage from a sector
3. Read a travel graph — distance at a time, stops, speed from steepness
4. Solve word problems using pie charts and travel graphs

Quick Recall: Angles Around a Point

Before we draw a pie chart, we need one fact:

What do angles around a point add up to?

Think for a moment...

• Angles around a point sum to 360°
• A full circle at its centre is 360°
• This is the foundation of every pie chart

From Shillings to Pie Sectors

A family spent 120,000 shillings on a trip:

• Food: 60,000/-
• Transport: 30,000/-
• Other: 30,000/-

What fraction of the money went on food?

Half the money → half the circle → half of 360° = 180°

The formula is just this fraction, applied to 360°.

The Sector Angle Formula Explained

The full circle (360°) represents the total. Each category gets its share:

Two-step habit:

1. Compute every sector angle using the formula
2. Check angles sum to 360° — catches missed ÷ total

Worked Example: Family Trip Budget

Find and Fix the Error

Fruits: Mango 20, Orange 10, Banana 10 (total = 40)

Their working:

• Mango:
• Orange:

Which step did they miss? Write the correct calculation before advancing.

Corrected Working: Mango, Orange, Banana

Your Turn: Pupils by Travel Mode

Now Read a Pie Chart Back

You've just learned to construct a pie chart: table → angles → picture.

Most exam questions go the other way:

You're given the finished chart. Work back to the quantities.

The same relationship, read in reverse:

Transport Sector (90°): Quantity and Percentage

Quantity:

Percentage:

Quick Check: Reading a Percentage-Labelled Chart

A survey of 200 families shows their main income source.
The chart is labelled with percentages: Farming 45%, Trading 30%, Teaching 25%.

How many families are in Farming?

How many families are in Trading? In Teaching?

Pie Charts Are Snapshots — What About Change?

A pie chart freezes one moment — how a total splits right now.

But some stories change over time:

• A bus leaves Kampala, reaches Jinja 60 km away, stops, then returns

How would you show where the bus is at every moment?

The Travel Graph: Read This First

Axes: Time (horizontal) · Distance from start (vertical)

State the scale before reading any value.

What the line shape tells you:

• Sloping upward → moving away
• Horizontal → stopped
• Sloping downward → returning
• Steeper → faster speed

State Scale Before Reading Any Value

Building the Journey: Segment by Segment

• 0–2 h: 0 → 60 km (moving away)
• 2–3 h: stays at 60 km — horizontal (stopped)
• 3–5 h: 60 km → 0 (returning home)

What Is the Traveller Doing Here?

Look at the graph segment between 2 h and 3 h.

In one sentence: what is the traveller doing? Write your answer before advancing.

Common wrong answers:

• "Going back to the start"
• "Travelling very slowly"
• "That time is skipped"

Reading Values Off the Journey Graph

1. Distance at 1 h? → 30 km
2. When is bus 60 km away? → 2 h to 3 h
3. Rest duration? → 1 hour
4. Arrives home? → 5 h

Time on x-axis → up to line → across to y-axis.

Why Steepness Means Faster Speed

Steeper = more distance in the same time = faster.

Steeper ≠ further:

• Two segments can reach the same distance
• The steeper one got there in less time → faster speed

Speed from the Graph: Two Segments Compared

• Outbound: 60 km in 2 h →
• Return (faster): 60 km in 1 h →

Watch Out: Four Common Errors

Pie Chart — Missing ÷ total: use

Travel Graph — Horizontal = stopped, not "going back"

Travel Graph — State scale first: "each square = ?"

Travel Graph — Steeper = faster, not further

Full Problem: The Matatu Journey

A matatu leaves Kampala at 8:00, reaches town 40 km away at 9:00, waits 30 min, returns by 10:30.

Answer — no scaffolding:

1. Average speed to town?
2. Total trip time?
3. Total distance travelled?

speed = distance ÷ time

What You Can Now Do

✓ Construct: ; angles sum to 360°

✓ Interpret: ; ×100% for %

✓ Read travel graph: scale first; horizontal = stopped; steeper = faster

✓ Speed:

Next — data-02: coordinate grid.