Math Explorer · Grade 5
Lesson progress0 of 10 missions
Chapter 2 · Simple Statistics · Lesson 2.4

Read a Journey on a Distance–Time Graph

A journey graph is a story written with axes, points, and line segments. Learn to tell when a traveler moves away, stops, returns, and changes speed.

Read the axes. Follow the line. Tell the journey.
Grade 5 enrichment 35–50 minutes 10 interactive missions No this lesson required

By the end, you can…

  • read the time and distance axes, including their units;
  • translate rising, horizontal, and falling segments into a journey story;
  • find travel time, stopping time, distance, and speed;
  • compare speeds using steepness;
  • decide whether an average-speed calculation should include stops.
A graph point answers two questions. At what time? How far from the starting point?
Open the mission map
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Mission 1

Meet the two axes

Not completed

In this lesson, a distance–time graph records distance from the starting point along one route, not the total distance travelled. The traveler moves out and back along that route. Returning home reduces the distance from home to zero even though the total distance travelled keeps increasing.

⏱️
Horizontal axis

Time since the journey began

📍
Vertical axis

Distance from the starting point

A point on a distance-time graph A graph with a point at 20 minutes and 2 kilometres. time (minutes)distance (km) 010203040 0123 (20 min, 2 km)
A point combines one time value and one distance value.
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Mission 2

Three line shapes tell three stories

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Rising segment

Horizontal segment

Falling segment

Important: A horizontal line does not mean “moving sideways.” It means the measured distance did not change. For the out-and-back journeys along one route in this lesson, that means the traveler stopped.
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Mission 3

Build Xiaohua’s complete journey

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Xiaohua cycles from home to a library 5 km away, stops once on the way, stays at the library, and then returns home. Use the graph below to put the five events in time order. Use each event exactly once.

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Xiaohua's distance-time journey The graph rises from home to two kilometres, stays horizontal, rises to five kilometres, stays horizontal at the library, then falls back to zero. time since leaving homedistance from home (km) 012345 020m40m1h1h402h20 HomeLibrary
Each small horizontal grid interval represents 10 minutes; each vertical grid interval represents 1 kilometre.
0 mintime
0.0 kmdistance from home
At homejourney event
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Mission 4

Read exact facts from the graph

Not completed

Use the graph above. A corner is a moment when the journey changes: moving becomes stopping, stopping becomes moving, or the direction changes.

Reading strategy

  1. Start at the time on the horizontal axis.
  2. Move vertically to the graph.
  3. Move horizontally to read the distance.
See a worked explanation

Turn minutes into hours

One hour is 60 minutes. Divide minutes by 60: 20 ÷ 60 = ⅓ hour; 40 ÷ 60 = ⅔ hour. For km/h, use kilometres ÷ hours.

A second route: 2 km in 20 minutes means 0.1 km each minute. In 60 minutes at that speed, 0.1 × 60 = 6 km. So the speed is 6 km/h.

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Mission 5

Use steepness to compare speed

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speed = distance travelled ÷ time spent travelling

On the same graph, a moving segment that is steeper upward or downward means more distance is covered in the same amount of time, so the speed is greater.

Moving segmentDistanceTimeSpeed
First part outward2 km20 min = ⅓ h km/h
Second part outward3 km20 min = ⅓ h km/h
Return trip5 km40 min = ⅔ h km/h
Compare steepness only when the axes use the same scales. Compare the size of the rise or fall over the same time interval. A downward segment can be faster than an upward one. A graph can be stretched taller or wider without changing the real journey.
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Mission 6

Average speed depends on the time window

Not completed

The words in the question decide which time belongs in the denominator.

Outward average using all elapsed time

She travels 5 km from 0 to 60 minutes. The 20-minute roadside stop is included.

5 km ÷ 1 h = km/h

Outward average using moving time only

She is actually cycling for 40 minutes, or ⅔ hour.

5 km ÷ ⅔ h = km/h
Ask before calculating: Is this total elapsed time, or moving time only?
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Mission 7

Misconception laboratory

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Mission 8

A tram journey with two stops

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A tram travels from Station A through Station B to Station C, then returns to A. It stops at B on the outward journey, stops at C, and returns without stopping. It follows the same route back. Its speed on both outward moving segments is 48 km/h.

Tram distance-time graph The tram travels from A to B in four minutes, stops one minute, travels to C by minute ten, stops to minute thirteen, then returns to A by minute nineteen. distance from Atime (minutes)045101319ABC
Travel: 0–4 min, stop: 4–5 min, travel: 5–10 min, stop: 10–13 min, return: 13–19 min.
48 km/h = 48 ÷ 60 = 0.8 km per minute
See a worked explanation

Return: 7.2 ÷ 6 = 1.2 km/min; 1.2 × 60 = 72 km/h. Moving-only round trip: 14.4 ÷ 15 = 0.96 km/min; 0.96 × 60 = 57.6 km/h. The 15 moving minutes are 4 + 5 + 6; the stops are excluded because the question says moving-only.

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Mission 9

Journey-graph workshop

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Part A — Choose the graph that matches the story

A runner travels 3 km away from home in 30 minutes, rests for 20 minutes, then returns home in 30 minutes.

Part B — Read a new journey

A walker’s graph joins the following points with straight line segments. Each pair gives (minutes since leaving home, kilometres from home):

(0 min, 0 km) → (15, 1.5) → (25, 1.5) → (45, 4) → (60, 4) → (90, 0)
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Mission 10

Exit ticket

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Try all five questions on your own first. If you need help, use a hint or check an attempt before opening worked review. The optional reflection is not graded.

Final check

Read the units. Decide which time interval the question uses. Then calculate.

Certificate of Mastery

Journey-Graph Navigator

This certifies that

can read distance–time axes, translate line segments into a journey story, identify stops and returns, and calculate speed from a graph.

Read the axes → Follow each segment → Check the units
Teaching notes

The English explanations, animations, segment-speed comparison, misconception tasks, workshop scenarios, feedback, and exit ticket are instructional expansions.