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 combines one time value and one distance value.
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Mission 2
Three line shapes tell three stories
Not completed
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
Not completed
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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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
Start at the time on the horizontal axis.
Move vertically to the graph.
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
Not completed
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 segment
Distance
Time
Speed
First part outward
2 km
20 min = ⅓ h
km/h
Second part outward
3 km
20 min = ⅓ h
km/h
Return trip
5 km
40 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
Not completed
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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.
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.
★
Mastery result
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.