Mathematics K–6 · Years 5–6
Change over time: a line graph of cooling water
Statistics and probability
School laboratory, not for home
In a school laboratory, with a teacher supervising, under the school's risk assessment. Not for home.
The idea
A line graph shows how a quantity changes over time, and the slope of the line shows whether the change is fast or slow.
Safety card
Setting: In a school laboratory, with a teacher supervising, under the school's risk assessment. Not for home.
Hazards
- hot water (up to 55 degrees Celsius) that can scald if a cup tips
- glass thermometer
Controls
- the teacher heats and pours the water and keeps it at or below 55 degrees; the cups stand in a tray at the back of the bench; children read the thermometers where they stand and do not touch or move the cups; spirit thermometers only
Note
Hot water only, heated and poured by the teacher; no burners or chemicals are used by learners, so the Chemical Safety in Schools package is not needed. Follow the school's own procedures for handling hot water.
What you need
- 2 spirit thermometers reading to 1 degree Celsius, one for each cup, and a stopwatch
- a paper cup and a foam cup of the same size, each holding 200 mL of warm water
- a table with columns time in minutes, paper cup temperature, insulated cup temperature
- grid paper with time on the horizontal axis and temperature on the vertical axis
How to do it
- The teacher pours 200 mL of warm water at about 55 degrees Celsius into each cup. Read the room temperature first and record it.
- Read both cups at time 0 and then every 2 minutes for 30 minutes, recording each reading.
- Plot both sets of readings on the same axes and join each set with straight segments.
- Read from the graph how much each cup cooled in the first 10 minutes and in the last 10 minutes, and how long each took to fall by 10 degrees.
- Draw a horizontal line at the room temperature and describe what the two graphs do as they approach it.
What you should see
Both lines fall more quickly at first and more slowly later, so the drop in the first 10 minutes is larger than the drop in the last 10 minutes for both cups. The paper cup line falls faster than the insulated cup line, so the gap between them grows at first and is still open at 30 minutes; the two lines would meet only on a much longer run, when both reach room temperature. Neither line goes below the room-temperature line, and each bends towards it. Reading a temperature between two plotted points from the segment gives a value close to a thermometer reading taken at that time.
What changes
- What you change
- time since pouring
- What you measure
- the water temperature
- What you keep the same
- 200 mL in each cup
- the same starting temperature
- both cups on the same bench away from draughts
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Water cools by the same number of degrees every minute.
- The water will keep cooling until it reaches zero.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-DATA-02MA3-DATA-01MAO-WM-01
- Australian Curriculum v9AC9M5ST02
Sources
The pages the author read to write this activity.