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Session 3. Measuring, Maths and Models in Science
Objective. Teach a routine for good measuring (check, repeat, mean, odd one out), turn tables into graphs and ratios that explain a pattern, and use models while asking what they show and what they get wrong.
Pupils often think that a measurement is either right or wrong. Real measurements come with a little doubt, and learning to say how much doubt is one of the most useful habits in science. Models are the same: they are not copies of the world but useful simplifications that can be tested. This lesson goes beyond the key ideas and shows how to compare two results fairly, how to report honest numbers, and how to use models that pupils build, test and improve.
Key ideas
Measure well: a routine pupils can follow
- Check the tool (Session 1), read at eye level to the nearest mark, write the unit every time. Three steps become a habit: measure, repeat, compare.
- Reduce timing error by timing 10 swings or 10 rolls together and dividing. Repeat each measurement three times.
- Look for the odd one out. Ask what happened, then repeat it. Do not delete a value just because it is awkward. If you find a cause, set it aside with a note; otherwise report the range.
From numbers to meaning: tables, graphs and ratios
- A table has the quantity and its unit in each heading, the thing you changed first, and means in the last column. A graph has labelled axes with an even scale and points marked before any line is drawn.
- Ask what the shape says. A straight line through zero means the quantities are proportional: dividing one by the other gives the same number every time. A curve means a different relationship.
- Science uses the same maths tools again and again: ratio and rate (speed = distance / time), mean, unit conversion (cm to m), scale. Name the tool when it appears.
Teach the maths when it is needed
- Pupils who can divide in a maths lesson often freeze when the same division appears in a science table. Model one worked example aloud, then let them do the next one.
- Agree with the maths teacher how the school writes ratios, graphs and units, so pupils meet one notation (see course 8.8 for cross-curricular links).
- Use sentence frames: 'When the length is ___ times bigger, the time is ___ times bigger.' Watch the usual traps: mixed units (cm and m), decimal places, an axis that skips unevenly.
Models: use them and question them
- A model is a simplified stand-in: an object (bottle lung), a diagram, an analogy (current as water), a scale model or an equation. It helps us explain and predict.
- Every model is right about some things and wrong about others. Always ask three questions: What does it show? What does it get wrong? How could we improve it?
- Modelling is a cycle like design: build the model, predict, test against real data, revise it. A model that fails a test is a step forward.
From measurement to model
Uncertainty in plain words
Every tool has a smallest step it can read. A ruler marked in millimetres cannot show a tenth of a millimetre, so a pupil who writes 12.3472 cm has invented digits. Teach 'write only what the tool can show'. When you repeat a measurement, the readings spread a little: the spread is the honest range, for example 14.1 to 14.3 s.
Use ranges to compare. If one group's marble takes 2.2 to 2.6 s and another's takes 2.5 to 2.9 s, the ranges overlap and the groups cannot claim a real difference yet. If the ranges are far apart, the difference is probably real. This simple rule lets Grade 6 pupils argue with evidence and avoid 'my group won' conclusions.
Models that earn their keep
A useful model makes a prediction that can be tested. A model of a lung predicts that a bigger space lets air in: test it by pulling the lower balloon. An analogy, such as current as water in pipes, helps with flow around a loop but misleads where a pipe could leak. Ask pupils to find where the model breaks and to improve it; this is deeper than being told 'models have limits'.
Maths provides models too: a number line, an area model for multiplication, a scale on a map. A scale is a ratio: 1 cm on paper for 2 m in the schoolyard. Let pupils make a model, use it to predict something, test the prediction, and revise the model. That cycle is what scientists and engineers do, and it connects to the design cycle in Session 2.
Examples from the classroom
Do the marbles really differ?
Scene. Dilnoza's Grade 8 class in Samarkand times a marble rolling 2 metres on two surfaces. Group A gets times from 2.2 to 2.6 s, group B from 2.5 to 2.9 s. Pupils at first say B is slower. Dilnoza asks them to draw the two ranges on a line. They overlap between 2.5 and 2.6 s, so the class agrees to repeat 10 more times before claiming a difference.
Insight. Comparing ranges stops pupils from claiming a difference that the data do not support.
One centimetre is two metres
Scene. Aziz's Grade 6 class in Tashkent measures the schoolyard with a rope: 40 metres long. On the board, 1 cm will stand for 2 metres. Pupils work out that the yard is 20 cm on paper, convert 40 m to 4000 cm to check, and draw it. A pupil checks by pacing the length and finds 52 paces, so a pace is about 77 cm.
Insight. A scale is a ratio, and converting units is the same maths in science and geography.
The water-pipe analogy breaks
Scene. Malika in Fergana teaches Grade 7 electric circuits with a water-pipe analogy: the battery is a pump, the wire a pipe. Pupils like it. Then she asks, 'What happens in your model if we cut the pipe?' They say water spills. 'And in a real wire?' Nothing flows, and nothing spills. They write down two things the analogy shows and one thing it gets wrong.
Insight. Asking where an analogy fails builds understanding of both the model and the idea.
Common pitfalls
- Reporting more digits than the instrument can read.
- Declaring a winner when the ranges of two groups overlap.
- Presenting a model as a copy of reality rather than a tool with limits.
- Assuming pupils who can do ratio in maths will use it in science without help.
Pendulum Data, a Graph and a Model Critique
- Open the Activity Kit: pendulum data for four string lengths, three trials of 10 swings each. Read the table and spot the odd value (5 min, pairs).
- Pairs (10 min): decide what to do with the odd value, then calculate the mean time for 10 swings and the time for one swing (the period) for each length.
- Pairs (10 min): draw the graph of period against length on squared paper. Test whether the quantities are proportional by dividing. Complete a sentence frame. Predict the time for 10 swings at 150 cm.
- Groups (8 min): critique the bottle-and-balloon lung model with the three model questions. Agree one improvement.
- Alone (7 min): write your classroom action task from the Kit.
Your facilitator will guide you through this activity in the session.
Questions to discuss
- What did you decide about the odd value, and what did you want to ask the pupils?
- What does the shape of the graph tell you that the table does not?
- Which maths step would your pupils find hardest, and how will you teach it?
Reflect
- Which maths idea (ratio, mean, units, graph) do your pupils struggle with most in science?
- Which model do you use that pupils may take as the real thing?
- Who is the maths teacher you could agree notation with?
Try it tomorrow
- Ask groups to report a range, not one number, in your next practical.
- Give two groups' results and ask pupils to decide whether the difference is real by drawing the ranges.
- Ask 'What does our model get wrong?' once in your next lesson that uses a model.
Further reading and links
Measure with a routine, graph before you conclude, name the maths tool, and ask every model what it shows and what it gets wrong.