Precision, Sample Size and Replication: a skill companion
A small set of reusable sheets that grow one inquiry skill at Year 10 depth: putting a size on the uncertainty of each reading, finding which reading limits a result, and using the uncertainty of repeated runs to decide whether another class has replicated a result. Print the scaffolds once and slot them into the science lessons you already teach.
What a skill companion is
Inquiry skills are not a topic of their own. They grow inside the units a class teaches all year. So this pack is not a full term of lessons. It is three reusable scaffolds, a map of where they fit, and a short stand-alone lesson for teaching the skill on its own first.
Start here: five minutes
- Read the pairing map on the next page: it gives the instrument, its uncertainty, a useful sample and a replication check for each topic.
- Print the uncertainty sheet when a class chooses equipment, and the replication sheet when two classes have results to compare.
- Cut out the cards once. They are reused all year.
- Open the free interactive unit on your board when you want a worked example of the skill.
- Run the one-page mini-lesson first if you want to teach the skill before folding it into a topic.
The step up from Year 9, and how we write these
The descriptor is the same in Years 9 and 10; the depth is not. In Year 9 students chose a step a tenth of the change and repeated until the mean settled. In Year 10 they give each reading a ± uncertainty (half the smallest division on a scale, one unit of the last digit on a display, about 0.2 s for a hand-held stopwatch), turn it into a percentage, add the percentages when readings are combined, and take half the range of a set of repeats as its uncertainty.
Slot the skill into your science lessons
Every measurement in the year asks how sure we are of each reading, how many readings make a useful sample, and whether another class would get the same answer. This map answers them for one measurement in each Year 10 topic.
| When you teach | The measurement | Instrument and uncertainty | A useful sample | Replication check |
|---|---|---|---|---|
| Heredity: Cell Division and Inheritance (AC9S10U01) | Ratio of purple to yellow kernels | Counts are exact; the uncertainty comes from the sample, not the instrument | Every kernel on several cobs, hundreds in all | Do other classes’ ratios fall near 3 : 1? |
| Evolution by Natural Selection (AC9S10U02) | Share of each colour left after a hunt | Counts, exact | Several hunts by different “birds”, pooled | Does the same colour win on the same background? |
| The Big Bang and the Universe (AC9S10U03) | Distance between dots on a balloon | A flexible tape read to the millimetre: ±0.5 mm | Five dots, each pair measured twice | Do the distance ratios match at each stage? |
| Energy Flow and Climate Change (AC9S10U04) | Rise in temperature of a bottle | A thermometer marked every 1 °C: ±1 °C on a rise; a digital probe is far better | Three pairs of bottles | Is the gap between the bottles the same sign each time? |
| Newton’s Laws of Motion (AC9S10U05) | Trolley acceleration | Light gates (±0.001 s), not a hand stopwatch (±0.2 s) | Ten runs at each mass | Do two classes’ means agree within their uncertainty? |
| Atomic Structure and the Periodic Table (AC9S10U06) | Colour of a flame test | A hand-held spectroscope showing the bright lines, or a printed colour chart | Three splints for each salt | Does another class name the same colour for each salt? |
| Reaction Types and Rates (AC9S10U07) | Mass lost by marble chips in dilute acid | A balance reading to 0.01 g, logged every 30 s | Three runs for each chip size | Do the curves of two groups lie within each other’s scatter? |
The three moves, and the picture that backs each one
When you want a worked example on the board, open the interactive unit and use the picture that matches the move.
- Repeat until the mean settles: “Measured acceleration as repeats are added”.
- See the scatter that sets the uncertainty: “Twelve logged runs of the same ramp test”.
- Check a stray run before trusting the mean: “A series of logged accelerations: find the stray run”.
Put a size on the uncertainty
Every reading carries an uncertainty. On a scale it is half the smallest division; on a digital display, one unit of the last digit; with a hand-held stopwatch, about one reaction time, 0.2 s. A percentage uncertainty compares it with the reading: uncertainty ÷ reading × 100. A rise worked out from two readings carries both readings’ uncertainties. The first row is done for you.
| Reading | Instrument | Uncertainty | Percentage |
|---|---|---|---|
| Length of the ramp: 0.8 m | a metre ruler marked in millimetres | ±0.0005 m | 0.063% |
| Time to roll down the ramp: 1.2 s | a stopwatch started and stopped by hand | ||
| Time to roll down the ramp: 1.204 s | a light gate showing three decimal places | ||
| Mass of the trolley: 512 g | a balance showing whole grams | ||
| Rise in temperature of a bottle, from 21 to 24 °C: 3 °C | a thermometer marked every 1 °C (two readings) |
B. Which reading limits the result?
The trolley’s acceleration is a = 2d ÷ t². Percentages add when readings are combined, and the time is squared, so its percentage counts twice.
Agreement within uncertainty
Three classes timed twelve runs of the same ramp test. For a set of repeats, take half the range as the uncertainty: mean ± half the range. Two results agree when their ranges overlap; if they do not, look for something that was different, not just for bad luck.
| Acceleration (cm/s²) | The twelve runs | Mean | ± half the range | From … to … |
|---|---|---|---|---|
| Class 10A | 207, 202, 205, 203, 206, 201, 204, 205, 202, 206, 203, 204 | |||
| Class 10C | 198, 202, 199, 201, 197, 200, 203, 199, 200, 198, 201, 202 | |||
| Class 10D | 212, 215, 211, 214, 213, 216, 212, 214, 213, 215, 212, 213 |
A. Compare
B. Explain
Teacher note: half the range is a simple Year 10 measure of spread; senior courses refine it. It is enough to see agreement or its lack.
Which uncertainty fits the instrument?
Cut out the twelve cards. Six describe a measurement; six give an uncertainty. Pair each measurement with the uncertainty its instrument allows. Then, for each one, say what would halve its uncertainty.
Teacher note: the answer sheet lists the pairs. A finer scale, a display with one more digit, or a light gate in place of a hand halves most of them.
How long does a ball take to fall?
A tennis ball dropped from 1.5 m falls in about 0.55 s. Timed by hand, each reading is uncertain by about 0.2 s, more than a third of the fall. A phone filming in slow motion at 240 frames a second times it to a few thousandths of a second. Pairs time the fall both ways, work out the acceleration of falling, g = 2h ÷ t², from each, and see which method gives a result worth trusting, and whether the whole class agrees.
We are learning to
- give a reading a ± uncertainty and a percentage uncertainty,
- find which reading limits a calculated result,
- use digital tools to make a measurement more precise.
Success criteria
- I can work out the percentage uncertainty in my hand-timed fall and in my video-timed fall.
- I can say whether my value of g agrees with the class’s, within its uncertainty.
You need
- for each pair: a tennis ball, a metre ruler and tape to mark 1.5 m on a wall, a stopwatch or phone timer, and a phone that films in slow motion,
- the uncertainty and replication sheets (scaffolds 1 and 2), and the cards from scaffold 3, one set per table. Drop from standing height: no chairs or desks.
Lesson flow (about 30 minutes)
| 7 min | By hand Pairs time five drops from 1.5 m with a stopwatch, writing every time down. Ask: “Your times differ by a tenth of a second or more. How sure is any one of them?” |
| 10 min | On video Pairs film three drops in slow motion beside the tape and count frames from release to the ball reaching the floor. Show the board (see the box). Ask: “One frame lasts about 0.004 s. What is the uncertainty in a time counted in frames?” |
| 8 min | Work out g Pairs work g = 2h ÷ t² from each method with its percentage uncertainty (twice the time’s, plus the height’s), then put their video value on the board. While the class compares, tables match the cards. Ask: “Do the video values agree within their uncertainty? Do the hand-timed ones tell us anything?” |
| 5 min | Make it better Pairs name the next improvement: a bigger drop, more drops, or a camera with a faster frame rate, and what each would change. |
Running it shorter? Stop after the video timings, and work out g in your next science lesson.
Watch for these ideas
- Trusting every digit a display shows: a stopwatch reading to 0.01 s is still started by a hand.
- Adding uncertainties in units when the readings are in different units: add the percentages.
- Calling two results different when their uncertainty ranges overlap.
Make it easier, make it bigger
- Easier: give pairs the formula with the numbers in place, and ask only for the two percentage uncertainties.
- Bigger: drop from 1.0, 1.5 and 2.0 m (a teacher holds the highest). Plot h against t²; the gradient is half of g.
Answers and look-fors
The next sheet has the worked uncertainties, the replication check for three classes, the card pairs, and a quick three-level guide.
Answers and look-fors
How sure is each reading?
| Reading | Uncertainty | Percentage | Why |
|---|---|---|---|
| Length of the ramp: 0.8 m | ±0.0005 m | 0.063% | Half of 1 mm |
| Time to roll down the ramp: 1.2 s | ±0.2 s | 17% | Reaction time, about 0.2 s |
| Time to roll down the ramp: 1.204 s | ±0.001 s | 0.083% | One unit of the last digit |
| Mass of the trolley: 512 g | ±1 g | 0.2% | One unit of the last digit |
| Rise in temperature of a bottle, from 21 to 24 °C: 3 °C | ±1 °C | 33% | Two readings, each ±0.5 °C |
For a = 2d ÷ t²: with the stopwatch, 0.063 + 2 × 17 ≈ 34%; with the light gate, 0.063 + 2 × 0.083 ≈ 0.23%. Upgrade the timer first: it limits the result, and squaring doubles its share. The bottle’s rise is better read with a digital probe to 0.1 °C (±0.2 °C on the rise, about 6.7%), or with a longer warming time so the rise is bigger.
Do two results agree?
Class 10A: 204 ± 3, from 201 to 207; Class 10C: 200 ± 3, from 197 to 203; Class 10D: 213.3 ± 2.5, from 210.8 to 215.8. 10A and 10C overlap (201 to 203), so they agree: the result replicates. 10A and 10D do not overlap: every 10D run is higher, which points to something different in the method, such as a steeper ramp, a lighter trolley or a gate placed elsewhere. 10D should check the ramp angle and the trolley’s mass against the written method first. Every class must record the angle, the mass, the gate spacing and all twelve runs.
Uncertainty cards (pairs)
| Cards | Measurement | Uncertainty |
|---|---|---|
| G and A | A length read on a ruler marked in millimetres | ±0.5 mm |
| D and J | A time from a stopwatch started and stopped by hand | ±0.2 s, about one reaction time |
| E and L | A mass on a balance showing two decimal places of a gram | ±0.01 g |
| B and H | A temperature on a thermometer marked every 2 °C | ±1 °C |
| K and F | A volume in a measuring cylinder marked every 5 mL | ±2.5 mL |
| I and C | A time from a light gate showing three decimal places of a second | ±0.001 s |
A quick three-level guide
| Move | Working towards | At standard | Beyond |
|---|---|---|---|
| Precision | writes every digit the display shows | gives each reading a ± uncertainty and a percentage | finds the reading that limits a result and upgrades that instrument |
| Sample size | trusts a single run | takes repeats and uses half the range as their uncertainty | decides how many repeats are worth taking from the scatter |
| Replication | calls any two different means a disagreement | checks whether two results overlap within their uncertainties | explains a real disagreement by a difference in method |
In the mini-lesson, a fall of about 0.55 s timed by hand is uncertain by about 36%, so g by about 73%: almost useless. Counted in frames (±0.004 s) it is about 0.73%, so g lands close to 9.8 m/s².