Students fit gears to a motor-driven winch, find by testing that a small gear driving a big one is slower and stronger by the same factor, work out ratio, speed, strength and lift time, choose pairs for a brief, meet a brief where constraints conflict, then write a brief of their own.
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Students will be able to
I can work out a gear ratio as driven teeth ÷ driver teeth.
I can explain that a ratio makes the output slower and stronger by the same factor.
I can check a design against every criterion in a brief.
I can explain what to do when no design meets every constraint.
Timing
Predict and Try 8 min · Worked example 12 min · Vary 12 min · Practise and Make 13 min
Before class
Try every board yourself. LEGO Technic or Meccano gears make a good start before the board: mark a tooth on each gear, turn the small one once and count.
Simplifications: no friction or losses (real gear meshes lose a few per cent each), the motor lifts exactly 200 g with no gears, and the bucket rises at a steady speed. Years 9–10 can add 80% efficiency per mesh.
Curriculum hooks: Design and Technologies, engineering principles and systems (primary); Science, forces and simple machines; Maths, ratio and rates (applied, not taught). If the class has not met ratio, do that first.
Maths for the time: 1 m ÷ 0.1 m a turn = 10 winch turns; turns ÷ turns a minute × 60 = seconds.
Running the lesson
Predict: ask a few students to say why they chose their option before the Try.
Try: the dot moves a third of a turn. Ask how many motor turns make one winch turn.
Worked example: model it live, line by line, before revealing the prepared lines.
Find the mistake: ask which gear is being driven in Sam's design.
Vary, too heavy: stop the class here. Who would they talk to, and what would they offer?
Make: compare briefs. Did anyone make one pass by speed and another by strength?
The hard part (on purpose)
Students treat speed and strength as separate. Keep returning to 'same factor, opposite directions', and to which gear is being driven.
When students get stuck
What you will see
A question to ask
The fix
A student says the bigger gear turns faster.
Count the winch turns for one motor turn. Is it more or less than one?
The big gear has more teeth to push past, so it turns less.
A student divides the driver by the driven gear (the ratio upside down).
Which gear is being driven? Put that one on top.
Ratio = driven ÷ driver.
A student changes only the speed (or only the strength).
Hang more load. Did the strength change as well as the speed?
Both change, by the same ratio.
A student checks only the load.
Your design lifts it. Is it fast enough?
Check every criterion in the brief.
Answers to the checks
small gear, big gear: The 8-tooth gear on the motor drives the 24-tooth gear on the winch. Compared with the motor, the winch turns… 3 times slower and 3 times stronger. The speed and the strength change by the same factor, in opposite directions.
Count the turns: Press Turn the motor once and watch the orange dot on the winch gear. How far round does it go?
A third of a turn: the 8 teeth of the motor gear push 8 of the winch gear's 24 teeth past, and 8 is a third of 24.
Find the stall: Add 50 g at a time and lift, until the winch stalls.
It lifts 600 g, then stalls at 650 g: three times what the motor lifts with no gears.
The heaviest lift: What is the heaviest bucket the winch lifted (in grams)? 600 600 g: 3 × 200 g. The gears make the winch 3 times stronger.
Check 8 → 24, then 16 → 40: Now 16 → 40 (ratio 2.5). How many turns a minute does the winch make? 48 120 ÷ 2.5 = 48 turns a minute.
Strength: 16 → 40: what is the heaviest bucket it can lift, in grams? 500 200 × 2.5 = 500 g.
Time and criteria: 16 → 40: how many seconds to lift the bucket 1 m? 12.5 1 m needs 10 winch turns. 10 ÷ 48 = 0.208 minutes = 12.5 s. It lifts 450 g (500 ≥ 450) within 15 s, so 16 → 40 passes too.
Find the mistake: Sam's winch stalls with the 450 g bucket. Click the line where Sam's working first goes wrong. line 2 Line 2: the ratio is driven ÷ driver. The 8-tooth gear is now the driven one, so the ratio is 8 ÷ 24 = 1/3. The winch turns 3 times faster and is 3 times weaker: it lifts only about 67 g.
A lighter bucket: The bucket is now 300 g. Find the pair that lifts it fastest within 15 s, and lift with it.
16 → 24 (ratio 1.5): exactly strong enough (300 g) and the fastest at 7.5 s. A lighter load lets you give up less speed.
A faster motor: A faster motor: 180 turns a minute, and the 450 g bucket again. Which pair is fastest now? Lift with it.
16 → 40 (8.3 s). 8 → 24 also passes (10 s); 8 → 40 is too slow (16.7 s).
Too heavy: The bucket is now 700 g. Find a pair that can lift it at all, and lift.
Only 8 → 40 (ratio 5, up to 1000 g) lifts it, and it takes 25 s. No pair is both strong enough and fast enough.
When nothing passes: No pair lifts 700 g within 15 s. What should the engineer do? Go back to the client with the trade-off: allow 25 s, lighten the load, or get a stronger motor When constraints conflict, an engineer shows what each choice costs and agrees which constraint can move.
Ratio: The 16-tooth gear on the motor drives the 24-tooth gear on the winch. What is the ratio? 1.5 24 ÷ 16 = 1.5.
Speed: Motor 120 turns a minute, ratio 5. How many turns a minute does the winch make? 24 120 ÷ 5 = 24.
Strength: The 24-tooth gear on the motor drives the 16-tooth gear on the winch. The motor lifts 200 g with no gears. What is the heaviest lift now, to the nearest gram? 133 Ratio 16 ÷ 24 = 2/3, so 200 × 2/3 ≈ 133 g. Faster, but weaker.
A bike: On a bike's lowest gear (small gear at the pedals, big gear at the back wheel) hills feel easy. What do you give up? Speed: you pedal many times for each turn of the wheel Small driving big: slower and stronger. Easy on hills, slow on the flat.
Exactly one pair: Change the bucket and the time limit until exactly one pair in the kit meets the brief.
One pair passes: you have reasoned from the criteria back to the gears.
Solutions
One possible solution for each task. Other correct programs are fine.
Vary: change one thing › A lighter bucket
Open task: any program that does what the step asks.
Vary: change one thing › A faster motor
Open task: any program that does what the step asks.
Vary: change one thing › Too heavy
Open task: any program that does what the step asks.
Vary: change one thing › When nothing passes
Open task: any program that does what the step asks.
write a brief › Exactly one pair
Open task: any program that does what the step asks.
write a brief › Evaluate
Open task: any program that does what the step asks.
Stretch and support
Stretch: Two pairs in a row (a compound train): 8 → 24, then 8 → 40 on the same axle. What is the overall ratio? Could it lift 700 g, and how long would it take?
Support: Give a table with columns ratio, winch speed, heaviest lift, time, and fill the 8 → 24 row together.
Exit ticket
An 8-tooth gear drives a 40-tooth gear. The motor turns 100 times a minute and lifts 50 g on its own. How fast does the output turn, and what can it lift?
Ratio 40 ÷ 8 = 5, so 100 ÷ 5 = 20 turns a minute, and 50 × 5 = 250 g.
What each step is for
small gear, big gear: Committing to what a small-to-big gear pair does tests the new move before students see it: slower and stronger, by the same factor. Each wrong option is a real slip: bigger is faster, or only one thing changes.
Try: turn it and load it: Counting winch turns settles the speed half of the prediction; adding load until it stalls settles the strength half. Numbers are hidden so students find both by testing.
Worked example: does 8 → 24 meet the brief?: The worked example models the move with numbers: ratio = driven ÷ driver, divide the speed, multiply the strength, then the time and both criteria. The faded example practises it on 16 → 40. Sam's upside-down ratio is planted after the method.
Vary: change one thing: Each task changes one thing in the brief: a lighter load, a faster motor, then a load so heavy that no pair meets both criteria. The last is the engineering point: constraints can conflict, and someone has to decide.
ratios: Ratio the right way up, divide for speed, multiply for strength, and a real-world trade-off.
write a brief: Writing a brief with exactly one passing pair reverses the process: students reason from the criteria to the gears, and the board tests every pair in the kit, as an engineer's checking tool would.
Where it leads
Next: Gear trains (idlers and compound trains), then levers and pulleys (planned).
Code links: a short Python loop can test every gear pair against the brief; the board's Make does this for them.
Physical computing: a motor and a servo on a real winch (Power and motors).