OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Make calculations using ratios and proportional reasoning to convert units…
Full specification wording
Physics on the move: make calculations using ratios and proportional reasoning to convert units and to compute rates (to include: conversion from non-SI to SI units)
Proportional reasoning means identifying which quantity is directly proportional to which and which is inversely proportional.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 3 of 8
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Proportional reasoning means identifying which quantity is directly proportional to which and which is inversely proportional. For a rate such as speed = distance ÷ time, doubling distance at fixed time doubles the speed, but doubling time at fixed distance halves it, because time sits in the denominator. Convert non-SI units to SI before substituting: 1 km = 1000 m, 1 minute = 60 s, 1 hour = 3600 s, 1 g = 1 × 10⁻³ kg and 1 cm³ = 1 × 10⁻⁶ m³. For example, 72 km/h becomes 72 × 1000 ÷ 3600 = 20 m/s. Use ratio methods to scale consistently, keep track of which variable changes and which is held constant, and check that the computed rate has sensible SI units such as m/s or kg/m³.
What earns the marks
- Identifies whether a named quantity is directly or inversely proportional to the variable being changed before predicting the effect on the rate.
- Converts non-SI units to SI using the correct factor, for example 72 km/h to 20 m/s or 250 g to 0.25 kg.
- Computes a rate by dividing the correct numerator by the correct denominator and attaches the correct SI unit.
- Explains that doubling a denominator variable at fixed numerator halves the rate, whereas doubling a numerator variable doubles it.
Common mistakes and how to put them right
States that doubling any variable doubles the rate.
Put it right: Check whether the variable is in the numerator or the denominator before predicting the change.
Converts kilometres to metres but leaves time in minutes.
Put it right: Convert every quantity to SI before dividing.
Multiplies by a conversion factor in the wrong direction, for example dividing by 1000 when changing km to m.
Put it right: Write the factor as a fraction so the unwanted unit cancels.
Exam tips
- Write the rate equation first, then mark which symbol is on top and which is underneath before reasoning about proportional change.
- Convert all non-SI values to SI in a separate line so a unit slip is easy to spot.
- Check the final unit against the quantity, for example m/s for speed and kg/m³ for density.
Try the lesson
The start of the Physics on the move: make calculations using ratios and proportional reasoning to convert units and to compute rates (to include: conversion from non-SI to SI units) lesson, made from checked teaching notes for this specification point.
Have a go first
A runner completes a 100 m sprint in 20 s. What is the runner's average speed in m/s?
Listen
Proportional reasoning means identifying which quantity is directly proportional to which and which is inversely proportional. For a rate such as speed = distance ÷ time, doubling distance at fixed time doubles the speed, but doubling time at fixed distance halves it, because time sits in the denominator. Convert non-SI units to SI before substituting: 1 km = 1000 m, 1 minute = 60 s, 1 hour = 3600 s, 1 g = 1 × 10⁻³ kg and 1 cm³ = 1 × 10⁻⁶ m³. For example, 72 km/h becomes 72 × 1000 ÷ 3600 = 20 m/s. Use ratio methods to scale consistently, keep track of which variable changes and which is held constant, and check that the computed rate has sensible SI units such as m/s or kg/m³. A strong answer earns marks for these points. Identifies whether a named quantity is directly or inversely proportional to the variable being changed before predicting the effect on the rate. Converts non-SI units to SI using the correct factor, for example 72 km/h to 20 m/s or 250 g to 0.25 kg. Computes a rate by dividing the correct numerator by the correct denominator and attaches the correct SI unit. Explains that doubling a denominator variable at fixed numerator halves the rate, whereas doubling a numerator variable doubles it. Exam tip: Write the rate equation first, then mark which symbol is on top and which is underneath before reasoning about proportional change.
Key words
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Direct and inverse proportionality
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Non-SI to SI conversion factors
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Rate equations and unit consistency
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Ratio scaling with one variable held constant
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See every definition
- Direct and inverse proportionality
- Identifying which quantity is directly proportional to which and which is inversely proportional.
- Non-SI to SI conversion factors
- Factors used to convert non-SI units to SI before substituting, such as 1 km = 1000 m and 1 minute = 60 s.
- Rate equations and unit consistency
- Computing a rate by dividing the correct numerator by the correct denominator and checking that the computed rate has sensible SI units.
- Ratio scaling with one variable held constant
- Using ratio methods to scale consistently while keeping track of which variable changes and which is held constant.
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