OCR · GCSE · Physics

    Course version: J249 · Version from Sept 2018

    Make calculations using ratios and proportional reasoning to convert units…

    Full specification wording

    Motion: make calculations using ratios and proportional reasoning to convert units and to compute rates (to include: conversion from non-SI to SI units)

    This criterion asks you to use ratios and proportional reasoning in two ways: converting between units and computing rates.

    Checked against the OCR J249 specification (opens in a new tab) on .

    • Point 7 of 14
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    This criterion asks you to use ratios and proportional reasoning in two ways: converting between units and computing rates. For unit conversion, build a ratio from known equivalences, such as 1 km = 1000 m or 1 hour = 3600 s, and multiply or divide by that factor. For example, 72 km/h becomes 72 × 1000 ÷ 3600 = 20 m/s. For rates, identify which quantity is divided by which: speed is distance ÷ time, so doubling the distance while time stays fixed doubles the speed, but doubling the time while distance stays fixed halves the speed. Reason about direction and size before calculating, then check the answer's units and magnitude.

    What earns the marks

    • Applies the correct conversion factor to change a non-SI quantity such as km/h into SI units such as m/s.
    • Identifies the numerator and denominator of a rate before substituting values.
    • Predicts correctly that doubling the denominator of a rate while holding the numerator fixed halves the rate.
    • Selects the option whose value and unit both follow from consistent proportional reasoning.

    Common mistakes and how to put them right

    • Assumes doubling any quantity in a rate doubles the result.

      Put it right: Check whether the quantity is in the numerator or the denominator.

    • Multiplies by a conversion factor when division is required.

      Put it right: Set the ratio so unwanted units cancel.

    • Mixes units within one calculation, such as kilometres with seconds.

      Put it right: Convert to SI first.

    Exam tips

    • Write the conversion as a fraction with units so you can cancel them and see the direction of the operation.
    • State which quantity is divided by which before computing a rate.
    • Sanity-check the answer: a speed in m/s should be smaller than the same speed in km/h.

    Try the lesson

    The start of the Motion: 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 distance is given as 250 cm. Using the fact that 1 m = 100 cm, what is this distance in metres?

    Listen

    This criterion asks you to use ratios and proportional reasoning in two ways: converting between units and computing rates. For unit conversion, build a ratio from known equivalences, such as 1 km = 1000 m or 1 hour = 3600 s, and multiply or divide by that factor. For example, 72 km/h becomes 72 × 1000 ÷ 3600 = 20 m/s. For rates, identify which quantity is divided by which: speed is distance ÷ time, so doubling the distance while time stays fixed doubles the speed, but doubling the time while distance stays fixed halves the speed. Reason about direction and size before calculating, then check the answer's units and magnitude. A strong answer earns marks for these points. Applies the correct conversion factor to change a non-SI quantity such as km/h into SI units such as m/s. Identifies the numerator and denominator of a rate before substituting values. Predicts correctly that doubling the denominator of a rate while holding the numerator fixed halves the rate. Selects the option whose value and unit both follow from consistent proportional reasoning. Exam tip: Write the conversion as a fraction with units so you can cancel them and see the direction of the operation.

    See it

    A top-down flowchart with two parallel strands. The first strand runs from a start node labelled non-SI quantity, to building a ratio from a known equivalence, to multiplying or dividing by the factor, ending at an SI quantity node. The second strand begins at a rate node asking to identify numerator and denominator, goes to dividing numerator by denominator, then to checking units and magnitude. Two side branches feed into the rate idea: one node says doubling the denominator with the numerator fixed leads to the rate halving, and another says doubling the numerator with the denominator fixed leads to the rate doubling.
    It shows the two proportional-reasoning routes in the note: converting a non-SI quantity to SI units using a ratio, and computing a rate while tracking how doubling the numerator or denominator changes it.

    Key words

    Say what each word means before you turn the card.

    Ratio and proportional reasoning

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    Conversion from non-SI to SI units

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    Computing rates

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    Checking magnitude and units of an answer

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    See every definition
    Ratio and proportional reasoning
    Used in two ways: converting between units and computing rates.
    Conversion from non-SI to SI units
    Building a ratio from known equivalences and multiplying or dividing by that factor.
    Computing rates
    Identifying which quantity is divided by which, such as distance divided by time for speed.
    Checking magnitude and units of an answer
    Reasoning about direction and size before calculating, then checking the answer's units and magnitude.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart with two parallel strands. The first strand runs from a start node labelled non-SI quantity, to building a ratio from a known equivalence, to multiplying or dividing by the factor, ending at an SI quantity node. The second strand begins at a rate node asking to identify numerator and denominator, goes to dividing numerator by denominator, then to checking units and magnitude. Two side branches feed into the rate idea: one node says doubling the denominator with the numerator fixed leads to the rate halving, and another says doubling the numerator with the denominator fixed leads to the rate doubling.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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