SI units and homogeneity: lesson plan (AS 9702, 1.1 to 1.2)

At a glance

The shape of the lesson

Topic

SI units and the homogeneity of physical equations (subtopics 1.1 to 1.2)

Syllabus reference

Cambridge International AS & A Level Physics 9702, 1.1 to 1.2 (Topic 1: Physical quantities and units)

Level

AS (first year)

Duration

60 minutes (single period)

Prior knowledge

Standard form and arithmetic with powers of ten

Central visual model

The base-unit balance: every term of a homogeneous equation has the same base units

Cooperative structure

Quiz-Quiz-Trade (full facilitation guide in the activity materials)

21st century skills

Communication, Collaboration

Assessment

An exit ticket (express the volt; test P = F v), plus circulation during the activity

Learning objectives

By the end of the lesson, learners can

AS (all learners)

recall the six SI base quantities and their units (mass, length, time, current, temperature, amount of substance)
express derived units in terms of SI base units (for example the newton, joule, pascal and volt)
use the SI prefixes from pico to tera and convert between them
test whether a physical equation is homogeneous by comparing the base units of each term
use homogeneity to find the base units of an unknown quantity or constant
explain that homogeneity is necessary but not sufficient for an equation to be correct

Key vocabulary

base quantity, base unit, derived unit, SI prefix, standard form, homogeneous, dimensionally consistent, pure number. Each term is introduced as it is first needed.

The core ideas

From six base units to everything else

Everything in the course is measured in units built from six base units. The newton, joule and pascal are not new ideas but shorthand: each is a combination of kilograms, metres and seconds. Setting the base units out first makes the prefixes and the homogeneity test fall into place.

The six SI base quantities and their units: mass in kilograms, length in metres, time in seconds, current in amperes, temperature in kelvin, amount of substance in moles.

The six SI base quantities required at this level

The newton comes from F equals m a and is kg m per second squared; the joule from one half m v squared is kg metre squared per second squared; the pascal from force over area is kg per metre per second squared.

Derived units are combinations of base units

A number line of SI prefixes from pico to tera, each step a power of ten, with the base unit at ten to the zero in the middle.

The prefixes from pico to tera: each step is a power of ten

Homogeneity: necessary, but not sufficient

An equation is homogeneous when every term reduces to the same SI base units, so the two sides balance. It is a quick and powerful check, but it cannot catch a wrong pure number: a missing factor of one half passes the test. Homogeneity is therefore necessary for a correct equation, but not sufficient.

A level balance: both sides of v squared equals u squared plus 2 a s reduce to metre squared per second squared, so the equation is homogeneous.

Both sides reduce to the same base units, so the balance is level

Lesson sequence

Sixty minutes, phase by phase

Time	Phase	What happens in the room	Resources
0 to 5 min	Starter	Why can a space mission fail over a unit mix-up? Pose: what makes a measurement meaningful? Learners agree a number needs a unit.	Slide 1
5 to 20 min	Teach: units	Introduce the base quantities and units; build the newton, joule and pascal from their defining relations in base units.	Slides 2 to 6, fig-base-units, fig-derived-units
20 to 25 min	Teach: prefixes	Present the prefixes pico to tera; model two conversions, keeping the power of ten explicit.	Slide 7, fig-prefixes
25 to 35 min	Teach: homogeneity	Define homogeneity; model checking an equation and finding the base units of a constant as a class.	Slides 8 to 10, fig-homogeneity
35 to 50 min	Activity	Quiz-Quiz-Trade with the unit and prefix cards: quiz a partner, coach, trade, find a new partner. The teacher notes the most-missed cards.	Quiz-Quiz-Trade card set
50 to 60 min	Plenary	Exit ticket, then review the most-missed cards.	Exit ticket slide

Worked example for the board

The joule, the pascal, and a homogeneity check

Express the joule and the pascal in SI base units, then check that E = ½ m v² + m g h is homogeneous.

Joule: from E = ½ m v², units are kg × (m s⁻¹)² = kg m² s⁻²

Pascal: from p = F / A, units are (kg m s⁻²) / m² = kg m⁻¹ s⁻²

Term ½ m v²: kg × (m s⁻¹)² = kg m² s⁻²

Term m g h: kg × (m s⁻²) × m = kg m² s⁻²

Verdict: both terms and the left side (energy) are kg m² s⁻², so the equation is homogeneous

Testing homogeneity, step by step

write each quantity in the equation in SI base units
work out the base units of every separate term
if every term has the same base units, the equation is homogeneous
to find an unknown unit, rearrange for the unknown and reduce the right side to base units. For F = k x, the spring constant k = F / x = kg m s⁻² / m = kg s⁻²

Running the cooperative task

Quiz-Quiz-Trade

Each learner holds one card with a prompt on the front and the answer on the back. Learners pair up: partner A quizzes partner B and coaches if needed, then they swap roles. Partners trade cards, thank each other, and find a new partner, repeating for about fifteen minutes while the teacher circulates and notes which cards are missed most. A full step-by-step facilitation guide, with the printable card set and a teacher answer key, is provided as the activity in this bundle, so it can be run faithfully, including by a cover teacher.

Why it suits this lesson. Fluency with units underpins the whole course, and it is built by repetition with feedback. Quiz-Quiz-Trade gives every learner many quick rounds of both answering and coaching, so participation is roughly equal and the most-missed cards surface for the plenary.

Examiner traps to pre-empt

What to head off, and how

Trap learners fall into	Teaching move that pre-empts it
Treating the kilogram as a prefix problem.	The kilogram is the SI base unit of mass, even though it carries the prefix "kilo". It is not "grams with a kilo on it" for these purposes.
Believing a homogeneous equation must be correct.	Homogeneity cannot detect a wrong pure number, such as a missing factor of one half. It is necessary but not sufficient.
Moving the digits, not the power of ten, in a prefix conversion.	Keep the power of ten explicit: 1 GW = 10⁹ W. Convert by changing the exponent, then tidy into standard form.
Confusing a derived-unit name with its base-unit form.	The newton is a name; its base-unit form is kg m s⁻². Build the form from the defining relation every time.

Differentiation and assessment

Support, challenge and the checks

Support: a base-unit reference strip and a part-worked homogeneity example with one term left blank.
Challenge: find the base units of the gravitational constant G from F = G m₁ m₂ / r², and explain why a homogeneous equation can still be wrong.
Language: rehearse the frames "the base units of ... are ..." and "this equation is homogeneous because ..." before learners write.

Assessment is formative. Exit ticket question 1: express the volt in SI base units. Exit ticket question 2: is P = F v homogeneous? Justify using base units. Circulating during Quiz-Quiz-Trade gives a quick read on which cards, and which learners, need another pass.

Equipment and resources

the printable Quiz-Quiz-Trade card set and the worksheet from this bundle
a base-unit reference strip for support, and the exit ticket from the final slide
the student topic page Physical quantities and units

Original work by the TheLucidSTEM team. Items are written in the style of the papers; no past paper question is reproduced. Supplied in editable formats so you can adapt them freely.

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