Cambridge Lower Secondary CheckpointStage 8

Thinking and Working Scientifically: Models and representations

Science Stage 8 Chapter Notes

What this chapter covers

Thinking and Working Scientifically: Models and representations
ShareWhatsAppPost
Thinking and Working Scientifically: Models and representations notes

Unable to load PDF

The notes viewer could not load. Please refresh the page.

Read online free. Download a watermarked copy with a free account.

Read the notes

The full Thinking and Working Scientifically: Models and representations notes as text: skim, search, and jump between subtopics.

~11 min read

In this chapter

  1. 1What Are Scientific Models?
  2. 2Different Types of Models
  3. 3Evaluating Scientific Models
  4. 4Representing Data with Graphs
  5. 5Diagrams, Equations, and Symbols

1. What Are Scientific Models?

In science, a model is not a fashion accessory or a toy car. It is a simplified representation of a real-world object, system, or idea. Scientists create models to help understand things that are too complex, too big, too small, too fast, or too dangerous to study directly. For example, we can't see atoms, so we use models to picture what they might look like and how they behave. Similarly, we use a globe as a model of the Earth to understand continents and oceans. Models are essential tools for explaining scientific concepts, making predictions, and communicating ideas to others.

Key term

Scientific Model: A simplified representation of an idea, object, process, or system that is used to describe and explain phenomena that cannot be experienced directly.

Examiner insight

Examiners reward students who can clearly state *why* a specific model is useful for explaining a particular scientific concept, linking the model's features to the science.

Fun fact

The first physical model of the DNA double helix, built by Watson and Crick in 1953, was made from bits of metal, wire, and cardboard. It was crucial in figuring out how genetic information is stored and copied.

Worked example 12 marks

A student uses a large foam ball to represent the Sun and a small marble to represent the Earth. They move the marble around the foam ball. Explain two reasons why this is a useful scientific model.

  1. 1
    1. Identify the purpose of the model: It represents the Sun-Earth system and Earth's orbit.
  2. 2
    1. State the first reason: The model helps to visualize a very large system. It simplifies the immense scale of the solar system into something that can be observed in a classroom, making the concept of orbit easier to understand.
  3. 3
    1. State the second reason: The model can be used to explain phenomena. For example, it can demonstrate how day and night occur as the 'Earth' (marble) spins on its axis, or how seasons occur due to the tilt of the Earth as it orbits the 'Sun' (foam ball).

Recap

  • A scientific model is a simplified representation of a complex reality.
  • Scientists use models to understand things that are difficult or impossible to observe directly.
  • Models are used to explain concepts, make predictions, and communicate ideas.
  • Examples of things modelled include atoms, the solar system, and chemical reactions.

Quick check

  1. State two reasons why a scientist might use a model instead of studying the real thing.2 marks

2. Different Types of Models

Scientific models come in various forms, each suited to different purposes. The main types are:

  1. Physical Models: These are 3D, tangible representations you can touch and see. Examples include a plastic model of a human heart, a ball-and-stick model of a water molecule (H₂O), or a model of the solar system.
  2. Conceptual Models: These are systems of ideas or analogies used to explain a phenomenon. The 'particle theory of matter', which states that all substances are made of tiny, moving particles, is a conceptual model. The 'lock and key' model for enzyme action is another.
  3. Mathematical Models: These use equations or formulas to describe how a system behaves. They show the relationship between different variables. Newton's Second Law, F = ma, is a mathematical model relating force, mass, and acceleration.
  4. Diagrammatic Models: These are 2D drawings that represent something. Examples are very common in science and include electrical circuit diagrams, food webs, ray diagrams for light, and drawings of plant cells.

Key term

Conceptual Model: A representation of a system made of the composition of concepts which are used to help people know, understand, or simulate a subject the model represents.

Worked example 13 marks

For each of the following, state what type of scientific model it is (Physical, Conceptual, Mathematical, or Diagrammatic):a) The equation: Speed = Distance / Timeb) A drawing of a food web for a woodland ecosystem.c) A plastic skeleton used in a biology lab.

  1. 1

    a) Speed = Distance / Time is a Mathematical Model because it is an equation that describes the relationship between speed, distance, and time.

  2. 2

    b) A drawing of a food web is a Diagrammatic Model because it is a 2D drawing representing the flow of energy in an ecosystem.

  3. 3

    c) A plastic skeleton is a Physical Model because it is a tangible, 3D object that represents the structure of the human skeleton.

Recap

  • Physical models are 3D objects you can touch, like a model of a molecule.
  • Conceptual models are ideas that explain how something works, like the particle theory.
  • Mathematical models are equations that describe relationships, like F = ma.
  • Diagrammatic models are 2D drawings, like circuit diagrams or cell drawings.

Quick check

  1. What type of model is a circuit diagram?1 mark
  2. Give an example of a mathematical model used in physics.1 mark

3. Evaluating Scientific Models

No model is a perfect copy of reality. Because they are simplifications, all models have strengths and limitations. A key scientific skill is to evaluate a model by judging how well it represents the real thing.

Strengths are the ways a model is useful. For example, the particle model is good at explaining diffusion and changes of state.

Limitations are the ways a model is inaccurate or incomplete. For example, the particle model shows particles as simple solid spheres, but in reality, they are not solid and have their own internal structure.

Science is a dynamic process. As new evidence is gathered through experiments, models are often tested, modified, or even completely replaced. The model of the atom has changed significantly over the last 200 years, from Dalton's simple sphere to the current quantum mechanical model, with each change prompted by new experimental discoveries.

Key term

Limitation (of a model): A way in which a model is not a completely accurate or complete representation of the real-world phenomenon it describes.

Examiner insight

Marks are often awarded for evaluating a model by stating both a strength and a limitation in a given context. Be specific about what the model does and doesn't show.

Worked example 12 marks

Ball-and-stick models are used to represent molecules. State one strength and one limitation of using a ball-and-stick model to represent a water molecule (H₂O).

  1. 1
    1. Identify a strength: A strength is that the model clearly shows which atoms are bonded together and the basic 3D shape of the molecule. It correctly shows that two hydrogen atoms are bonded to one oxygen atom.
  2. 2
    1. Identify a limitation: A limitation is that the model does not accurately represent the true scale. The 'sticks' representing bonds are not real objects, and the atoms themselves are not solid spheres with fixed positions but are clouds of electrons. Also, the model doesn't show the movement of electrons.

Recap

  • All scientific models are simplifications and have limitations.
  • Evaluating a model involves identifying its strengths and weaknesses.
  • A model's strength is how it helps explain or predict phenomena.
  • A model's limitation is how it is inaccurate or incomplete.
  • Scientific models can change over time as new evidence becomes available.

Quick check

  1. State one limitation of representing the planets in the solar system with small balls.1 mark

4. Representing Data with Graphs

Graphs are a type of model used to show the relationship between variables visually. When plotting graphs from experimental data, you must follow standard conventions. The independent variable (the one you change) goes on the horizontal x-axis. The dependent variable (the one you measure) goes on the vertical y-axis. Key skills include:

  • Choosing a scale: The scale should be easy to use (e.g., increments of 1, 2, 5, or 10) and make your plotted data cover at least half of the graph paper.
  • Labelling axes: Both axes must be labelled with the quantity and its units (e.g., 'Time / s').
  • Plotting points: Points should be marked accurately with a small 'x' or a dot in a circle.
  • Drawing a line of best fit: This is a single, smooth line or curve that passes through or close to as many points as possible, with roughly equal numbers of points on either side. Do not 'join the dots'.
  • Interpreting graphs: You can describe the trend (e.g., 'as temperature increases, the rate of reaction increases'), identify anomalous results (points far from the line of best fit), and calculate the gradient, which often represents a physical quantity like speed or rate of reaction.

Gradient = change in y / change in x (Δy/Δx)

Key term

Line of best fit: A straight line or curve drawn through the centre of a group of data points on a scatter graph to show the trend.

Examiner insight

Examiners look for correctly labelled axes with units, a sensible scale, accurately plotted points, and a smooth line of best fit. When calculating a gradient from a straight-line graph, always draw a large triangle on the line of best fit to improve accuracy.

Worked example 14 marks

A student measures the temperature of cooling water every minute. The results are: Time (min): 0, 1, 2, 3, 4. Temperature (°C): 80, 65, 54, 46, 39. Plot a graph of Temperature (y-axis) against Time (x-axis) and draw a curve of best fit.

  1. 1
    1. Draw and label the axes. Put 'Time / min' on the x-axis and 'Temperature / °C' on the y-axis.
  2. 2
    1. Choose a sensible scale for both axes. For the x-axis, use 2 cm per minute. For the y-axis, use 1 cm per 10°C, starting from 30°C.
  3. 3
    1. Plot each point accurately using a small 'x'. For example, the first point is at (0, 80) and the second is at (1, 65).
  4. 4
    1. Draw a smooth curve of best fit that passes as close as possible to all the points. Do not use a ruler to join the dots, as the trend is a curve.
  5. 5
    1. Check that the graph has a title, such as 'Graph of Temperature against Time for Cooling Water'.

Recap

  • The independent variable goes on the x-axis; the dependent variable goes on the y-axis.
  • Axes must be labelled with the quantity and units.
  • Use a sensible scale that utilises at least half the graph area.
  • Draw a single, smooth line or curve of best fit; do not join the dots.
  • The gradient of a line graph represents the rate of change.

Quick check

  1. When plotting a graph of distance travelled against time, which variable goes on the y-axis?1 mark
  2. What is an anomalous result on a graph?1 mark

5. Diagrams, Equations, and Symbols

Science uses a universal language of diagrams and symbols to represent complex information concisely. This allows scientists worldwide to communicate ideas clearly, regardless of their spoken language.

  • In Chemistry, chemical equations model what happens in a reaction. A word equation like 'Methane + Oxygen → Carbon Dioxide + Water' describes the change. A balanced symbol equation like 'CH₄ + 2O₂ → CO₂ + 2H₂O' also models the law of conservation of mass, showing that the number of atoms of each element is the same on both sides.
  • In Physics, circuit diagrams use standard symbols to represent components like cells, lamps, resistors, and switches. This allows anyone to build or analyse the circuit correctly. Free-body force diagrams use arrows to model the forces acting on an object.
  • In Biology, diagrams are essential for showing the structure of cells, organs, and organisms. Food webs are diagrammatic models that show the complex feeding relationships and energy flow within an ecosystem.

Reactants → Products

Key term

Chemical Equation: A symbolic representation of a chemical reaction, showing the reactants on the left and the products on the right.

Fun fact

The simple 'stick figure' diagrams used to represent organic molecules in chemistry were developed by Friedrich Kekulé in the 19th century after he supposedly dreamt of a snake seizing its own tail, which gave him the idea for the ring structure of benzene.

Worked example 13 marks

Draw a diagram using standard symbols for an electrical circuit containing one cell, a closed switch, and a lamp connected in series.

  1. 1
    1. Recall the standard symbol for a single cell (a long line and a shorter, thicker line).
  2. 2
    1. Recall the standard symbol for a closed switch (a line with a break, with the gate drawn connecting the two ends).
  3. 3
    1. Recall the standard symbol for a lamp (a circle with a cross inside).
  4. 4
    1. Draw these three components connected one after another in a single, continuous loop using straight lines for the connecting wires.

Recap

  • Standard symbols and diagrams are a universal language in science.
  • Chemical equations model chemical reactions and the conservation of mass.
  • Circuit diagrams use standard symbols to represent electrical components.
  • Food webs are diagrams that model energy flow in an ecosystem.

Quick check

  1. In the chemical equation 2H₂ + O₂ → 2H₂O, what are the reactants?1 mark
  2. Draw the scientific symbol for an open switch.1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Define the term 'scientific model' and give one reason why a scientist might use a model to study the solar system.2 marks
  2. A student uses a plastic model of a human torso to learn the positions of the organs. What type of model is this? State one strength and one limitation of this model.3 marks
  3. Describe the difference between a conceptual model and a mathematical model, giving one clear example of each.4 marks
  4. The particle theory is a model used to explain the properties of solids, liquids, and gases. Explain how this model accounts for the fact that gases can be easily compressed but liquids are considered almost incompressible.3 marks
  5. A student investigates how the extension of a spring changes with the mass added. The results are in the table below. Plot a graph of extension (y-axis) against mass (x-axis). Draw a line of best fit and determine the extension for a mass of 350 g. Data: Mass/g: 0, 100, 200, 300, 400, 500. Extension/cm: 0.0, 2.1, 3.9, 6.0, 8.1, 10.2.5 marks
  6. Explain why scientists' model of the atom has changed several times over the past 200 years.3 marks
  7. Draw a diagram of a simple electrical circuit containing a battery of two cells, a closed switch, and a lamp, all connected in series. Use standard scientific symbols.3 marks
  8. Write the balanced symbol equation for the reaction between hydrogen (H₂) and oxygen (O₂) to form water (H₂O). Explain how this equation models the law of conservation of mass.4 marks
  9. A bar chart is used to show the number of students in a class who prefer different fruits. A line graph is used to show how the temperature of a beaker of water changes over time. Explain why a different type of graph is used for each investigation.4 marks
  10. Evaluate the use of a food web as a model for an ecosystem. In your answer, you should state one way it is a useful representation and one way it is limited.2 marks

Go deeper

Practise and revise with member-only material for this chapter.

Workbook

Exam-style practice questions with full worked solutions.

Unlock with a plan

Chapter at a Glance

A single-page summary of every key idea for fast revision.

Unlock with a plan

Free notes are just the start.

Unlock every Workbook and Chapter at a Glance, and generate your own worksheets and predicted papers.

Explore plans

Related chapters

Thinking and Working Scientifically: Scientific enquiry: purpose and planningThinking and Working Scientifically: Carrying out scientific enquiryThinking and Working Scientifically: Scientific enquiry: analysis, evaluation and conclusionsBiology: Structure and functionBiology: Life processesBiology: Ecosystems