Math // Data & Statistics

Line graphs

Construct and interpret line graphs for continuous data (e.g. temperature over time, plant growth); read intermediate values, identify trends, and solve comparison and difference problems

Ages
10 to 11
Type
Representation
Builds on
2 topics
Leads to
1 topic
Standards
1 code

Quick check

If the learner recorded the temperature outside every hour for a day, could they plot those readings on a line graph with proper labels — and then use it to answer questions like 'when was it warmest?' or 'how much did it drop between 3pm and 6pm?'

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Read values from a line graph showing temperature over a day, including estimating between plotted points
  • Construct a line graph from a table of continuous data, choosing an appropriate scale and labelling axes correctly
  • Use a line graph to solve a two-step problem, such as finding the time period with the greatest rate of change

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Pictograms and tally charts (age 6+)Required

    Data & Statistics // Ages 6 to 9

    Constructing and interpreting line graphs requires vocabulary: axis, scale, continuous data, line graph

  • Line graph problemsRequired

    Data & Statistics // Ages 9 to 10

    Y6 line graph construction and interpretation directly extends Y5 line graph problem-solving

You are here

Line graphs

Ages 10 to 11 // Representation

Leads to

1 topic
  • Understanding fractions (age 10+)Helpful

    Mathematical Thinking // Ages 10 to 11

    Line graphs are one of the representation types referenced by Y6 representation fluency

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For ages 10–11, construct a complete line graph from a table of continuous measurements and use it to answer questions. Choose labelled numerical scales, preserve actual time spacing, plot paired readings and join in order. Read observations, describe trends, compute differences and estimate between observations under an explicit straight-line assumption. With unequal intervals, distinguish total change from change per hour.

Common misconceptions

  • Treats rows as equally spaced times when the time gaps differ.
  • Uses a changing numerical scale along an axis.
  • Swaps coordinates or reads graph height without the time/value units.
  • Treats a line segment as an exact record of every unmeasured value.
  • Names the highest point when asked for the largest change or fastest increase.

Useful representations

  • A paired table and a pupil-constructed time/temperature graph.
  • Axes with equally spaced numerical intervals and visible units.
  • A straight segment between two observations labelled as a model-based estimate.
  • Two intervals showing why total change and change per hour can differ.

Teaching practices

  • Begin with a small familiar table and discuss the variables, units and observation times before drawing.
  • Choose evenly spaced numerical scales that include the data; label each axis and unit.
  • Plot every time/value pair, checking both coordinates before joining points in time order.
  • Introduce unequal time intervals only after equal intervals, preserving the numerical spacing of time.
  • Ask for a trend and a numerical difference, then for an intermediate estimate with its assumption.

Activities to try

  1. 1

    Build a line graph from a table

    Why it works: A line graph is a constructed mapping between paired measurements and labelled numerical axes, not a copied silhouette.

    1. Use temperatures at 09:00 12°C, 10:00 16°C, 11:00 18°C, 12:00 17°C and 13:00 19°C. Name time as the horizontal variable and temperature as the vertical variable.
    2. Choose equal-hour spacing and a vertical scale covering 12–19°C; a 0–20°C axis with equal 2°C intervals and clear minor divisions is one option. Label time and temperature (°C).
    3. Plot each pair yourself, check its horizontal and vertical coordinates, join points in time order, and add an informative title.
    4. Compare your plotted points with the table before viewing a worked answer.
  2. 2

    Read, compare and estimate on your graph

    Why it works: Point height, change and estimated intermediate values answer different questions.

    1. Identify the highest recorded temperature and the interval with the largest increase.
    2. Find the 10:00–11:00 change, then estimate 10:30 using the straight segment and state the assumption.
    3. Explain a flat or falling segment in terms of the measured quantity; distinguish the line from a picture of a journey or landscape.
  3. 3

    Keep unequal time intervals honest

    Why it works: Numerical time spacing determines the plotted rate: 4°C per hour is faster than 3°C per hour although 6°C is the larger total rise.

    1. Plot a second table: 09:00 10°C, 10:00 14°C and 12:00 20°C. Make the 10:00–12:00 gap twice the 09:00–10:00 gap.
    2. Compare the first rise, 4°C in one hour, with the later rise, 6°C in two hours. Calculate change per hour before saying which interval warmed faster.
    3. Explain why the larger total increase is not necessarily the steeper rise when time intervals differ.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma6/5.1a

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