Math // Number Representation & Place Value

Measuring temperature

Use negative numbers in context (temperature, finance, sea level); calculate intervals across zero

Ages
10 to 11
Type
Method
Builds on
1 topic
Leads to
5 topics
Standards
1 code

Quick check

If a bank account goes from −£45 to +£120, can the learner work out the total change — counting through zero to get £165?

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.
  • The temperature falls from 3°C to −5°C — what is the drop? (8 degrees)
  • Calculate the difference between a bank balance of −£120 and £350
  • Order −7, −3, 0, 2, 5 on a number line and find the interval from −7 to 5

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

1 topic
  • Negative numbers in contextRequired

    Number Representation & Place Value // Ages 9 to 10

    Calculating intervals across zero extends Y5 negative number context

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Measuring temperature

Ages 10 to 11 // Method

Leads to

5 topics
  • Coordinates (age 10+)Required

    Geometry // Ages 10 to 11

    Negative coordinates require understanding of negative numbers

  • Fractions on a number line (age 11+)Required

    Number Representation & Place Value // Ages 11 to 12

    Ordering with inequality symbols extends Y6 work with negative numbers in context

  • Positive and Negative NumbersRequired

    Addition & Subtraction // Ages 11 to 13

    Negative number arithmetic extends Y6 using negative numbers in context

  • Linear number sequencesHelpful

    Algebra // Ages 10 to 11

    Sequences crossing zero require negative number understanding

  • Numbers to Ten MillionHelpful

    Number Representation & Place Value // Ages 10 to 11

    Negative number problems may appear in context

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: use negative numbers in directed real-world contexts (temperature, bank balance, sea level) and calculate intervals across zero as a distance on the number line. The key insight is that an across-zero interval decomposes at zero into two magnitudes that ADD (e.g. −2 to 3 = 2 + 3 = 5), and that ordering depends on direction, not digit size (−5 sits below −3 even though 5 > 3). Signed +/−/× arithmetic rules are deferred to later study.

Common misconceptions

  • Treating −5 as larger than −3 because '5 > 3' (ignoring direction)
  • Counting the interval across zero without including the step onto/over 0, or double-counting zero
  • Adding the numbers instead of finding a distance (−5 to 3 answered as −2)
  • Believing there is no number between −1 and 1 other than described, or that zero is negative/positive
  • Reading a fall in temperature as a rise because the digit gets 'bigger' (−2 to −8 seen as warming)

Useful representations

  • Vertical number line / thermometer spanning below and above zero
  • Horizontal number line with zero as the crossing point and interval arcs
  • Real-context strips: temperature scale, sea-level cross-section, bank balance line
  • Interval arcs decomposed at zero (−5→0 is 5, 0→3 is 3, total 8)

Teaching practices

  • Anchor every negative in a directed context (temperature, sea level, bank balance) so the sign means a direction, not a smaller ordinary number
  • Compute intervals across zero as a distance on the number line — count/measure through zero, or add the two sides' magnitudes
  • Use a VERTICAL number line (thermometer) for temperature/sea level so 'colder/lower' maps to physically down
  • Keep the focus on ordering and intervals; defer signed +/−/× arithmetic rules to KS3
  • Contrast 'the difference between −5 and 3' (interval = 8) with the values themselves, so distance is not confused with a single number's value

Activities to try

  1. 1

    Dragging across zero on a vertical number line (thermometer)

    Why it works: An interval that spans zero is the sum of the two distances on each side of zero; direction (not the size of the digit) sets the order of negative numbers, so −5 lies below −3.

    1. Set a start value (e.g. −2°C) and an end value (e.g. 3°C) on a vertical number line scaled like a thermometer.
    2. Drag a marker from the start up through zero to the end, watching the interval light up as two arcs meeting at zero: '2 below → 0' and '0 → 3'.
    3. Read the running interval as it decomposes: 2 + 3 = 5, rather than a single subtraction.
    4. Switch the context (temperature → sea-level cross-section → bank balance, e.g. −£120 below zero and £350 above) while the same number line stays, and repeat the drag.
    5. Compare the positions of −5 and −3 on the scale and state which is lower and why.
  2. 2

    Explain-the-error dialogue: 'convince me on the line'

    Why it works: Verbalising why the zero crossing must be counted exposes the 'subtract the magnitudes' error and reinforces that the interval is the sum of both sides.

    1. Consider a claim such as: 'The temperature fell from 3°C to −5°C, so it dropped 2 degrees.'
    2. Decide whether it is right or wrong, and use a number line to justify your answer.
    3. State where zero is in the journey and how far you travel on each side of it.
    4. Explain in words why the answer is not simply 5 − 3 = 2.
  3. 3

    Ordering and interval consolidation

    Why it works: Ordering negatives and computing across-zero intervals become reliable once the number-line intuition is applied consistently across contexts.

    1. Order a set such as −7, −3, 0, 2, 5 from lowest to highest and place them on a number line.
    2. Find the interval from −7 to 5 by splitting at zero: 7 (below) + 5 (above) = 12.
    3. Set a temperature after a stated fall (e.g. start 3°C, fall 8 degrees → −5°C) by marking it on the line.
    4. Find the difference between a balance of −£120 and £350 and check it against the 'add both sides' method: 120 + 350 = 470.

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
Ma6/2.1c

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