Negative numbers in context

Activities to try

1. 1

   Count the gap through zero on a thermometer/number line

   Why it works: An interval that spans zero is found by counting the gap along the line through zero — so many steps up to zero, then so many more beyond — not by a sign rule; you can count both forwards and backwards across zero, and negatives in different contexts behave the same positionally.

   1. Set a starting value in a real context, e.g. the temperature is −4°C, marked on a vertical thermometer or horizontal number line.
   2. Apply a change, e.g. 'it rises by 7 degrees', and move a marker one step at a time, saying each value aloud: −4 → −3 → −2 → −1 → 0, then 1 → 2 → 3.
   3. Deliberately split the count into two parts: how many steps up to reach zero (4), then how many steps beyond zero (3), and record the landing value (3°C).
   4. Count backwards through zero as well: start at 3 and step down in ones — 3, 2, 1, 0, −1, −2 — saying what comes after 0, so you can move both forwards and backwards across zero.
   5. Switch the SAME line into a different context — sea-level depth or a bank balance — keep the start and change equivalent, and notice the number behaves identically even though it means something different.
2. 2

   Order and place mixed negatives and positives

   Why it works: On the number line, further left (colder / lower / deeper in debt) means smaller, so −4 < −1 < 0 < 2 < 5 — the size of the digit does not decide the order for negatives.

   1. Arrange a mixed set such as −4, −1, 0, 2, 5 from smallest to largest on a number line.
   2. Place a single value such as −3 at its correct spot on a labelled line.
   3. Decide which of two values is colder/lower/more in debt, e.g. 'Which is colder, −7°C or −3°C?', and justify using position on the line.
   4. Explain why −4 is smaller than −1 even though 4 is a bigger digit than 1, referencing left-is-less on the line.
3. 3

   Explain the context (optional spoken/role-play extension)

   Why it works: Negatives describe real quantities (depth, temperature, balance); talking through changes rehearses counting through zero in meaningful situations, while noting that not every change actually crosses zero.

   1. Take on a role such as a submarine pilot describing depths below sea level, or a weather presenter describing temperature changes.
   2. Pose and answer questions like 'We were at −30 m and rose 12 m — where are we now?' (−18 m, still below the surface) and 'It was −3°C and rose 8° — how warm now?' (+5°C, passing up through zero), and explain the crossing of zero where it happens.
   3. Reason aloud about which depth/temperature is higher or lower and how you know.