M1.4 Stage 2 Measurement

Temperature

Temperature (°C); read & measure with thermometers.

Temperature tells us how hot or cold something is, measured in degrees Celsius (°C) and read off a thermometer.

What it means

Temperature is a number that says how hot or cold something is. We measure it in degrees Celsius, written °C. A colder thing has a lower number; a hotter thing has a higher number.

We read temperature from a thermometer — a scale, usually drawn as a tall line of numbered marks, with a coloured level (liquid or a digital readout) that rises when it gets hotter and falls when it gets colder. Reading a thermometer is exactly like reading a number line stood on its end: you find the mark the level reaches and say that number.

On the Celsius scale two everyday points anchor everything:

Water freezes to ice at 0 °C.
Water boils at 100 °C.

So a cold winter day might be 2 °C, a comfortable room is about 20 °C, and a warm bath is around 40 °C. Body temperature is about 37 °C.

Because the scale can go below zero, temperature is a first, gentle meeting with negative numbers. −1 °C is one degree below freezing — colder than 0 °C, warmer than −5 °C. On the thermometer these numbers sit below the zero mark, counting downward, just as positive numbers count upward.

To read a scale you also need to notice its step: the gap between neighbouring marks. If marks are labelled 0, 10, 20 but there are ten little lines between them, each small step is 1 °C. Count on from the last labelled mark to find the exact reading.

Worked examples

Reading a thermometer. The scale is labelled every 10 °C. The level sits two small marks above the 20 line, and each small mark is 1 °C.

20 + 2 = 22 °C

Comparing. Which is colder, 3 °C or −4 °C? Below zero is colder, so −4 °C is colder. On the line, −4 is to the left of (below) 3.

Change up. It is 15 °C in the morning and rises by 6 °C by noon.

15 + 6 = 21 °C

Change through zero. It is 2 °C and drops 5 °C overnight.

2 − 5 = −3 °C   (two steps down to 0, then three more below)

The generative-art connection

Temperature is a scale from cold to hot — and colour is too. Artists call blues, greens and violets cool colours and reds, oranges and yellows warm colours. That gives temperature a natural picture: map every degree to a colour, and a rising number sweeps the art from icy blue toward glowing red.

The nico.art hue-pulse tool does exactly this — a central dot rotates through a hue wheel, so you can pin one end to 0 °C (cool) and the other to 40 °C (warm) and watch a temperature as a colour. You can also build a thermometer as a plain vertical number line in the Math Learning Center app, drop a marker at today’s reading, and colour the bar below it — the height and the warmth of the colour say the same number two ways.

Common misconceptions

“Bigger number always means bigger temperature — even below zero.” With negatives it flips: −8 °C is colder than −2 °C, even though 8 looks bigger. Read them on the number line — further below zero is colder.
“Every line on the scale is one degree.” Not always. Check the step first: marks might jump by 2, 5 or 10. Count the little lines between two labels to find what one step is worth.
“0 °C means no temperature.” Zero is just the freezing point of water, a chosen landmark — it is still a real temperature, and it can get colder still, into the negatives.

What a learner should be able to solve

The benchmark for mastering this concept — the problems a child at this stage is expected to be able to work through.

A thermometer is labelled every `10 °C` (…10, 20, 30…) and has ten little lines between each label, so each small step is `1 °C`. The coloured level reaches three small marks above the `20` line. What is the temperature?

Answer

`23 °C`. Start at the labelled `20` mark and count on `3` small steps of `1 °C` each: `20 + 3 = 23`.

Art hook Draw a vertical number line 0–40 as a tall bar of stacked cells. A slider sets the level; fill the bar up to that many cells and tint each filled cell along a blue→red ramp so the height AND the colour both read the number.
Put these four temperatures in order from coldest to warmest: `5 °C`, `−3 °C`, `0 °C`, `−7 °C`.

Answer

Coldest → warmest: `−7 °C`, `−3 °C`, `0 °C`, `5 °C`. Further below zero is colder, so `−7` is coldest; then `−3`; then freezing `0`; then `5` above zero.

Art hook Plot the four values as dots on a vertical thermometer number line and connect them coldest-to-warmest with a line that climbs from deep blue at the bottom to warm orange at the top — a visual sorted temperature ladder.
On a winter night it is `3 °C`. By morning the temperature has dropped by `8 °C`. What is the morning temperature?

Answer

`−5 °C`. Count down `3` steps to reach `0 °C`, then `5` more below: `3 − 8 = −5`.

Art hook Animate a marker sliding down a vertical thermometer from 3 through 0 into the negatives, the bar recolouring cool-blue as it crosses zero — the crossing point flashes to mark freezing.
A thermometer is labelled `0, 5, 10, 15, 20` and there are five little lines between each pair of labels. How many degrees is one small step, and what temperature is two small marks above the `10` line?

Answer

Each labelled gap is `5 °C` split into `5` steps, so one small step is `5 ÷ 5 = 1 °C`. Two marks above `10` is `10 + 2 = 12 °C`.

Art hook Interactive ruler-reader: user picks the step size (1, 2, or 5) and the app re-draws the little tick lines between labels, so you SEE how a coarser step stretches the same colour bar over fewer marks.
Which is colder, `−9 °C` or `−4 °C`? Explain how you know.

Answer

`−9 °C` is colder. Both are below zero, and `−9` sits further down the thermometer (further below `0`) than `−4`, so it is the colder one — even though `9` looks bigger than `4`.

Art hook Two dots placed on the same vertical thermometer line; the lower (colder) dot glows icy blue and the higher one warmer, making 'further down = colder' unmistakable at a glance.

Training exercises

Practice problems, easier first, that build toward the bar above. Each doubles as a seed for an interactive artwork.

Water freezes into ice at `0 °C` and boils at `100 °C`. Is a warm bath at about `40 °C` hotter or colder than freezing?

Answer

Hotter. `40 °C` is well above `0 °C` (freezing), so a warm bath is much hotter than ice.

Art hook A colour-wheel-style dial where 0 °C shows icy blue and 100 °C shows glowing red; the user drags the needle to 40 and watches the tint land in the warm-orange zone.
A thermometer is labelled every `10 °C`. The coloured level reaches exactly the `30` line. What is the temperature?

Answer

`30 °C`. The level sits right on a labelled mark, so you just read the label — no counting-on needed.

Art hook A read-the-level game: a marker snaps to whichever labelled line the fill reaches; when it lands exactly on a label the number flashes green, so 'sits on the label = just read it' is the reward.
On a scale with each small step worth `1 °C`, the level is four small marks above the `20` line. What is the reading?

Answer

`24 °C`. Count on from the labelled `20` mark: `20 + 4 = 24`.

Art hook Number-line-on-its-end: user clicks up/down arrows to move a marker one small step at a time, the live reading number updating as the fill colour warms.
Which is warmer, `18 °C` or `9 °C`?

Answer

`18 °C` is warmer, because `18` is the bigger number and both are above zero, so the higher number is the hotter temperature.

Art hook Two thermometers side by side, filled to 18 and 9; the taller, warmer-coloured bar visibly wins.
It is `12 °C` in the morning and the day warms up by `7 °C` by lunchtime. What is the lunchtime temperature?

Answer

`19 °C`. Add the rise: `12 + 7 = 19`.

Art hook Animate the coloured level climbing 7 cells up the bar, the tint shifting a little warmer as it rises.
Spot the mistake. Sam says: 'It was `1 °C`, then it dropped `4 °C`, so now it is `3 °C`.' Is Sam right? If not, give the correct answer.

Answer

Sam is wrong — dropping means going down, not up. Count down `1` step to `0`, then `3` more below: `1 − 4 = −3 °C`.

Art hook Show two markers on a vertical thermometer: Sam's wrong jump up to 3 in grey, and the correct slide down through 0 to −3 in blue, so the mistake is the arrow pointing the wrong way.
Order these from coldest to warmest: `7 °C`, `0 °C`, `−2 °C`.

Answer

Coldest → warmest: `−2 °C`, `0 °C`, `7 °C`. Below zero is coldest, then freezing, then above zero.

Art hook Three dots dropped onto a vertical thermometer, then snapped into cold-to-hot order with a blue→red colour trail linking them.
A thermometer is labelled `0, 2, 4, 6, 8, 10`, with two little lines between each pair of labels. How many degrees is one small step?

Answer

One small step is `1 °C`. Each labelled gap is `2 °C` split into `2` steps: `2 ÷ 2 = 1`.

Art hook Step-size explorer: change the label spacing and tick count, and the app tells you what one little line is worth — reinforcing 'always check the step first.'
It is `4 °C` and overnight it drops `6 °C`. What is the new temperature?

Answer

`−2 °C`. Count down `4` steps to `0 °C`, then `2` more below: `4 − 6 = −2`.

Art hook Marker slides down a thermometer past the glowing 0 line into the blue negative zone, which brightens as it crosses freezing.
Which is colder, `−1 °C` or `−6 °C`? How do you know?

Answer

`−6 °C` is colder. It is further below zero than `−1 °C` on the thermometer, so it is the colder one.

Art hook Two dots below the zero line of a vertical thermometer; the deeper (colder) one is painted a darker, icier blue.
On a thermometer where each small step is `2 °C`, the level is three small marks above the `10` line. What is the reading?

Answer

`16 °C`. Each step is `2 °C`, so three steps is `3 × 2 = 6`, and `10 + 6 = 16`.

Art hook Grid where each cell is worth 2 °C; fill 3 cells above the 10 mark and label the running total so skip-counting-by-2 becomes visible.
The temperature at midnight is `−3 °C`. By midday it has risen by `5 °C`. What is the midday temperature?

Answer

`2 °C`. Rising means going up: count up `3` steps to `0 °C`, then `2` more above: `−3 + 5 = 2`.

Art hook Animate a marker climbing from −3 up through the zero line into positive territory, the bar recolouring blue→warm as it passes freezing.