Mass & capacity
Mass/weight (g, kg, t) and capacity/volume (ml, l): compare, measure, estimate.
Mass is how much stuff an object is made of; capacity is how much a container can hold. Both are things we measure with agreed units so that “heavy” and “full” become numbers we can compare.
What it means
Mass measures the amount of matter in an object. In everyday life we call it weight, and we measure it with a balance or scale. The metric units, from small to large, are:
- gram (g) — a paperclip is about
1 g - kilogram (kg) — a bag of sugar is about
1 kg;1 kg = 1000 g - tonne (t) — a small car is about
1 t;1 t = 1000 kg
Capacity measures how much liquid a container can hold. Volume measures how much space something takes up; a container’s capacity is the volume of liquid it holds when full. The metric units are:
- millilitre (ml) — a teaspoon holds about
5 ml - litre (l) — a large water bottle holds about
1 l;1 l = 1000 ml
Three skills go together. Compare: decide which of two objects is heavier, or which jug holds more. Measure: read a number off a scale or a marked jug. Estimate: give a sensible guess before measuring — knowing that an apple is roughly 100 g, not 100 kg, is real understanding. Because each big unit is 1000 of the smaller one, the skip-counting and place value from N2.1 (numbers to 1000) are exactly what you use to convert between them.
Worked examples
1. Convert kg to g. A cat has a mass of 4 kg. Since 1 kg = 1000 g, multiply: 4 × 1000 = 4000 g.
2. Add masses in mixed units. A bag holds 2 kg of flour and 500 g of butter. Convert to the same unit first: 2 kg = 2000 g, then 2000 + 500 = 2500 g, which is 2 kg 500 g.
3. Compare capacities. Jug A holds 1 l 200 ml, jug B holds 950 ml. Convert A: 1 l 200 ml = 1200 ml. Since 1200 ml is more than 950 ml, jug A holds more.
4. Estimate then check. Guess a full mug: about 250 ml? Fill it, pour into a marked jug, read the level. Estimation 180 turns this guess-then-reveal loop into a game.
The generative-art connection
Measurement becomes art when a number drives a picture. Bind a measured mass or capacity to a visual quantity and the reading turns into something you watch change. In the dot-multiplier tool, a single dot multiplies into a starburst — let each 100 g you pour in add one dot, and the growing burst is the mass, counted radially. Or draw a jug as a rectangle and fill a fraction of its height equal to measured ÷ capacity: 750 ml in a 1 l jug fills three-quarters of the bar, and the same rule animates a live “how full” meter. The art makes the abstract unit concrete: bigger number, bigger picture, in exact proportion.
Common misconceptions
- “Bigger is heavier.” Size is not mass. A huge beach ball is lighter than a small metal ball; you must weigh, not eyeball.
- “Millilitres are for liquids, litres for big things.” They measure the same thing at different scales —
1 l = 1000 ml— just as1 kg = 1000 g. Pick the unit that keeps the number tidy. - Losing the unit.
2 kgand2 gare wildly different. A number without its unit means nothing when measuring.
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.
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A watermelon has a mass of `3 kg`. How many grams is that? (Remember `1 kg = 1000 g`.)
Answer
`3 × 1000 = 3000 g`. Skip-count in thousands: 1000, 2000, 3000.
Art hook A radial mass counter: place one dot on a circle for every `1000 g`, evenly spaced. `3 kg` shows 3 dots at 120° apart forming a triangle; type a bigger mass and watch the ring of dots grow and re-space evenly.
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A bottle holds `1 l 250 ml` of juice and a carton holds `900 ml`. Which holds more, and by how much?
Answer
Convert the bottle: `1 l 250 ml = 1250 ml`. Compare: `1250 > 900`, so the bottle holds more, by `1250 − 900 = 350 ml`.
Art hook Two vertical jug bars side by side, each `1 l` (1000 ml) tall. Fill each to its measured level; the taller fill lights up green and a small label shows the `350 ml` gap between the two liquid surfaces.
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Put these masses in order from lightest to heaviest: `500 g`, `2 kg`, `1 kg 300 g`, `750 g`.
Answer
Convert all to grams: `500 g`, `2000 g`, `1300 g`, `750 g`. Order: `500 g`, `750 g`, `1 kg 300 g`, `2 kg`.
Art hook A horizontal number line from 0 to 2000 g. Drop a dot for each mass at its true position; dots spaced by real value, not by typing order, so the ordering appears visually as you add them.
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You want about `2 l` of water for a recipe. You have a `500 ml` cup. How many full cups do you need to pour?
Answer
`2 l = 2000 ml`. Count in 500s: 500, 1000, 1500, 2000 — that is `4` cups.
Art hook An animation that pours one `500 ml` cup into a `2 l` tank per click; the tank fills in four equal blue steps and a counter ticks 1, 2, 3, 4 until it reaches the full line.
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Pick the sensible estimate. Is a full school backpack about `4 g`, `4 kg`, or `4 t`?
Answer
`4 kg`. `4 g` is about four paperclips (far too light) and `4 t` is heavier than a car, so `4 kg` is the only reasonable choice.
Art hook A three-way slider labelled g / kg / t. Drag a picture of an object onto the correct band; a correct drop snaps it in place with a gentle colour pulse, a wrong one bounces back.
Training exercises
Practice problems, easier first, that build toward the bar above. Each doubles as a seed for an interactive artwork.
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Which unit would you use to measure how heavy a big dog is: grams `g` or kilograms `kg`?
Answer
Kilograms `kg` (a big dog is roughly `20`–`30 kg`; measuring it in grams would give a huge, messy number).
Art hook A unit-picker wheel: an object appears in the centre and you click the matching unit segment (g, kg, t, ml, l) around it; the chosen segment lights up.
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How many millilitres are in `1 litre`?
Answer
`1 l = 1000 ml`.
Art hook A tall jug that fills in ten steps of `100 ml`; each click adds a shaded band, and when ten bands are stacked the jug tops out at the `1000 ml` = `1 l` line.
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A spoon holds `5 ml`. If you pour `4` spoons into a glass, how much liquid is in the glass?
Answer
`4 × 5 = 20 ml`.
Art hook Skip-count-by-5 drips: each spoon-click drops liquid and moves a marker along a number line marked 5, 10, 15, 20; the drops pool into a rising puddle.
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A bag of apples is `2 kg`. How many grams is that?
Answer
`2 × 1000 = 2000 g`.
Art hook Two dots on a circle (one per kg) each spawn a burst of 1000 tiny grams; the two bursts together visualise `2000 g`.
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Order these from lightest to heaviest: `900 g`, `1 kg`, `300 g`.
Answer
`300 g`, `900 g`, `1 kg` (since `1 kg = 1000 g`, which is the largest).
Art hook Three bars grow to heights matching their mass on a 0–1000 g scale (taller = heavier); arranged left to right they read straight off as the lightest-to-heaviest order.
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A jug is marked in `100 ml` steps. The water reaches the `600 ml` mark. How much water is in the jug?
Answer
`600 ml`. Read the level straight off the mark.
Art hook A draggable water level on a marked jug; as you drag, the readout snaps to the nearest `100 ml` mark and shows the number, teaching scale-reading by feel.
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A melon is `1 kg 500 g`. Change this into grams only.
Answer
`1 kg = 1000 g`, so `1000 + 500 = 1500 g`.
Art hook A split bar: a full `1000 g` block plus a half `500 g` block slide together to build one `1500 g` bar, showing kg-and-g as two joined pieces.
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Bottle A holds `750 ml`. Bottle B holds `1 l`. Which holds more?
Answer
Convert B: `1 l = 1000 ml`. Since `1000 > 750`, bottle B holds more.
Art hook Two jug bars filled to `750 ml` and `1000 ml`; the fuller one glows and a bracket marks the `250 ml` difference between their surfaces.
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You need about `1 l 200 ml` of milk. You have a `200 ml` cup. How many cups is that?
Answer
`1 l 200 ml = 1200 ml`. Count in 200s: 200, 400, 600, 800, 1000, 1200 — that is `6` cups.
Art hook Six `200 ml` cups tip one after another into a jug; the jug fills in six even steps up to the `1200 ml` line while a counter tracks each pour.
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Spot the mistake: Sam says, "My dog is `12 g` because `g` means big." What is wrong?
Answer
`g` means grams, which are tiny (`12 g` is about twelve paperclips). A dog should be measured in kilograms — maybe `12 kg`. Sam mixed up what the unit means.
Art hook A 'unit swap' toggle on a dog picture: flip between `12 g` and `12 kg` and watch the scale needle jump from barely moving to a heavy tilt, making the size of the unit obvious.
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A big feather and a small metal bolt sit on a balance. The bolt's side goes down. Which has more mass, and why can't you tell just by looking at their sizes?
Answer
The bolt has more mass — its side of the balance went down. Size does not equal mass: metal is much heavier than the same-sized puff of feather, so you must weigh, not eyeball.
Art hook An interactive balance beam: drop objects on each pan and the heavier side dips with a spring animation; a 'size' slider changes how big each object looks without changing its mass, proving looks can deceive.
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Estimate first, then say how you would check: about how much water fits in a normal drinking glass — `25 ml`, `250 ml`, or `2500 ml`?
Answer
About `250 ml` is the sensible estimate. `25 ml` is only a few spoons and `2500 ml` is more than two big bottles. To check, pour the glass into a marked jug and read the level.
Art hook An estimate-then-reveal game: pick your guess on a `25 / 250 / 2500` dial, then a jug fills to the true `250 ml` and the gap between guess and truth is shaded to score your estimate.