You put a linear scale in front of the class. It runs from 0 mL to 100 mL and has six equally spaced marks, including both labelled endpoints. A student counts the six marks and divides by six.
Ask them to stop and count the spaces between the labelled marks.
Six marks enclose five spaces. The four marks between the endpoints are unlabelled, but that doesn’t change the calculation. A mark identifies a position. A space is the interval from one mark to the next. The unit, mL, tells us what the scale measures.
Find what one space is worth
Ask, “What amount are we sharing, and into how many equal spaces?”
The labelled difference is 100 − 0 = 100 mL. Share that amount across five equal spaces:
100 ÷ 5 = 20 mL per space
On a linear scale, each equal interval represents the same increase, as explained by the NSW Mathematics K–10 Syllabus glossary. Check the result by adding five increments: 20 + 20 + 20 + 20 + 20 = 100 mL.
| Spaces after zero | Reading |
|---|---|
| 0 | 0 mL |
| 1 | 20 mL |
| 2 | 40 mL |
| 3 | 60 mL |
| 4 | 80 mL |
| 5 | 100 mL |
If a student divides by six, ask them to trace each gap with a finger while counting. What they point to shows you whether to revisit the spaces, the labels or the division.
Change the number of spaces
Keep the endpoints at 0 mL and 100 mL, but use ten equal spaces. Each space is now worth 100 ÷ 10 = 10 mL.
Compare the third mark after zero on the two scales. Zero isn’t the first mark after zero. On the five-space scale, three intervals represent 3 × 20 = 60 mL. On the ten-space scale, they represent 3 × 10 = 30 mL.
Ask students why the readings differ even though the endpoints match. The point is simple: a tick mark doesn’t have a fixed value. Its reading depends on the labelled difference and the number of equal spaces.
Start somewhere other than zero
For the next example, use 100 mL and 200 mL as the labelled endpoints with five equal spaces between them. The difference is 200 − 100 = 100 mL, so one space is worth 100 ÷ 5 = 20 mL. The third mark after 100 mL reads 100 + (3 × 20) = 160 mL.
You can also change the span from 100 mL to one litre. One litre equals 1000 millilitres, as set out in the WA Department of Education capacity lesson notes. A scale running from 0 L to 1 L spans 1000 mL. Across five equal spaces, that’s 1000 ÷ 5 = 200 mL per space. This changes the endpoint amount; it isn’t merely a new label for the original 100 mL scale.
Check the jug in front of you
Now use a real calibrated jug. Have students identify the unit and choose two labelled marks. They count every intervening space, check that the scale uses equal increases, calculate one interval and justify the amount of liquid at a marked level.
Different jugs can have different scales, so the labels and divisions on the jug in front of them matter. The WA lesson notes on reading scales make the same practical point. Don’t rely on physical spacing alone to establish equal volume increments on every container.
Keep the language precise as well. A reading describes the amount of liquid currently in the jug. Capacity is the total amount the container can hold. Practical measuring equipment and reasoning between numbered markings are suitable Year 4 contexts in the Mathematics Hub Year 4 guidance.
For further practice
Year 4 Measurement: Unmarked Scales and Partial Units is useful when you want to continue this work across measurement contexts. The unit teaches students to identify labelled values, count equal spaces, calculate the value of one interval and estimate readings between marks. The jug examples above are separate activities.
Listen for the three-part connection
Finish with this challenge: “Choose two labelled marks on a jug. Show the spaces between them, work out what one space represents, then explain one reading.”
Listen for the student to connect the difference between the labelled values, the number of equal spaces and the unit. If the answer is unexpected, ask, “Show me the spaces you counted.” Then check the labels and calculation together.