Read scales on measuring instruments
Read positive, negative and fractional instrument scales, subtract ruler positions and distinguish a tick reading from a between-ticks estimate.
Exam scope and assessment notes
Foundation and Higher share the seven published F:4.4A–G Measures rows. The Higher table says See Foundation Tier; there are no additional H4.4 rows. The chosen eight-lesson split covers instrument scales, time intervals, estimates, nearest-degree angle measurement, three-figure bearings, average speed, density and pressure. Eight lessons and thirty-two original worked/staged cases are StudyForA’s design, not a syllabus-prescribed count. Each structural source link requires the corresponding complete teaching record carrying that source ID, a worked explanation and all Guided, Independent and Transfer stages. F4.4F requires the complete speed lesson; broad F4.4G requires all three speed, density and pressure lessons, not a speed-only partial link. Source binding and substantive structure must belong to the same record; a separate untagged duplicate cannot supply missing evidence. These are structural links, not exhaustive subskill or specialist approval. Preserve the actual calibrated instrument ticks, pointer/meniscus positions, ruler endpoints, units and protractor alignment action. Read labelled scales rather than assuming CSS pixels are millimetres. Use only diagrams explicitly supplied as accurate for measurement; ordinary examination diagrams need not be to scale and must not be measured without instructions. Numerical reference readings, protractor openings and the measured bearing remain hidden before a calibrated learner attempt; revealing a reference is not proof of instrument operation. Keep ideal model values separate from approximate human readings and nearest-degree rounding; no universal automatic tolerance or measurement competence is established. Bearings start at the named origin and run clockwise from declared north, with parallel north assumptions stated and leading zeros retained. Distinguish reverse rays, interior route angles and forward heading changes; no magnetic or globe-navigation correction is inferred. Clock intervals retain am/pm, noon/midnight and day order. Average speed uses total route distance over the full named elapsed interval, including stated stops; displacement and instantaneous speed are different. Calculating time by division requires positive speed: at constant zero speed a positive distance is impossible, while zero distance alone does not determine elapsed time. Keep density mass/volume units compatible and volume positive; liquid displacement is final minus initial level. Combined volumes are added only under the stated no-void/no-volume-change assumption. The pressure formula is supplied in every pressure stage; do not infer that the density or average-speed formula is also supplied. Use a provided force in newtons, positive contact area, correct squared-area conversion and an explicitly limited average-pressure model. No real-world safety or route-feasibility certification follows. The source assessment context uses SI units and may require mathematical instruments. These lessons do not complete4.5 nearest-mm line drawing, formal shape/compass constructions or scale-drawing problems,5.2 transformations,4.8 bearing trigonometry,4.9/4.10 full mensuration or4.11 map/similarity work. No blanket formal-proof waiver is imported. Written practice is self-checked, not automatically marked; acknowledgements and attempts do not award marks or establish mastery. Specialist approval and formal assessment validation remain unestablished. Publisher navigation is separate evidence: literal F4.4D appears in Book2 Shape and Space6, map physical10/pages128–160, and Hub36 Bearings and Scale Drawings, co-tagged F4.5C/F4.11B; those co-tags confer no construction/map credit here. Literal F4.4G appears in Book1 Number5, map physical5/pages255–268, and Hub13 Compound Measures. A/B/C/E/F have no literal4.4 chapter or Hub tag in that map; do not invent one from nearby time or scale-drawing topics. Book1 public uncorrected-proof contents start Number5/Compound measures at256 and end its summary at269, conflicting with map255–268; preserve both references. Book2 chapter start128 and next start161 agree with its map range, but no explicit bearings contents heading locates every skill. Neither relevant chapter body is present in the public samples. Full final-book/Teaching Hub content and pagination alignment remain unverified; chapter links are not full-book or modular teaching credit. The current2026/2027 manual lists linear4MA1 F/H in November2026 and June2027; FR/HR are June2027 only, based on centre eligibility. Vietnam is on the regional-centre list; learner residence alone does not choose an option. The table points to page2 although the list is on physical/printed3. Modular4XMAF/4XMAH cash-ins and4WM units remain separate entries for international centres. This entry context does not create a2027 revision of the Issue2 specification.
Before you begin
- Subtract and divide decimal numbers.
- Order negative numbers and add a positive increment.
- Recognise mm, cm, mL, kg and temperature units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
A scale from 0 to 20 has four equal spaces. What is the value of one interval?
What you will learn
- Find the value of one interval by counting spaces between labelled ticks.
- Read different instruments with their units and handle a nonzero starting position.
- Explain the precision supported by a scale rather than adding unsupported decimal places.
Read the two supplied labelled instrument diagrams. The thermometer has uniform ticks from −10°C to 0°C in five equal intervals; its pointer is three intervals above −10°C. The jug has uniform ticks from 400 mL to 600 mL in eight equal intervals; the indicated liquid level is five intervals above 400 mL. Explain each interval and give both readings. Read the designated liquid level, not the top of the jug.
Read, draw and calculate before comparing. Every requested part and explanation needs your own attempt. The teal protractor and orange rays show your actual placements, including wrong ones. Comparisons do not award marks or establish practical instrument competence.
Coordinates use the original worksheet grid. The entire drawing and your tools rotate together; clockwise bearings retain their direction. Case or orientation changes clear all responses, placements and references. Named given points can be placed exactly; other drawing clicks use the nearest half-unit grid point and never snap to a solution.
Given panel 1
Given scale unit: °C. Read the labelled graduations; screen size is not a physical instrument calibration.
Given panel 2
Given scale unit: mL. Read the labelled graduations; screen size is not a physical instrument calibration.
For this water-like surface, read the lowest central point of the concave meniscus at eye level.
The board retains the last submitted valid placement. Editing a draft invalidates its submission without moving the last drawing; submit again before comparison.
Count spaces before reading the pointer
A scale turns a position into a measurement. First name the quantity and its unit, then choose two numbered ticks. Subtract their values and count the equal spaces between them. The difference divided by the number of spaces gives one interval. Five tick marks from one end to the other make four spaces, so counting marks instead of gaps changes every later reading.
Start from a known labelled tick and move the required number of intervals towards the pointer. Keep the direction of increase shown by the numbers. On a thermometer, moving upwards from −10°C towards 0°C adds positive intervals even while the readings remain negative. A dial can be read in the same way when the question states that its divisions are uniform; do not assume a decorative or irregular dial has equal numerical steps.
Keep the instrument, unit and starting point
A jug might be labelled in millilitres while a mass dial is labelled in kilograms. A numerical reading without its unit is incomplete. Follow the indicated liquid surface convention, reading the stated meniscus level at eye height rather than the rim of the container. On an actual instrument, line up your eye with the pointer or level to reduce the apparent shift caused by looking from the side.
For a ruler, the position of an object’s right end is not its length unless the left end is at zero. Read both endpoints and subtract the starting position from the finishing position. A drawing on a screen has no automatic physical centimetre calibration: use the printed tick labels to read it. Drawing and checking a physical line to a required millimetre accuracy is a separate instrument task, not established merely by reading this scale.
Choose a defensible reading precision
A model pointer exactly on a marked tick has the model reading at that tick. If the pointer lies halfway between two ticks, you can estimate halfway between their values, but say that you estimated. An instrument with coarse marks does not justify a string of extra decimal places. Record enough information to show the scale value, the estimated part and the unit.
Before accepting a result, check that it lies between the surrounding labelled values and has the right sign. If the ticks are missing, the unit is unclear or equal spacing has not been specified, identify the missing information instead of inventing a calibration. Human readings can vary with the quality of a print or display; the reference model is a comparison aid, not evidence that someone has operated a real instrument accurately.
Sources for this lesson
Pause and explain
An object extends from the 22 mm tick to the 61 mm tick. Which is its length?
Worked example
Read the two supplied labelled instrument diagrams. The thermometer has uniform ticks from −10°C to 0°C in five equal intervals; its pointer is three intervals above −10°C. The jug has uniform ticks from 400 mL to 600 mL in eight equal intervals; the indicated liquid level is five intervals above 400 mL. Explain each interval and give both readings. Read the designated liquid level, not the top of the jug.
Show the worked solution
- For the thermometer the change is 0−(−10)=10°C over five spaces, so each interval is 10÷5=2°C. Count spaces, not the six endpoint-and-intermediate marks.
- The thermometer pointer is three intervals above −10°C. Add 3×2=6°C to the starting value: −10+6=−4°C. The negative answer fits between −10°C and 0°C.
- For the jug the change is 600−400=200 mL over eight spaces, so each interval is 25 mL. Five intervals add 125 mL; the level is 400+125=525 mL.
- Both model pointers sit on ticks, so the reference readings are −4°C and 525 mL. Include the units and keep the thermometer and volume scales separate.
Answer Thermometer: −4°C, with 2°C per interval. Jug: 525 mL, with 25 mL per interval.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
On the supplied ruler, an object’s ends align with 12 mm and 47 mm. Find its length in mm and cm. A separate mass dial runs uniformly from 1.0 kg to 1.5 kg in ten equal intervals, with the pointer seven intervals after 1.0 kg. Read the mass and explain the interval.
Give me a hint
Subtract ruler positions. For the dial, divide the half-kilogram change by ten spaces.
Compare my reasoning
- Read the two ruler endpoint positions as 12 mm and 47 mm. Their separation is 47−12=35 mm, even though neither end is at zero.
- There are 10 mm in 1 cm, so 35 mm÷10=3.5 cm. Keep the ruler length distinct from either endpoint reading.
- The dial interval is (1.5−1.0)÷10=0.05 kg. Seven intervals add 7×0.05=0.35 kg to 1.0 kg.
- The mass is 1.35 kg. It lies between 1.0 kg and 1.5 kg, which checks the reading.
Length: 35 mm=3.5 cm. Dial mass: 1.35 kg, using 0.05 kg per interval.
Look for these in your work
- Subtract the ruler’s starting reading from its finishing reading.
- Convert 35 mm to 3.5 cm without changing the length.
- Explain the dial’s ten spaces and label the 1.35 kg reading.
Read both fresh instrument diagrams independently. A pressure gauge runs uniformly from 0.8 bar to 1.2 bar in eight equal intervals. A thermometer runs uniformly from −6°C to −2°C in eight equal intervals. The pointers are drawn but have no numerical value labels; count their positions on the actual scales. State each interval and each reading, showing how far each pointer lies from a known tick.
Give me a hint
Write the labelled numerical difference first. The thermometer increases towards −2°C.
Compare my reasoning
- The pressure change is 1.2−0.8=0.4 bar. Divide by eight spaces to obtain 0.05 bar per interval.
- Three intervals beyond 0.8 bar give 0.8+3×0.05=0.95 bar. This is a scale reading; no pressure-formula calculation is needed here.
- The thermometer change is −2−(−6)=4°C. Divide by eight spaces to obtain 0.5°C per interval.
- Five intervals add 2.5°C to −6°C, giving −3.5°C. It remains negative and lies between the labelled endpoints.
Gauge: 0.95 bar, with 0.05 bar per interval. Thermometer: −3.5°C, with 0.5°C per interval.
Look for these in your work
- Derive both interval values from the labelled endpoints and space counts.
- Keep the negative temperature’s direction of increase correct.
- Give both readings with their different units.
A measuring cylinder has 50 mL steps. The marked meniscus is halfway between the 100 mL and 150 mL ticks. Estimate its reading and explain why 125.000 mL is unjustified. On a separate labelled ruler, an object extends from 1.3 cm to 6.8 cm. Find its length. Use the tick labels rather than trying to measure screen pixels.
Give me a hint
Half of a 50 mL gap is 25 mL. The ruler still requires a difference.
Compare my reasoning
- The meniscus lies halfway through a 50 mL interval, so estimate 100+25=125 mL. State that this is a between-ticks estimate.
- Writing 125.000 mL would suggest a much finer measurement than the shown 50 mL spacing supports. Extra zeros do not improve the instrument.
- For the object, subtract the starting ruler position: 6.8−1.3=5.5 cm. A finishing position of 6.8 cm is not the object’s length.
- Report approximately 125 mL and a ruler separation of 5.5 cm, with the different precision and quantity clear.
Estimated cylinder reading: about 125 mL, without unsupported decimal places. Object length: 5.5 cm.
Look for these in your work
- Interpolate halfway between the stated ticks and call it an estimate.
- Explain why 125.000 mL overstates the supported precision.
- Subtract nonzero ruler positions and preserve the cm unit.
Common mistakes
- Counting tick marks rather than the equal intervals between them.
- Reversing the direction of a negative scale or ignoring the instrument’s unit.
- Using a ruler’s finishing reading as the length, or giving invented decimal precision.
What can you explain now?
Two labelled ticks are 2 kg and 3 kg, with five equal spaces between them. What is one interval, and what is a pointer two spaces above 2 kg?
Compare with the explanation
One interval is 0.2 kg; the pointer is 2.4 kg.
The numerical difference is 1 kg. Divide by five spaces, then add two such intervals to 2 kg. There are six bounding tick marks but only five intervals.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Without looking back, state the three operations: find one interval, count from a known tick, and attach the unit. Then explain why ruler length may require a subtraction and why an estimated liquid reading is not exact.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.