Reading Scales and Measuring Instruments
11+ papers often test reading values from analogue scales, such as rulers, weighing scales, measuring jugs and thermometers, where the marked intervals are not always single units, so a student must first work out the value of one small division before reading off the pointer, dial or liquid level accurately.
Method
- Before reading any scale, find two neighbouring labelled numbers and count the number of small divisions between them.
- Divide the difference between the two labelled numbers by the number of divisions to find the value of one small division.
- Count how many small divisions the pointer, liquid level or mark sits along from the lower labelled number, then multiply this by the value of one division.
- Add this amount to the lower labelled number to find the exact reading.
- Pay close attention to the units marked on the scale, such as kg versus g, or ml versus litres, and to whether the scale counts up in twos, fives or tens rather than ones.
- On a thermometer or a scale that includes negative values, take extra care when counting across zero.
Worked example
A measuring jug is marked with a labelled line at 200 ml and the next labelled line at 300 ml, with 5 equal divisions between them. The water level is 3 divisions above the 200 ml mark. How much water is in the jug?
- Find the difference between the two labelled marks: 300 - 200 = 100 ml.
- Divide by the number of divisions between them: 100 / 5 = 20 ml per division.
- The water level is 3 divisions above the 200 ml mark, so this represents 3 x 20 = 60 ml above 200.
- Add this to the lower labelled mark: 200 + 60 = 260 ml.
- The jug contains 260 ml of water.
Practice questions
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Q1A ruler is marked in centimetres, with 10 small divisions between each centimetre mark. What does each small division represent?Show answer
Answer: 1 mm (0.1 cm)
Q2A weighing scale has labelled marks at 0 kg and 1 kg, with 4 equal divisions between them. What does each division represent?Show answer
Answer: 0.25 kg (250 g)
Q3On the scale in the previous question, the pointer sits 3 divisions above the 0 kg mark. What weight is shown?Show answer
Answer: 0.75 kg (3 x 0.25 kg)
Q4A thermometer has labelled marks at 0 and 10 degrees C, with 5 equal divisions between them. What temperature does each division represent?Show answer
Answer: 2 degrees C (10 / 5)
Q5A measuring cylinder has marks at 100 ml and 150 ml, with 5 equal divisions between them. What does each division represent?Show answer
Answer: 10 ml ((150-100)/5)
Q6On the cylinder in the previous question, the liquid level is 2 divisions above the 100 ml mark. What is the volume of liquid?Show answer
Answer: 120 ml (100 + (2 x 10))
Q7A thermometer is marked from -10 to 0 degrees C, with 5 equal divisions. What temperature is shown 2 divisions above -10?Show answer
Answer: -6 degrees C (each division is 2 degrees, so -10 + (2 x 2) = -6)
Q8A set of kitchen scales is labelled every 100 g, with 5 small divisions between each label. What does each small division represent?Show answer
Answer: 20 g (100 / 5)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A measuring jug has labelled marks at 400 ml and 600 ml, with 4 equal divisions between them. The water level is 3 divisions above the 400 ml mark. How much water is in the jug?
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A set of bathroom scales is labelled every 10 kg, with 5 equal small divisions between each label. The pointer lies 2 divisions past the 60 kg mark. (a) What does each small division represent? (b) What weight, in kg, does the pointer show? (c) Convert this weight into grams.
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Free printable worksheet
Want more practice on paper? Download the reading scales and measuring instruments worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 12 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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