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Reading Scales, Axes and Graphs

Maths · Year 6 Selective
Year 6
Lesson Guide
Explanation
Before reading any dial, jug or axis, work out what one mark is worth: take two labels, subtract, and divide by the number of gaps between them — five marks make four gaps, not five. Labels at nought and two kilograms with four gaps make each mark half a kilogram, so a pointer seven marks round reads three and a half. Never judge the position by eye, because the same-looking pointer could be seven point five on one scale and seventy-five on another.
Your Turn
Labels every 2 kg with 4 gaps between them. What is one mark worth? Check: 0.5 kg.
Watch Out
Halfway between two marks is half a GAP. With 2 kg labels and no smaller marks, halfway is 1 kg.
Explanation
On this paper the reading is almost never the answer. A scale showing fourteen hundred grams with a two-hundred-and-fifty-gram jar on it holds eleven hundred and fifty grams of flour, and if the recipe needs fifteen hundred you are three hundred and fifty short. Three steps, and only the first one was reading the dial. Write the reading down, then read the last line of the question again before doing anything else with it.
Your Turn
A scale reads 1 400 g including a 250 g jar. How much flour is in it? Check: 1 150 g.
Watch Out
Subtract the container before comparing with anything. The scale weighs the jar too.
Explanation
When the question gives an empty reading and a loaded one, subtract before you divide. An empty tray reading two kilograms and a loaded one reading fourteen means twelve kilograms of blocks, and if there are two blocks each is six. Halving the fourteen to get seven forgets the tray entirely. Subtract first, then divide, always in that order.
Your Turn
Empty 2 kg, loaded 14 kg, three identical blocks. What does one weigh? Check: 12 ÷ 3 = 4 kg.
Watch Out
Subtract the empty reading BEFORE dividing. Dividing first gives a number that includes part of the tray.
Explanation
Often the reading is only the input to the real calculation. A jug marked every fifty millilitres with the level three marks up holds a hundred and fifty. Six times as much of a second liquid is nine hundred millilitres, and the total is one thousand and fifty. Six times as much means six times the first amount, not six times the total — and read carefully whether the question wants the second amount on its own or everything added together.
Your Turn
A jug holds 150 mL and you add six times as much of another liquid. What is the total? Check: 150 + 900 = 1 050 mL.
Watch Out
"Six times as much" and "six times as much altogether" are different. Check what is being multiplied.
Explanation
Graph claims on this paper often change the unit. An axis in millimetres and a claim in centimetres are a factor of ten apart, so a bar at a hundred and twenty millimetres is twelve centimetres — a claim of twelve is true and one of one point two is not. And the same question will usually also carry a word trap: more than twice May's sixty needs strictly more than a hundred and twenty, and a hundred and twenty is exactly twice, so that claim fails. Check the unit and the word. Quiz and exercises now.
Your Turn
A bar reads 90 mm. How many centimetres is that? Check: 9 cm.
Watch Out
Convert the claim into the axis's unit, not the other way round. It is easier and there is less to go wrong.
📌 Key Points — this lesson in a nutshell
  • Work out what one mark is worth before reading anything: the gap between two labels, divided by the number of gaps.
  • A reading is rarely the answer. Expect to subtract a container, halve for one item or compare with a target afterwards.
  • Check the units: a graph in millimetres and a claim in centimetres are a hundredfold apart.
  • Halfway between two marks is half a gap — with 2 kg marks that is 1 kg, not 0.5 kg.
Step 1: Introduction
Step 1 of 5
Labels every 2 kg, a mark every 0.5 kg 02468 0 to 2 kg4 gaps2 ÷ 4one mark0.5 kg Count the GAPS between two labels, not the marks: 5 marks make 4 gaps. Labels at 0 and 2 with 4 gaps means each mark is 0.5 kg. The pointer here is 7 marks round: 3.5 kg. Never read the position by eye. A dial that looks "about three quarters" could be 7.5 on one scale and 75 on another.
Subtract the jar 050010001500 scale reads 1 400 g− jar 250 g1 150 g of flourrecipe needs 1 500 gshort by 350 g These questions almost never stop at the reading. Expect one or two more steps. Read 1 400 g, take off the 250 g jar to get 1 150 g of flour, then compare with the 1 500 g the recipe needs: 350 g short. Write the reading down, then read the last line of the question again before doing anything else.
Two identical blocks on the scale 024681012141618 empty tray reads 2 kgloaded reads 14 kg14 − 2 = 12 kgtwo blocksone block 6 kg Take the empty reading off the loaded reading, then divide by how many items are on it. 14 − 2 = 12 kg for two blocks, so one block is 6 kg. Halving 14 to get 7 forgets the tray. Subtract first, then divide — always in that order.
Six times as much of the second liquid 100200300400500 jug reads 150 mL× 6900 mL of the othertotal1 050 mL Marks every 50 mL: the level is three marks up, so 150 mL. Six times as much of the second liquid is 900 mL, and the total is 150 + 900 = 1 050 mL. "Six times as much" means six times the first, not six times the total. Then read whether the question wants the second amount or the total.
The axis says mm; the claim says cm 020406080100120MarAprMayJun rainfall in millimetres "June had 12 cm of rain" the bar reads 120 mm 120 mm = 12 cm ✓ TRUE 10 mm in a centimetre When a claim uses a different unit from the axis, convert before judging it. 120 mm is 12 cm, so that claim is true. A claim of "1.2 cm" would be wrong by a factor of ten. And "June had more than twice May's rain" needs 120 against 2 × 60 = 120 — exactly twice, so false. Two traps in one question: the unit, and the word. Check both. Quiz and exercises now.
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