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Reading Scales with Awkward Intervals

Maths · Stage 3
Year 5
Lesson Guide
Explanation
A scale rarely marks every unit. Before you read the pointer, find what one mark is worth: take two labelled values, count the spaces between them, and divide. Labels every ten kilograms with five spaces means two kilograms a mark. Labels every hundred grams with four spaces means twenty-five. Count spaces, not lines — between the twenty line and the thirty line there are five spaces and four lines. Then reading is counting: start at the label just below the pointer and add a mark's worth for every mark.
Your Turn
A jug is labelled 0, 200, 400 mL with 4 spaces between labels. What is one mark? Check: 200 ÷ 4 = 50 mL.
Watch Out
Four lines between two labels means FIVE spaces. Count the gaps you would step across, not the lines.
Explanation
A pointer that sits between two marks is read as a fraction of a mark. Halfway between seven hundred and eight hundred grams is seven hundred and fifty. Halfway between twenty-six and twenty-eight kilograms is twenty-seven. Tests nearly always place the pointer exactly halfway, so that is the word to look for. Write the two neighbouring values down first; then the reading has to sit between them, and you cannot be a whole mark out.
Your Turn
Marks every 2 kg; the pointer is halfway between 40 and 42. Reading? Check: 41 kg.
Watch Out
Halfway between 700 and 800 is 750, not 705. Half of the GAP, not half of one.
Explanation
A scale weighs everything on it, so when a jar of sauce is on the scale, the sauce is the reading minus the jar. Seven hundred and fifty on the scale, three hundred and thirty for the empty jar, four hundred and twenty grams of sauce. If the recipe needs six hundred and fifty, that is two hundred and thirty more. Three steps in one question — read the scale, subtract the container, compare with what is needed — and each is easy, so write the numbers down as you go.
Your Turn
A jug of water reads 650 g; the empty jug is 200 g. How much water? Check: 450 g.
Watch Out
Subtract the container, do not add it. The reading already includes it.
Explanation
The hardest scale question on the selective paper. Empty, the pointer is one mark below ten kilograms; with two blocks on, two marks above forty. First the mark value: ten kilograms in five spaces, two each. So empty is eight and loaded is forty-four. The blocks together are thirty-six, and each is eighteen. An empty scale that does not read zero is a container in disguise, and the reason the mark value comes first is that one mark below ten is eight, not nine. Then read how many things are on the scale, and share.
Your Turn
Marks every 5 kg. Empty: one mark below 20. With three equal bags: one mark above 50. Each bag? Check: 15 and 55; 40 ÷ 3 — not whole, so re-read: empty 15, loaded 55, bags 40 kg together; the question would give a number of bags that divides 40.
Watch Out
Find the mark value before reading "one mark below". One mark below 10 on a 2-kg scale is 8.
Explanation
When several jugs are shown, each has its own scale, and the water heights mean nothing until each is read on its own marks. Jug A is marked every fifty and holds one hundred and fifty; jug B is marked every ten and holds sixty, though the water looks as high; C holds a hundred; D three hundred. B has the least. The picture invites you to compare heights; compare the readings. And a reading feeds the next step, as in Jan's jug: a hundred and fifty of orange juice, six times as much apple, one thousand and fifty altogether. Quiz and exercises now.
Your Turn
Jug X is marked every 25 mL and filled to the 4th mark. Jug Y is marked every 100 mL and filled to the 1st mark. Which holds more? Check: X = 100, Y = 100 — equal.
Watch Out
Two jugs filled to "the third mark" hold different amounts if their marks are worth different amounts.
📌 Key Points — this lesson in a nutshell
  • First find what one mark is worth: the gap between two labels ÷ the number of spaces between them.
  • A pointer between marks is read as halfway (or a quarter) of a mark.
  • A container on a scale: subtract the empty container to get the contents.
  • Two jugs with different scales: compare the amounts, not how high the water looks.
Step 1: Introduction
Step 1 of 5
Labels every 10 kg, five spaces between them 010203040 between 20 and 30 there are 5 spaces 10 ÷ 5 = 2 kg per mark pointer: 3 marks past 20, and a bit more = 26 … then halfway to 28 = 27 Never assume a mark is 1. Count the SPACES between two labels and divide the gap by that count. Labels every 100 g with 4 spaces: 25 g a mark. Every 50 mL with 5 spaces: 10 mL. Every 200 with 4: 50. Spaces, not lines. From the 20 line to the 30 line there are 5 spaces and 4 lines in between. Then reading is counting: start at the label below the pointer, add one mark's worth per mark.
The pointer is halfway between 700 g and 800 g 0100200300400500600700800900 labels every 100 g, marks every 50 g pointer exactly on the mark between 700 and 800 reading: 750 g halfway between two values is their average A pointer between two marks is read as a fraction of a mark: halfway is half a mark's worth added on. Marks every 2 kg, pointer halfway between 26 and 28: 27 kg. Marks every 50 mL, pointer a quarter past 150: about 162 mL. Tests usually put the pointer exactly halfway, so "halfway" is the phrase to look for. Write the two neighbouring values first. Then the reading is between them, and you cannot be a whole mark out.
The jar and the sauce together weigh 750 g. The empty jar weighs 330 g. 750 g− jar 330420 g sauceneed 650230 g more The scale weighs everything on it. Sauce = reading − jar = 750 − 330 = 420 g. Rana needs 650 g of sauce: 650 − 420 = 230 g more. A jug and water weigh 650 mL on the scale; the jug alone is 200: 450 mL of water. Three steps hide in one question: read the scale (halfway!), subtract the container, then compare with what is needed. Write each number down. "750, 420, 230" on the page beats holding them in your head.
Empty, the pointer is one mark below 10 kg. With two blocks on, it is two marks above 40 kg. 010203040 empty: 8 kg 010203040 two blocks: 44 kg one mark = 10 ÷ 5 = 2 kg blocks together: 44 − 8 = 36 each block: 36 ÷ 2 = 18 kg Four steps: mark value, empty reading, loaded reading, subtract, share. Every one is small. "One mark below 10" is 8, not 9 — because a mark is 2. That is why the mark value comes FIRST. An empty scale that does not read 0 is a container in disguise: subtract it exactly as you would a jar. Then "two equal blocks" means halve. Read how many things are on the scale.
Which jug holds the least? 50100150200A: 150 mL 50100B: 60 mL 100200300400500C: 100 mL 5001000D: 300 mL Read each jug on ITS OWN scale. B has the least — 60 mL — even though its water looks as high as A's. Jug A is marked every 50; jug B every 10; jug C every 100; jug D every 100 up to 1 000. Same height, different amounts. The picture invites you to compare heights. The scale is what to compare. Jan's jug: marks every 50 mL, orange juice to 150; six times as much apple juice is 900; total 1 050 mL. Quiz and exercises now.
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