GCSE · Maths · OCR · Spec J560

Units of measurement

Can you turn cups into grams? Hold that thought. First, drag the ounces below and watch the grams keep pace: it's the whole lesson in one gesture.

Maths · Converting units

Ounces to grams, both ways
0 oz1 oz2 oz3 oz4 oz5 oz6 oz7 oz8 oz9 oz10 ozdrag the ounces →

Ounces: 10/10. Ounces 10 oz. Grams (1 oz ≈ 28 g) 280 g. Grams (170 g ≈ 6 oz) 283.3 g

Ounces10 ozGrams (1 oz ≈ 28 g)280 gGrams (170 g ≈ 6 oz)283.3 g

Drag the handle to choose a number of ounces. The first grams readout uses 1 oz ≈ 28 g, so it scales by the same step every time: 10 oz ↔ 280 g is just the pair 1 oz ↔ 28 g with both sides times 10. Now go backwards: drag until it reads 252 g and see how many ounces that is.

Watch out: The second grams readout starts from a different given relationship (170 g ≈ 6 oz) and lands on a slightly different answer. Neither is 'the' answer — both are approximate, because the relationships they start from are.

Maths · Same thing?

Sort the units by what they measure

What does each unit measure? Pick a unit, then pick its home.

Still to sort

Length (0)

How long, how far.

Mass (0)

What grams, ounces and stone measure.

Volume / capacity (0)

How much space, how much liquid.

Where the line is: A cup is an amount of space, not an amount of mass. That is why it lives here and not with the grams.

10 of 10 still to sort.

The metric system is built on three base units: the metre, the gram and the litre. Imperial units are an older system with no prefixes like milli, centi and kilo, and they are not linked to each other by powers of 10. Either way, each unit measures one kind of thing.

Watch out: Cups, tablespoons and teaspoons measure volume, while grams measure mass. So 'how many grams in a cup?' has no fixed answer.

Maths · Metric ratio tables

Your turn to fill in the gaps

Convert 75,000 grams to kilograms. Then convert 0.32 kilometres to centimetres.

  1. The prefix tells you the factor. Kilo means 1000 times, centi means 1/100 and milli means 1/1000, and they work on every metric unit.
  2. Part 1, 75,000 g to kg. Start with the known pair in a ratio table: 1 kg ↔ 1000 g.
  3. missing step
Which line is step 3?

Maths · Comparing lengths

Shortest to longest: commit before you convert

How long each distance is, with the shortest at the top

1 · Shortest5 · Longest

  1. 80 m

  2. 79 cm

  3. 800 cm

  4. 0.87 m

  5. 682.4 mm

Watch out: 800 looks bigger than 80. But 800 cm is 8 m, and 80 m is ten times that.

Stone to kilograms is a straight line

01.534.56010203040Mass in stoneMass in kilograms (approx.)(3, 19)

Mass in stone: 3. Mass in kilograms (approx.): 19

Drag the point along the line →

Watch out: Every point on this line is an estimate, because the relationship it is drawn from, 3 stone ≈ 19 kg, is approximate.

Maths · Reading scales

Count the gaps, then place the readings

This ruler section runs from 2 to 3 inches. Count the gaps between the marks first, and work out how big one gap is. Then place each reading.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Convert, compare and read scales with one tool: the ratio table.

What you need to know

  • Metric units are built on the metre, gram and litre, and each is linked to the others by a power of 10.
  • Centi means 1/100, milli means 1/1000 and kilo means 1000 times, and these prefixes work on every metric unit.
  • Have a goSam says: '3 kilograms is 300 grams, because kilo just means 100.' What should Sam have written?

    3,000 grams

    Kilo means 1000 times; the 1/100 belongs to centi, so Sam multiplied by the wrong prefix's factor.

  • You can only convert between units that measure the same thing: length to length, mass to mass, volume to volume.
  • A cup measures volume and a gram measures mass, so a cup never converts to a fixed number of grams.
  • Have a goOne of these pairs can be converted and one can't. Which can: millimetres to kilometres, or grams to litres?

    Millimetres to kilometres

    Both measure length. Grams measure mass and litres measure volume, so there is no conversion between those two.

  • Imperial units are an older system with no prefixes, and they are not linked to each other by powers of 10.
  • A ratio table does the converting: write the known pair, then multiply or divide both sides by the same number.
  • Metric to imperial needs a given approximate relationship, like 1 ounce ≈ 28 grams, so your answers are approximate too.
  • Have a goUsing 1 ounce ≈ 28 grams, about how many grams is 5 ounces?

    About 140 grams

    Scale both sides of the ratio table by 5, and keep the ≈, because 28 g per ounce is only approximate.

  • Before comparing measurements, put them in the same unit. 800 cm is shorter than 80 m.
  • A conversion graph is a straight line through the origin, y = kx, and you can read approximate conversions off it.
  • To read a scale, count the intervals between two labelled values and work out the increment. It is not always 1.
  • Have a goA scale has 10 intervals between 240 g and 260 g. How big is each interval?

    2 g

    The 20 g between the labels is shared by 10 intervals. It is not 1 g and not 10 g, because you count and divide rather than assume.

The big picture

Converting units is one multiplicative step on a ratio table: a power of 10 inside the metric system, a given approximate relationship between metric and imperial. Only convert units that measure the same thing, compare after putting measurements in one unit, and read a scale by working out its increment.

Key points

1A conversion is one multiplicative step: multiply or divide both sides of a ratio table by the same number.
2Inside the metric system the factor is a power of 10, and kilo, centi and milli tell you which one.
3Metric to imperial uses a given approximate relationship, so the answer is approximate as well.
4Only convert units that measure the same thing, and put measurements in one unit before comparing them.
5To read a scale, count the intervals and work out the increment.

Worked example

Problem

A recipe needs 420 g of flour, but the scales only show ounces. Using 1 ounce ≈ 28 grams, roughly how many ounces is 420 g?

⚠ Watch out

Comparing the numbers instead of the amounts. 800 cm looks bigger than 80 m, but 800 cm is only 8 m. Put both in the same unit, then compare.

🧠

Memory hook

Same thing? Same unit? Then one step on the table.

✓

Check yourself

No peeking. (1) 3.4 kilolitres in litres? (2) Which is longer, 350 mm or 0.4 m, and what did you do first? (3) 3 stone ≈ 19 kg: about how many kilograms is 12 stone?

Flashcards

(12)
What are the three base units of the metric system?
The metre, the gram and the litre.
What does the prefix centi mean?
1/100. One centimetre is 1/100 of a metre.
What does the prefix milli mean?
1/1000. One millimetre is 1/1000 of a metre.
What does the prefix kilo mean?
1000 times. One kilogram is 1,000 grams and one kilolitre is 1,000 litres.
When can you convert from one unit to another?
Only when both measure the same thing: length to length, mass to mass, volume to volume.
Why can't you turn a cup into a fixed number of grams?
A cup measures volume and a gram measures mass.
How are imperial units different from metric?
They are an older system, with no prefixes, and they are not linked by powers of 10.
How many ounces in a pound, and pounds in a stone?
1 pound = 16 ounces and 1 stone = 14 pounds.
How do you convert with a ratio table?
Write the known pair, then multiply or divide both sides by the same number.
What shape and form is a metric to imperial conversion graph?
A straight line through the origin, y = kx.
3 stone ≈ 19 kg. What is 1 stone approximately?
About 19/3 kilograms.
How do you read a scale whose marks are unlabelled?
Count the intervals between two labelled values and work out the increment. Don't assume 1 or 10.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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