GCSE · Maths · AQA · Spec 8300
Standard units of measure
A journey takes 1.2 hours. That's 1 hour 20 minutes, right? It looks exactly right, and it's wrong. By the end you'll know why, and never fall for it again.
AQA mark scheme: when a time works out as 9.2 hours, writing 9 hours 12 minutes earns full credit, while 9 hours 20 minutes gains only special-case credit.
Metric units · Length, mass, capacity
Drag along the bar. It is always the same distance; only the unit it is written in changes.
Money · Pounds and pence
Right amount? Right notation? Sort each one.
Each card says what someone MEANT, then what they WROTE. Decide which kind of card it is.
Still to sort
Correct as written (0)
Right amount, written the right way.
Right amount, wrong notation (0)
The value is fine; the way it's written isn't.
Where the line is: If what's written still shows the amount that was meant, it's a notation slip. If it shows a different amount, it's the wrong amount.
Wrong amount (0)
What's written is a different amount of money.
One pound is worth 100 pence, so a penny is one hundredth of a pound. Pounds become pence × 100 (£14 = 1,400p) and pence become pounds ÷ 100 (2,500p = £25).
AQA mark schemes: a money answer has been accepted in either pounds or pence (6.10 or 610p); a pounds answer with one decimal place, such as 13.5 or 14.0, has been described as incorrect money notation, even where no mark was taken off for it; and 65.50, from adding 60 and 5.50 in mixed units, received only special-case credit.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Every unit change is × or ÷ by one number. The trick is knowing WHICH number, because it isn't always 10.
What you need to know
- Convert between metric units of length, mass and capacity using kilo (× 1,000 of the unit), centi (a hundredth) and milli (a thousandth).
- Convert area units with the squared factor and volume units with the cubed factor.
- Change a decimal number of hours into hours and minutes by multiplying the decimal part by 60.
- Convert between seconds, minutes, hours and days using 60, 60 and 24.
- Write money correctly in pounds (two decimal places) or in pence, never both at once.
- Work out speed, density and pressure by dividing, and give the unit built from the two quantities.
The big picture
Changing units always means multiplying or dividing by a fixed factor. Before you calculate, ask what the factor is for THIS unit: 10, 100 or 1,000 for metric length, mass and capacity; the length factor squared for area and cubed for volume; 60 and 24 for time; 100 for money. Going to a smaller unit, multiply; going to a bigger one, divide. Compound measures such as speed, density and pressure divide one quantity by another, and their units are built from those two quantities.
Key points
Worked example
Problem
A car travels 60 km in 1 hour 20 minutes. Work out its average speed in km/h.
⚠ Watch out
Treating time as if it were decimal. 1 hour 20 minutes is not 1.2 hours, and 4.5 hours is 4 hours 30 minutes, not 4 hours 50. Multiply the decimal part of an hour by 60 to get minutes.
Memory hook
Ask "what's the factor?" before you touch the calculator: metric 10, 100 or 1,000; squared for area; cubed for volume; 60 and 24 for time; 100 for money. Smaller unit, bigger number: multiply.
Check yourself
Without a calculator: write 2.5 hours in hours and minutes, change 2 m³ into cm³, and say which two quantities you divide to find a density. Then check each answer against its factor.
Flashcards
(15)What are the three standard metric units for length, mass and capacity?
What do the prefixes kilo, centi and milli mean?
Write 7 km in metres, centimetres and millimetres.
How do you change grams into kilograms?
Write 6,050 ml in litres.
How many cm² are in 1 m²?
How many cm³ are in 1 m³, and how many mm³ are in 1 cm³?
Write 6.25 hours in hours and minutes.
Why can't 1 hour 20 minutes be written as 1.2 hours?
How do you change hours to minutes, or minutes to seconds?
How many days in a week, months in a year and days in a year?
Why is £2.5 not a correct way to write two pounds fifty?
Write £14 in pence, and 2,500p in pounds.
What is density, and what units is it given in?
What is pressure, and what units is it given in?
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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Keep me postedMore AQA GCSE Maths topics
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