Here are three amounts written in three different ways: 3/5, 0.55 and 58%. One of them is the biggest and one is the smallest. Which single form would make it easiest to line them up and decide?

You are about to see the same kind of battery three times over, and each one shows a single amount as a percentage, a fraction and a decimal all at once. Start with the first, three fifths, and use it as your anchor. Then look at where the other two sit beside it, and read all three as decimals before you decide which is biggest.

Today we work through one full problem together, in three stages: convert, compare, then take a discount two ways.

Stage 1 and 2 — convert and compare. Set the slider to each of the three values in turn and read the decimal off. One of them catches people out because the number in front of the per cent sign looks big, so say each decimal aloud before you check it. Then put the three in order from smallest to biggest.

Stage 3 — a discount two ways. A €48 jacket has 25% off. How much do we take off? Let's do it both ways and show they agree.

• Fraction method: 25% is the same as 1/4, so find a quarter of €48.
• Percentage method: 25% is 0.25, so work out 0.25 × 48.

Four number mysteries, each one harder than the last. Every mystery carries its own clues, and each one has to be pinned down as a decimal, a fraction in its simplest form and a percentage. Work them together, one mystery at a time.