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?

Three battery snapshots, each showing one amount as a percentage, a fraction and a decimal. The first one is our anchor, three fifths. Notice where the other two sit beside it, and look at all three written as decimals.

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. The values are 7/10, 0.72 and 68%. Set the slider to each in turn and read the decimal off. The 68% catches people out because '68' looks big next to 0.72, so we say each decimal aloud before we check it. Then put them in order from smallest to biggest.

Both roads should reach the same amount off — that is what we mean by two methods that agree.

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.