Here is a question that catches people out. How many days is it from 28 February to 3 March? Have a think, then hands up.

And here is the twist: does the answer change depending on which year it is?

We count durations by hopping along a day-line, not by subtracting the date numbers. A day-line is just a number line where each step is one day. Look at the three counts marked on the day-line. For each one, notice how the count crosses the end of the month.

First count, worked all the way through: start at 15 March (marked 15 on the line) and hop forward until you reach 33 on the line. March ends at the marker on 31, so the next hop is 1 April (not day 32 of March), then 2 April at 33. That is 18 hops, so the duration is 18 days and the target date is 2 April.

Second count: hop in sevens for 91 days and notice where you land.

The last one is a leap-year February. Be ready to say how many days it is from 28 February to 3 March, and why that is different from an ordinary year.

Today we work through these durations together on the day-line, crossing the end of May each time. Day 0 on the line is 1 May, and each hop is one day. May has 31 days, so the end of May is marked at day 30 and 1 June is marked right after it. We'll point to the end of May before we hop past it.

• count on 25 days from 1 May, staying inside May
• count on 40 days from 1 May, crossing the end of May into June
• count on 21 days from 1 May, which is exactly 3 weeks

Today we work through these problems together, each one a step harder. For each one, spot the action words, choose the operation, and count carefully across the calendar.

• a library book due back in 21 days
• a school term running 12 weeks
• a leap-year February count
• how many days of the year have passed by the end of February