Happy New Year! It’s 2020 and the start of a new term, so why not kick things off by asking your Year 5 and 6 learners a nice warm-up question?

Here’s a question for you… how many days are there in 2020 years? The answer is trickier than it looks and makes for an interesting start-of-year activity.

## Classroom activity: how many days are there in 2020 years?

Sounds straightforward right? Just a bit of multiplication.

But hang on a minute, what about those pesky leap years? Here’s where the question gets interesting.

You can guide learners to the answer with effective questioning. As well as requiring problem-solving and reasoning skills, getting to the true answer tests learners skills in multiplication, dividing by 4, working with multiples of 100, and addition and subtraction.

Why not try this question as a class activity with your learners and challenge them to tap into their problem-solving skills?

**Get started by asking your class how many days there are in a year. Does every year have the same number of days? Does anyone know what a leap year is?**

Some children might be familiar with the idea of a leap year (especially if their birthday is on the 29th of February!).

Explain that we need a leap year to keep the calendar year lined up with the Earth’s orbit around the Sun. You could watch this video as a class which offers a nice child-friendly explanation.

### Check to see if the learners know the rules for leap years

Some learners might say that there is a leap year every four years. For the most part, this is true, but the rules are actually a bit more complicated than that.

The official leap year rules are, a year is a leap year if:

**Rule #1**: the year is divisible by 4.**Rule #2**: if the year is divisible by 100, it is NOT a leap year, unless…**Rule #3**: the year is also divisible by 400. Then it is a leap year.

Who knew? Full disclosure, I only discovered rules two and three when I started to write this post. And wouldn’t you know, I also learned that Superman was born on a leap year.

Once your learners know the rules, ask them about the effect of leap years on the number of days. Every time there is a leap year, another day is added.

**Step 1: work out the answer by asking: how many days would there be if every year had 365 days? **

There are **2020** years and **365** days in a year, so multiply them together and you get **737,300**.

Ask your learners to explain how they carried out this multiplication. Did they use long multiplication or split **2020** into **2000** and **20** and work out **730,000 + 7,300**? Or maybe they used a different method. Discuss which methods are more efficient.

Now we can start thinking about the leap years.

### Step 2: ask the class: how many leap years are there in 2020 years?

If we have a leap year every four years, then the answer would be **2020 ÷ 4 = 505**. But the answer is trickier than that!

Some of these 505 years are divisible by 100 (and not 400), so we need to exclude them from the total.

Now, let’s look at the years that are divisible 100s. You could make a list and then cross out the ones that are divisible by 400.

**100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900 and 2000**

There are 15 years that **are not** leap years.

The leap years add on an extra **505 – 15 = 490** days. That’s more than a year of leap years!

### Step 3: the final answer

Almost done. To get to the final answer, ask your learners to add on the leap years.

There are **737,300 + 490 = 737,790** days in **2020** years.

So there you have it. Hopefully, this has been a good warm-up to get learners thinking mathematically in the new term.

*As with most problem-solving questions, there is always more than one way to find the answer. We’d love to see what your learners come up with. Share your experiences with us on Twitter by tagging @MathsNoProblem*