Class activity: how many days are there in 2020 years?

Editor’s note: This is an updated version of a blog post published on January 6, 2020.

Here’s a question for you… how many days are there in 2020 years? The answer is trickier than it looks. Try this problem with your Year 5 and 6 learners as a fun way to wind down for the holidays.

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.

In this Year 5 and 6 problem, you can guide learners to the answer by using effective-questioning techniques. This question requires problem-solving and reasoning skills. It tests learners’ skills in multiplication, dividing by 4, working with multiples of 100, and addition and subtraction.

Try this question as a class activity with your learners and challenge them to tap into their mathematical problem-solving skills.

Start by asking learners how many days 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 29 February).

Explain that we need leap years 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 good, child-friendly explanation.

Check if learners know the rules for leap years

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

The official rules are that 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’s a leap year.

Who knew? Full disclosure, I only discovered Rules 2 and 3 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’s a leap year, another day is added.

Let’s go through the steps to solving this problem.

Step 1: Ask “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 “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: Work out the final answer

Almost done. To get 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. We hope this has been a fun challenge for your learners before they go on break.

As with most problem-solving questions, there’s 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