# Calendar Sorting

The pages of my calendar have got mixed up. Can you sort them out?

## Problem

Do you know those calendars that are a series of cards, one for each month?

I have one of those on my desk at home.

Image

The cat jumped on my desk while I was at school yesterday and knocked it off on to the floor.

Now they are all muddled up.

I do not know which month is which and I don't know how to put them back in the right order.

Can you help?

Here is a sheet you can print off and cut up into twelve cards, one for each month. Or you could use the interactivity below which allows you to drag the month cards so you can try out your ideas.

Can you put the cards in the right order?

## Getting Started

How might you start?

What do you know about the number of days in each month?

What do you know about the number of days in each month?

## Student Solutions

Rida and Regan, Layan and Mariam, Parisa, Diana and Rehan, Halena, Oubaidah and Khaled, Muhammad, Dylan and Yousef, and Daniel all from Greenacre Public School sent in solutions.

Esme from Ambler School in the United Kingdom wrote:

First, I thought of the rhyme ''30 days hath September, April, June and November - all the rest have 31, except for February alone" then I realised that February must be the second month so I put it into place. Then I realised that January must start on the day before February starts, so I found one with 31 days, ending on the day February starts. Then I thought of March, so I found one with 31 days, starting on the day after Feb ended. Then I did the same thing for each month until I got to the end.

Lucia from Willowbank in New Zealand sent in this solution:

So, first of all, you find February, and you will know it is February because the end of the month, the last day will be the 28th. Now you have to find out what goes in front (January). how to do this is you look at the front of February and look at the date from the days. For example, February started with Saturday, so January must have ended on Friday because after Friday is Saturday. If there are two months ending with Friday, look at the date. January should be ending with the date 31st. Now you've got two months done!

Time for number 3! March! to find out what March is, you will have to look at February's end date. For example, February ended with a Thursday, then the calendar will start with a Friday! If both months start on a Friday, make sure March ends with a 31st! The fourth month is the same but ends with a 30th. The fifth month is the same too but ends with a 31st. So the pattern goes like this: 31st, 28th, 31st, 30th, 31st, 30th, 31st, 30th, and that's how you solve it!:)

For the first time we had a solution in from Malaysia. Dohyeon and Taegeon from Tunku Putra School wrote:

First, we started with February, because it is the only one with 28 days, so it is unique. Then, we worked out January. February starts on a Saturday, so we know that January must finish on a Friday and have 31 days. We know that March is 31 days and must start on a Saturday as February finishes on a Saturday. We then repeated this process until we got to September. The only tricky moment was there was a choice of two months that started on Monday, but the 30 days one was the correct choice.

This is our first solution from Shanghai. Julian and Hanusha from Western International School of Shanghi in China wrote:

We had fun doing our first NRICH puzzle!

We first found February because it has 28 days. Since it starts on Saturday so we needed to find a month that ends on Friday so that would be January. February ends on Friday so we needed to find a month to be March that starts on Saturday. So we used the same strategy for the other months. Here is a photo of our solution.

Thank you for all the solutions that came in, obviously, there was just the one correct solution.

Esme from Ambler School in the United Kingdom wrote:

First, I thought of the rhyme ''30 days hath September, April, June and November - all the rest have 31, except for February alone" then I realised that February must be the second month so I put it into place. Then I realised that January must start on the day before February starts, so I found one with 31 days, ending on the day February starts. Then I thought of March, so I found one with 31 days, starting on the day after Feb ended. Then I did the same thing for each month until I got to the end.

Lucia from Willowbank in New Zealand sent in this solution:

So, first of all, you find February, and you will know it is February because the end of the month, the last day will be the 28th. Now you have to find out what goes in front (January). how to do this is you look at the front of February and look at the date from the days. For example, February started with Saturday, so January must have ended on Friday because after Friday is Saturday. If there are two months ending with Friday, look at the date. January should be ending with the date 31st. Now you've got two months done!

Time for number 3! March! to find out what March is, you will have to look at February's end date. For example, February ended with a Thursday, then the calendar will start with a Friday! If both months start on a Friday, make sure March ends with a 31st! The fourth month is the same but ends with a 30th. The fifth month is the same too but ends with a 31st. So the pattern goes like this: 31st, 28th, 31st, 30th, 31st, 30th, 31st, 30th, and that's how you solve it!:)

For the first time we had a solution in from Malaysia. Dohyeon and Taegeon from Tunku Putra School wrote:

First, we started with February, because it is the only one with 28 days, so it is unique. Then, we worked out January. February starts on a Saturday, so we know that January must finish on a Friday and have 31 days. We know that March is 31 days and must start on a Saturday as February finishes on a Saturday. We then repeated this process until we got to September. The only tricky moment was there was a choice of two months that started on Monday, but the 30 days one was the correct choice.

This is our first solution from Shanghai. Julian and Hanusha from Western International School of Shanghi in China wrote:

We had fun doing our first NRICH puzzle!

We first found February because it has 28 days. Since it starts on Saturday so we needed to find a month that ends on Friday so that would be January. February ends on Friday so we needed to find a month to be March that starts on Saturday. So we used the same strategy for the other months. Here is a photo of our solution.

Image

Thank you for all the solutions that came in, obviously, there was just the one correct solution.

## Teachers' Resources

Why do this problem?

This activity will help learners become more familiar with our calendar. In particular, the task will reinforce the order of months in a year and the number of days in each month.#### Possible approach

Introduce the task by telling the story about your cat jumping on to your desk and knocking the calendar onto the floor (or something similar). You need the class' help to sort out the calendar cards.It would be a good idea to say little else at this stage. Give pairs or small groups a copy of the cards and give them plenty of time to have a go. If you have access to tablets or a suite of computers, you could invite learners to use the interactivity. Emphasise that you are particularly keen to understand

*how*they approach the task, not simply to know their answer.

At an appropriate point, you may like to draw everyone back together for a class sharing of ideas (mini plenary). Some learners may be stuck and need some help to see how to move forward. Others may benefit from articulating their emergent ideas. You can then give them more time to continue with the task.

Each pair/group could make a poster about the task, outlining the reasoning that has led to the solution. They could stick down the cards to show the completed calendar.

#### Key questions

How might you start?What do you know about the number of days in each month?

#### Possible extension

For an extra challenge, why not give children the cards from these sheets which are the months from a three-year calendar. This time, they have to sort them into the three consecutive years, month by month.#### Possible support

These cards (word, pdf) follow the same idea but with more support. The months are from a different year to the main task, and are colour coded according to the season. Key dates are marked with pictures to provide some starting points for the children.It might also help to have several current calendars available so children can remind themselves of its structure.