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Primary maths activities for Leap Day

Monday, 8 February 2016
Have a special maths activities lesson for leap day on February 29th. Of course it lends itself to looking at calendars, the number of days in each month and rules to calculate which years are leap years. It is also a good way to revisit, reinforce and practice maths topics such as number and calculations. There are maths ideas here for FS2/R, KS1 and KS2  - all around the number 29. 

Were you born in a leap year?

 
There are some rules around leap years that your class will need to know:

1. Can the year be divided by 4?  2016 can be divided by 4, so it is a leap year -  unless...

2. It can also be divided by 100, such as 1900, then it is not a leap year - unless...

3. It can also can be divided by 400, such 2000, which is a leap year.



So, what year were you born and was it a leap year?
1907863

People with leap day birthdays


Some people born on leap day say their age as "I am 8 at two"
This means they are 8 normal years old on their second leap day birthday.

Write the age of someone who will be 40 normal years old this year on 29 February 2016 and the number of leap day birthdays.


I am ___ at ____

Write their age in this way, for every leap day birthday they will have ever had. What do you notice?


Hannah Mills is a British sailor who won a silver medal in the 2012 Olympic Games.
She was born on 29 February 1988.

Use the rules to check this was a leap year.
How many leap day birthdays will she have celebrated on 29 
February 2016?


Cullen Jones is an American swimmer who won a gold medal in the 4 x 100 metre medley in the 2012 Olympic Games.
On 29 February 2016 he will celebrate his eighth leap birthday.

What year was he born and how old will he be this year in normal years?
 


The Queen will be 90 years old on 21 April 2016.
What year was she born? Was she born in a leap year?
 

Why do we have leap years?


The Earth takes approximately 365.242375 days to circle the sun.
Can your class round this to the nearest whole number?

This is what we call a year and rounded to the nearest whole number it is 365 days.

However there is 0.242375 of a day left over each year.
Can your class round this to the nearest hundredth or to 2 decimal places?

0.24 is close to 0.25 or ¼, so after 4 years 4/4 makes one extra day and that is our leap day on 29
 February.
 
However 0.24 may be close to ¼ (0.25) but the difference is 0.01  - what happens if this is mulitplied by 100?

It gives one day every 100 years. So every 100 years we don’t have a Leap year.
 
However there is still a very small difference and this adds up to about a day every 400 years, so then we do have a leap year.
 
Then everything is pretty close to 265.242375, the exact length of a year - the time it takes for the Earth to circle the sun.
 
(A day is the time the Earth takes to rotate on its axis, we round this to 24 hours, however it is actually 23 hours, 56 minutes and 4.1 seconds!)

Leap Day Maths Activities

FS2 / KS1  


Counting 29
•  Make trays or plates of 29 objects. Use different objects in each set.
Compare sets of large objects with sets of small objects, which set looks like it has more?
Count the sets, laying them in line and matching them to show there is the same amount, 29 of each. Use a calendar for February this year and place one item on each date to count to 29.


Odds and evens
Place the objects in one set in pairs.
What do you notice? Is 29 an even or odd number?
 

Y2, Y3 and Y4

Adding to 29

Y2 use sets of 29 objects. Randomly split one set of objects into two 2 groups.
Can you count the objects in one group?
How could you work out how many are in the other group?

Repeat a few times to make different additions to 29.

Y3 and 4 write the addition calculations without the use of objects. 

Record your results  ___ + ____ = 29
How many different additions with a total of 29 can you make?
What if the first number is a multiple of 2 and the second number is a multiple of 3?

 

Taking away from 29
Randomly take a handful of objects away from one set.
Count how many you have taken away. How many are left?
Repeat taking away different amounts from 29.

Record your results  29  -  __ = __

How many different subtraction calculations can you make?
 

 
Teaching points
• Children are asked, how many calculations can you make? You are not asking them to make all the possible calculations, some children might be able to do this, but others may find 4 or 5 and that would be a great achievement too.

• You can point to inverses, 29-9=20, 29-20=9...
What do you notice? Can you make other calculations using inverses to help?

You can highlight the patterns of taking away or adding consecutive numbers 28+1, 27+2, 26+4….

What do you notice? Can you continue with this pattern? 
How will you know if you have all the possible addition calculations that total 29?

KS2

I am thinking of a number


Ask you class to answer these:

It is half of 58. What is my number?
It is a prime number between 24 and 30. What is my number?
The digits in this number total 11 and it is a number less than 35. What is my number?
It is the total of 22 and 52. What is my number?
The total of two numbers is 59 and the difference between these two numbers is 1. What is the smaller number?

        
What do they notice about all the answers?  
They have the same answer 29.
        
 
Write 29 different calculations that have the answer 29.
 
Provide some rules for your class, focus on a particular maths topic or vary the rules to differentiate between groups.

Can you write 29 different calculations using +, -, x and ÷ , so that 29 is always the answer?
 
• Include a 3-digit number in 6 of your calculations
• Include brackets in 5 of your calculations
• Include decimal numbers in 4 of your calculations
• Include a square number in 3 of your calculations
• Include a negative number in 2 of your calculations
• Include a prime number in 1 of your calculations.


Complete a 29 doubling chain
Start at 29 and double each number to give the next number in the chain:

29   58   116    232    464    912   1824  3648  7296

What do you notice about the numbers in this doubling chain?
The last two digits in 3-digit numbers can be divided by 4. Can each whole number be divided by 4? 
All the numbers after 29 are even. Ask when a number is doubled is the answer always, sometimes or never even?



Days in a Leap Year 

Children use a calendar to find the day of the week for their birthday in 2016. Then compare it with the day of the week for their birthday in 2015, 2014, 2013, 2012, 2011 and 2010.

What do they notice about the day of the week, how does it change?

How many full weeks are there in a normal year and leap year? How many days are left over in a normal year compared to a leap year? How does this explain which day of the week your birthday will be next year? 



What do you get when you multiply a frog by a calendar?

A leap year!

Related articles

Teaching calendars in time

Calendar board games for February, learning about the days of the week.

Consecutive dates - great time for an investigation

When was the last consecutive date? 11.12.13, can you find others?
What happens when you add consecutive numbers?

Finding palindromic dates

The last palindromic date was 21.11.12. When was there one before that? When is the next?
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