Stage Four
Birthdays
On what day of the week will your 100th birthday fall?
Investigate this and other days of interest.
Consider your next few birthdays.
From year to year what changes occur in the day on which your birthday falls?
Does the same thing always happen from year to year? If not, what causes any change?
For non-leap years, what happens from one year to the next?
What happens as you go from a non-leap year to a leap year?
What happens as you go from a leap year to a non-leap year?
For which other years will your birthday fall on the same day of the week as it does this year?
When will this next happen?
After this, when will it occur again?
On what day of the week will your 100th birthday fall?
On what day were you born?
Can you find a quick way to determine the day of the week for any date this century?
Will your method work for other centuries?
If not, what can be modified to do so?
Select some other important or interesting dates and find out the day of the week for them.
Investigate the occurence of Black Fridays (ie. Friday the 13th).
Lots of things to do here, but the basis to this question is what happens to the day of the week a date falls on from year to year.
There are 2 cases to consider here: normal years and leap years.
A normal year has 365 days. 365 divided by 7 gives 52 full weeks with one day left over. So from year to year, a date moves to the next day of the week.
A leap year has 366 days, giving 52 full weeks with 2 days left over. So every time you pass a 29th of February (every 4 years) the date will move on an extra day.
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
In the table, the leap years are shown in bold. By counting the number of years between two dates, and noting the number of 29th Februaries (in leap years) between the dates it is possible to work out how many days the date would move.
Give it a try. The day I am writing this is Sunday 17th June 2001. On this date in 2021, 20 years have passed, including 5 leap years, giving a movement of 25 days. This give 3 full weeks and 4 more days. So the day will be 4 days after a Sunday: Thursday.
Using this information, and some common sense, it is possible to word out the day for any date.