Investigating months in the calendar with the FX82AU+

This resource was written by Derek Smith with the support of CASIO New Zealand. It may be freely distributed but remains the intellectual property of the author and CASIO.

Numerical and algebraic patterns can be found in many places. 
On your calculator you can generate sequences of numbers based on the operations +, -, × and ÷.

Examples

The sequence <1, 3, 5, 7, …> can be generated by entering 1 then pressing [EXE] then [+] 2 then follow with repeated [EXE], [EXE], [EXE], …
The sequence <10, 7, 4, 1, …> can be generated by entering 10 then pressing [EXE] then [-] 3 then follow with repeated [EXE], [EXE], [EXE], …
The sequence <2, 4, 8, 16, …> can be generated by entering 2 then pressing [EXE] then [×] 2 then follow with repeated [EXE], [EXE], [EXE], …
The sequence <100, 50, 25, 12.5, …> can be generated by entering 100 then pressing [EXE] then [÷] 2 then then follow with repeated [EXE], [EXE], [EXE], …

Activity
Generate the following sequences on your calculator and find the 10^th and 15^th term for each.

1.      <7,11, 15, 19, …>

2.      <72,61, 50, 39, …>

3.      <3,9, 27, 81, …>

4.      <1000,500, 250, 125, …>

Calendar calculations

The Calendar can also be another interesting source to see patterns. There are only two things that can make one calendar different from another:
1.  the day of the week on which January 1 falls
2.  whether it is a leap year or not. 

Following is the Calendar for June 2012.

This year, June had 5 Fridays, 5 Saturdays and 5 Sundays. Any month with 31 days has four days of the week appearing four times (in each of the four whole weeks of the month) and three days that appear five times (in each of the four weeks and also as one of the `extra` 3 days that make up a 31 day month).

Investigate

When was the last time 5 Fridays, 5 Saturdays and 5 Sundays happened? When will it happen again? 

Activity

Take any ‘2×2 block’ of dates in a calendar month. There must be 6 dates inside the block.

What do you notice? Can you see any patterns? 

For example:

     1.      add pairs horizontally and compare the sums.

     2.      add pairs vertically and compare the sums
3.   add pairs diagonally and compare the sums

What about patterns by multiplying

Extension Activity

1.      Take any ‘2×3 block’ of dates in a calendar month. There must be 6 dates inside the block.

What do you notice? Can you see any patterns?

     2.      Take any ‘3×2 block’ of dates in a calendar month. There must be 6 dates for example, in the June 2012 month the 3×2 blocks in red are not    
           allowed but the one 3×2 blocks in green are allowed.

What do you notice? Can you see any patterns?

3.      Take any ‘3×3 block’ or ‘3×4 block’ or ‘4×3 block’ or ‘4×4 block’ of dates in a calendar month. There must be 9 dates enclosed.

What do you notice? Can you see any patterns? 

4.      Can there be a ‘5×5 block’ on any calendar month? Justify your decision.

Birthday calculations

Often you will need to read and use charts and tables to collect and analyse information. Use the following three tables to find what day people were born on.

Table 1: Month code numberð}ð}ð‰Õ
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