### Prompt Cards

These two group activities use mathematical reasoning - one is numerical, one geometric.

### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

# Calendar Calculations

##### Age 7 to 11 Challenge Level:

These investigations required you to use what you know about the multiples of seven.

How is this for a full explanation from James?

If you start the week, for example, on the 7th and add all of the numbers together, the result is 70. If you multiply the first number of the week - in this case the 7th - by 7 (7 X 7 = 49) and then add 21, you also get 70. Equal numbers will be reached whichever number you start with. If you multiply the smallest number by 7 (the number of days in a week) then each day you will get an extra number which will go up by one each day (8=7+1, 9=7+2 up to 6). The total of these numbers, 1+2+3+4+5+6 = 21. This is the same wherever you start on the calendar.

Scott also explains, "The 21 stands for the difference between the number of the first day of the week and the remaining days' numbers".
Christina agrees with Scott and James, "You add 21 because 1+2+3+4+5+6=21 and these are the differences of the numbers between the first day of the week and the other days."

The Reedmans showed their answer in a table:
Monday = 1
Tuesday = 2
Wednesday = 3
Thursday = 4
Friday = 5
Saturday = 6
Sunday = 7

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.

Multiply the number of the first day of the week by 7. Add 21 to the product:

 Monday = 1 1 x 7 = 7 7 + 21 = 28.

"The final numbers are the same!!!"