Technology required. Open a blank spreadsheet. Use "fill down" to recreate this table of equivalent ratios. You should not need to type anything in rows 3–10. 

A list of numbers is made with this pattern: Start with 11, and subtract 4 to find the next number.

Here is the beginning of the list: 11, 7, 3, . . .

Explain how you could use "fill down" in a spreadsheet to find the tenth number in this list. (You do not need to actually find this number.)

Here is a spreadsheet showing the computations for a different version of the birthday trick:

A spreadsheet with rows 1 to 10 and columns A and B. A 1 contains “month”. A 2, “day”.  A 4, “multiply month by 50”. A 5, “add 30”. A 6, “multiply by 2”. A 7, “add the day”. A 8, “subtract 60”. B 1, 7. B 2, 4. All other cells are blank.

Explain what formulas you would enter in cells B4 through B8 so that cell B8 shows a number representing the month and day. (In this example, cell B8 should show 704.) If you have access to a spreadsheet, try your formulas with a month and day to see whether it works.