IM Alg1.1.8 Lesson: Spreadsheet Shortcuts
Here is a table of equivalent ratios: Complete the table with the missing values.
Use the applet (below) to answer the questions.
[list][*]In cell B4, we want to enter = B1 * 5 to multiply the month by 5. Enter this, but when you are about to type B1, instead, click on cell B1. This shortcut can be used any time: click on a cell instead of typing its address.[/*][/list][list][*]Practice this technique as you program each cell in B5 through B10 to perform the right computation.[/*][*]When you are finished, does cell B10 show a number that contains the month and day of your birthday? If not, troubleshoot your computations.[/*][/list][list][*]Try changing the month and day in cells B1 and B2. The rest of the computations should automatically update. If not, troubleshoot your computations.[/*][/list]
Why does this trick work? Try using [math]m[/math] for the month and [math]d[/math] or the day, and writing the entire computation as an algebraic expression. Can you see why the resulting number contains the month and day?
The spreadsheet applet below contains a table of equivalent ratios.
[list][*]Use spreadsheet calculations to continue the patterns in columns A and B, down to row 5. Pause for discussion.[/*][/list][list][*]Click on cell A5. See the tiny blue square in the bottom right corner of the cell? Click it and drag it down for several cells and let go.[/*][*]Repeat this, starting with cell B5.[/*][/list]
IM Alg1.1.8 Practice: Spreadsheet Shortcuts
Use "fill down" on the spreadsheet on the left to recreate this table of equivalent ratios on the right. You should not need to type anything in rows 3–10.
A list of numbers is made with the pattern: Start with 11, and subtract 4 to find the next number.
[size=150]Here is the beginning of the list: 11, 7, 3, . . .[/size][br][br]Explain how you could use "fill down" in a spreadsheet to find the tenth number in this list. (You do [i]not [/i]need to actually find this number.)
Here is a spreadsheet showing the computations for a different version of the birthday trick:
[img]data:image/png;base64,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[/img][br][br]Explain what formulas you would enter is cells B4 through B8 so that cell B8 shows a number representing the month and day. (In this example, cell B8 should show 704.)
Try your formulas with a month and day to see whether it works.
Write a formula you could type into a spreadsheet to compute the value of each expression.
[math]\frac{2}{5}[/math] of [math]35[/math]
[math]25\div\frac{5}{3}[/math]
[math]\left(\frac{1}{11}\right)^2[/math]
The average of [math]0,3,[/math] and [math]17[/math][br]
The data set represents the number of cars in a town given a speeding ticket each day for 10 days.
2 4 5 5 7 7 8 8 8 12[br][br]What is the median? Interpret this value in the situation.
What is the IQR?[br]
The data set represents the most recent sale price, in thousands of dollars, of ten homes on a street.
85 91 93 99 99 99 102 108 110 115[br][br]What is the mean?[br]
What is the MAD?[br]