by Courrey J. Alexander

Here are some situations taken from EMAT 7050 (Teaching Secondary School Mathematics) with Dr. Larry Hatfield where using a spreadsheet, EXCEL, simplified the following investigations.

Create a spreadsheet to investigate age relationships.

a.    When will my mother be twice my age?

b.    When will the ratio of my motherÕs age to my daughterÕs age be 3?

c.    Investigate other age relationships using the spreadsheet.

 Mom's age My age My wife's age Santrelle's age Jr.'s age Ratio (Mom & me) Ratio (Mom & Santrelle) 25 0 0 0 0 Undefined Undefined 26 1 0 0 0 26 Undefined 27 2 0 0 0 13.5 Undefined 28 3 0 0 0 9.333333333 Undefined 29 4 1 0 0 7.25 Undefined 30 5 2 0 0 6 Undefined 31 6 3 0 0 5.166666667 Undefined 32 7 4 0 0 4.571428571 Undefined 33 8 5 0 0 4.125 Undefined 34 9 6 0 0 3.777777778 Undefined 35 10 7 0 0 3.5 Undefined 36 11 8 0 0 3.272727273 Undefined 37 12 9 0 0 3.083333333 Undefined 38 13 10 0 0 2.923076923 Undefined 39 14 11 0 0 2.785714286 Undefined 40 15 12 0 0 2.666666667 Undefined 41 16 13 0 0 2.5625 Undefined 42 17 14 0 0 2.470588235 Undefined 43 18 15 0 0 2.388888889 Undefined 44 19 16 0 0 2.315789474 Undefined 45 20 17 0 0 2.25 Undefined 46 21 18 0 0 2.19047619 Undefined 47 22 19 0 0 2.136363636 Undefined 48 23 20 0 0 2.086956522 Undefined 49 24 21 0 0 2.041666667 Undefined 50 25 22 0 0 2 Undefined 51 26 23 0 0 1.961538462 Undefined 52 27 24 0 0 1.925925926 Undefined 53 28 25 1 0 1.892857143 53 54 29 26 2 0 1.862068966 27 55 30 27 3 1 1.833333333 18.33333333 56 31 28 4 2 1.806451613 14 57 32 29 5 3 1.78125 11.4 58 33 30 6 4 1.757575758 9.666666667 59 34 31 7 5 1.735294118 8.428571429 60 35 32 8 6 1.714285714 7.5 61 36 33 9 7 1.694444444 6.777777778 62 37 34 10 8 1.675675676 6.2 63 38 35 11 9 1.657894737 5.727272727 64 39 36 12 10 1.641025641 5.333333333 65 40 37 13 11 1.625 5 66 41 38 14 12 1.609756098 4.714285714 67 42 39 15 13 1.595238095 4.466666667 68 43 40 16 14 1.581395349 4.25 69 44 41 17 15 1.568181818 4.058823529 70 45 42 18 16 1.555555556 3.888888889 71 46 43 19 17 1.543478261 3.736842105 72 47 44 20 18 1.531914894 3.6 73 48 45 21 19 1.520833333 3.476190476 74 49 46 22 20 1.510204082 3.363636364 75 50 47 23 21 1.5 3.260869565 76 51 48 24 22 1.490196078 3.166666667 77 52 49 25 23 1.480769231 3.08 78 53 50 26 24 1.471698113 3 79 54 51 27 25 1.462962963 2.925925926 80 55 52 28 26 1.454545455 2.857142857

How large a cube is needed to hold all of the human blood on Earth? (from John Allen PaulosÕ Innumeracy:  Mathematical Illiteracy and Its Consequences)  The average adult male has about six quarts of blood, adult women slightly less, children considerably less—letÕs assume 1 gallon per person.  Assume about 6 billion people.  There are 7.5 gallons per cubic foot and 4 quarts per gallon.

 Number of people Number of Gallons per person Total Gallons Gallons/Cubic Ft. Length of Side of Cube 6000000000 1 6000000000 7.5 800000000

Create a spreadsheet to investigate time equivalents (hours, days, years) for time (seconds ranging from .001 to a trillion using an incremental factor of 10).  How old (in hours, days, years) will you be when you have lived a billion seconds?  A trillion seconds?

 Hours Days Years Time in seconds 0.001 0.000002777777778 0.000000115740741 0.000000000317098 0.01 0.000027777777778 0.000001157407407 0.000000003170979 0.1 0.000277777777778 0.000011574074074 0.000000031709792 1 0.002777777777778 0.000115740740741 0.000000317097920 10 0.027777777777778 0.001157407407407 0.000003170979198 100 0.277777777777778 0.011574074074074 0.000031709791984 1000 2.777777777777780 0.115740740740741 0.000317097919838 10000 27.777777777777800 1.157407407407410 0.003170979198376 100000 277.777777777778000 11.574074074074100 0.031709791983765 1000000 2777.777777777780000 115.740740740741000 0.317097919837646 10000000 27777.777777777800000 1157.407407407410000 3.170979198376460 100000000 277777.777777778000000 11574.074074074100000 31.709791983764600 1000000000 2777777.777777780000000 115740.740740741000000 317.097919837646000 10000000000 27777777.777777800000000 1157407.407407410000000 3170.979198376460000 100000000000 277777777.777778000000000 11574074.074074100000000 31709.791983764600000 1000000000000 2777777777.777780000000000 115740740.740741000000000 317097.919837646000000

Solving for x

Create a spreadsheet to Òsolve for xÓ by finding when:

a.    2x+1=13-x

b.   –7-3x=5x-23

c.    3-5x=x+25.8

 x 2x+1=13-x x -7-3x=5x-23 x 3-5x=x+25.8 0 1 13 0 -7 -23 0 3 25.8 1 3 12 1 -10 -18 -4.5 25.5 21.3 2 5 11 2 -13 -13 -4.45 25.25 21.35 3 7 10 3 -16 -8 -4.4 25 21.4 4 9 9 4 -19 -3 -4.35 24.75 21.45 5 11 8 5 -22 2 -4.3 24.5 21.5 6 13 7 6 -25 7 -4.25 24.25 21.55 7 15 6 7 -28 12 -4.2 24 21.6 8 17 5 8 -31 17 -4.15 23.75 21.65 9 19 4 9 -34 22 -4.1 23.5 21.7 10 21 3 10 -37 27 -4.05 23.25 21.75 11 23 2 11 -40 32 -4 23 21.8 12 25 1 12 -43 37 -3.95 22.75 21.85 13 27 0 13 -46 42 -3.9 22.5 21.9 14 29 -1 14 -49 47 -3.85 22.25 21.95 15 31 -2 15 -52 52 -3.8 22 22 16 33 -3 16 -55 57 -3.75 21.75 22.05 17 35 -4 17 -58 62 -3.7 21.5 22.1 18 37 -5 18 -61 67 -3.65 21.25 22.15 19 39 -6 19 -64 72 -3.6 21 22.2 20 41 -7 20 -67 77 -3.55 20.75 22.25 21 43 -8 21 -70 82 -3.5 20.5 22.3 22 45 -9 22 -73 87 -3.45 20.25 22.35 23 47 -10 23 -76 92 -3.4 20 22.4 24 49 -11 24 -79 97 -3.35 19.75 22.45 25 51 -12 25 -82 102 -3.3 19.5 22.5 26 53 -13 26 -85 107 -3.25 19.25 22.55 27 55 -14 27 -88 112 -3.2 19 22.6 28 57 -15 28 -91 117 -3.15 18.75 22.65 29 59 -16 29 -94 122 -3.1 18.5 22.7 30 61 -17 30 -97 127 -3.05 18.25 22.75 31 63 -18 31 -100 132 -3 18 22.8 32 65 -19 32 -103 137 -2.95 17.75 22.85 33 67 -20 33 -106 142 -2.9 17.5 22.9 34 69 -21 34 -109 147 -2.85 17.25 22.95 35 71 -22 35 -112 152 -2.8 17 23 36 73 -23 36 -115 157 -2.75 16.75 23.05 37 75 -24 37 -118 162 -2.7 16.5 23.1 38 77 -25 38 -121 167 -2.65 16.25 23.15 39 79 -26 39 -124 172 -2.6 16 23.2 40 81 -27 40 -127 177 -2.55 15.75 23.25

Spreadsheets have the amazing capacity to minimize lots of calculations.  It is as simple as inserting the necessary numerical values in the correct cells, deriving a formula, and letting Excel do all the work.

Also, when inserting incremental numerical values, using the fill option minimizes a lot of time for entering numerical values.  Simply enter a few numerical values (3 or 4), highlight the cells to be used to create the remainder of the incremental numerical values, click on the right corner of the last cell, and drag the cells down.  Excel automatically fills in the incremental numerical values.

Spreadsheets are fun and easy to use!

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