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 |
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!