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.

 

Situation 1

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

 

Situation 2

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Situation 3

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 Ōsolve for xĶ 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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