Write-up #12

The Spreadsheet in Mathematics Explorations

by Beverly Hales and Mark Cowart

Using Excel or any type of spreadsheet can be an excellent means to connecting mathematics to computer technology and software. In addition to learning mathematics, the students are given the opportunity to learn software that is commonly used in the work force.

Once the students learn simple format techniques of Excel, they are able to express an equation as a function of a previous row or column. By manipulating simple values of the spreadsheet, a graph, chart, or table can be quickly changed so that students can look for patterns in data.

In Algebra, the spreadsheet can be used for values of the t-chart which is helpful for Algebra 1 students when graphing equations.

The spreadsheet begins with a collection of values for x and f(x). To express the rows as consecutive numbers without entering each number separately, the students would look for ways to express row 2 in relation to row 1. In order to express y=x as f(x), the students must relate the value of column A to column B. This would be easy since the value of y equals the value of x.

For more equations that involved a multiple of operations, the students must learn to use the function key to express the equation in terms of Excel. For example to express the square root function, the students must recognize that the value of a negative square root does not exist. Students could experiment with different ways to enter the formula in order to get an appropriate graph for both positive and negative values of x.

Once the values are determined the graphs can be made by selecting the row and columns that are to be graphed. Under Insert, choose chart and the computer will guide the student through the set-up of the graph. Some defaults for the design may need to be changed to get the desired result.

Values and graphs spreadsheet

In statistics, spreadsheet can be used to discuss measures of central tendency. Students could set-up spreadsheets to find the values of mean, z-scores, etc. depending on the needs and abilities of the class.

An example is available that gives a set of data and allows the student to determine the values need to find various statistical measures.

Statistics spreadsheet

In terms of patterns and counting methods, Excel is an opportunity for the teacher to prepare the data prior to class and then use the spreadsheet for the students to examine.

Consider the following question, "If n lion cages are connected on a railroad train, how many different ways can two lions be placed in the cages if the lions can not be placed in consecutive cages?"

Beyond answering the question for each value of n, spreadsheet allows you to discuss the answers in terms of a recursive formula and a closed formula. The question of whether the lions are distinguishable can also be considered.

Lions spreadsheet

Identification numbers and modular arithmetic can also be discussed with the help of spreadsheets.

ID spreadsheet

In terms of Geometry, students can use a spreadsheet to discuss Pick's theorem. By using rows and columns to express the border points and interior points, students can better examine the changes in the area of the polygons.

Pick's spreadsheet

In terms of finance, students can use spreadsheets to determine budgets, payments, or salaries.

A mortgage spreadsheet is available that allows the students to enter values for deposits, interest rate, etc., to calculate the payments on a home. Teachers have the opportunity to discuss a variety of topics within this spreadsheet from calculations of interest to the mathematical set-up of the functions for each cell in the mortgage calculations.

Mortgage spreadsheet

Information over the internet can also be examined using Excel. Although only the table may be available to the student, the teacher could ask the students to develop a function to determine the different cells of the spreadsheet without calculating or typing each value into the chart separately.

Any spreadsheet like the salary chart placed on the web page of the Georgia Department of Education can be used to discuss functions. It gives the salaries for teachers in the public schools for the upcoming school years. This spreadsheet could be used as mentioned above or used to discuss budgets relative to the mortgage spreadsheet. The students could be ask to recreate the spreadsheet with a 5% increase.

Education spreadsheet

Using Excel, different sequences can be examined.

Below is a spreadsheet of the Fibonnaci sequence. In addition to the terms of the sequence, the ratio of each pair of adjacent terms of the sequence were found. This allows the students to discuss concepts of convergence.

Term # Fibonnaci Ratio n1/n2 Ratio n1/n3
0 1 0 0
1 1 1 0
2 2 0.5 0.5
3 3 0.666666666666667 0.333333333333333
4 5 0.6 0.4
5 8 0.625 0.375
6 13 0.615384615384615 0.384615384615385
7 21 0.619047619047619 0.380952380952381
8 34 0.617647058823529 0.382352941176471
9 55 0.618181818181818 0.381818181818182
10 89 0.617977528089888 0.382022471910112
11 144 0.618055555555555 0.381944444444444
12 233 0.618025751072961 0.381974248927039
13 377 0.618037135278515 0.381962864721485
14 610 0.618032786885246 0.381967213114754
15 987 0.618034447821682 0.381965552178318
16 1597 0.618033813400125 0.381966186599875
17 2584 0.618034055727554 0.381965944272446
18 4181 0.618033963166707 0.381966036833293
19 6765 0.618033998521803 0.381966001478197
20 10946 0.618033985017358 0.381966014982642
21 17711 0.618033990175597 0.381966009824403
22 28657 0.618033988205325 0.381966011794675
23 46368 0.618033988957902 0.381966011042098
24 75025 0.618033988670443 0.381966011329557

The Lucas sequence can be found on the spreadsheet with the Fibonnaci sequence.

Fibonnaci spreadsheet

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