using a spreadsheet - nelson · using a spreadsheet getting started a spreadsheet is a computer...

Technical Skills GuideCopyright © 2011 by Nelson Education Ltd.

USING A SPREADSHEETGetting StartedA spreadsheet is a computer program that can be used to create a table of values (from data or an equation) and then graph the values as a scatter plot. A spread-sheet can also be used, when necessary, to determine the equation of the line or curve of best fit using regression.

A spreadsheet consists of cells that are identified by column letter and row number, such as A2 or B5. A cell can hold a label, a number, or a formula.

The following table of values shows the time and height of a ball that was thrown into the air.

Time (s) 0 1 2 3 4 5

Height (m) 2.0 22.1 32.4 32.9 23.6 4.5

Note: Different spreadsheets have different commands. Check the instructions for your spreadsheet to determine the proper commands to use. The instructions below are for some versions of Microsoft Excel.

Entering Data to Create a Table

1. To create a spreadsheet for the data, open the program to create a new worksheet.

Label cell A1 “time (s)” and cell B1 “height (m)”.

2. Enter the initial values. Enter “0” in A2 and “2.0” in B2. Repeat this process to enter the rest of the time data in column A and the

corresponding heights in column B, in rows 3 to 7.

Creating a Scatter Plot

1. Use the cursor to highlight the part of the table that you want to graph. For this example, select columns A and B in rows 1 to 7.

2. Use the spreadsheet’s graphing command ( Chart Wizard for this program) to graph the data.

A scatter plot will appear. Notice that axes labels are included.

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USING A SPREADSHEETEntering DataThe following frequency table shows the lengths of Emmanuella’s walks with her golden retriever during one month. To work with this data, you will need to enter it into a spreadsheet and also calculate midpoints for the intervals.

Length of Walk (min) 5–10 10–15 15–20 20–25 25–30 30–35 35–40 40–45 45–50 50–55 55–60

Frequency 1 3 7 10 6 11 8 5 4 2 3

1. Set up column headings.To create a spreadsheet for the data above, open the program to create a new worksheet. Label cell A1 “Length of Walk (min)”. Then, label cell A2 “lower” and cell B2 “upper”. Label cell C1 “Midpoint (min)” and cell D1 “Frequency”.

2. Enter the data.Enter the data from the frequency table in columns A (lower limits of intervals), B (upper limits of intervals), and D (frequencies). In cell C3, enter the function command “�(A3�B3)/2”. Then, copy or fill down this entry for the rest of the cells in column C, down to the last line of the data. The cell addresses will automatically adjust.

The spreadsheet now shows the midpoints as well as the intervals and frequencies for the data.


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USING A SPREADSHEET Determining Mean, Median, Mode, Range, and Standard DeviationDetermine key statistics for the following data.

1. Enter the data.Label cell A1 “Test scores”, and place the data in column A.

2. Calculate the mean, median, mode, and standard deviation.Enter the function “�AVERAGE(A2:A26)” in cell D2. This cell will display the mean of the data. Also enter the functions “�MEDIAN(A2:A26)”, “�MODE(A2:A26)”, and “�STDEVP(A2:A26)”in cells D3 through D5 to display the median, mode, and standard deviation of the data.

3. Determine the range.To determine the range, you may first need to determine the maximum and minimum data values, and then calculate their difference. Enter the functions “�MAX(A2:A26)” and “�MIN(A2:A26)” in cells D6 and D7. Then, calculate their difference by entering “�D6-D7” in cell D8.




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Unit 1 Test

81 76 73 71 64

80 75 73 71 63

79 75 73 68 61

79 74 73 67 58

78 73 72 66 57

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3. Determine the sum of the squared deviations.Create a new column headed “f*(x-xbar)^2” in column F. In cell F3, enter “�D3*(C3-$B$16)”. Copy this down for each data row. (The $ signs make sure that the spreadsheet always uses the mean value from cell B16.) Then, in cell F15, enter “�SUM(F3:F13)”.

4. Determine the standard deviation of the grouped data.Enter “�SQRT(F15/D15)” in cell B17 to

determine É a f 1x 2 x 2

n .

This displays the standard deviation.

1. Determine the sum of the grouped data.Create a new column headed “f*x” in column E. In cell E3, enter “�D3*C3”. Copy this down for each data row. The cell addresses will automatically adjust. Then, in cell E15, enter “�SUM(E3:E13)”.

2. Determine the mean of the grouped data.To determine the value of n, sum the frequencies by entering “�SUM(D3:D13)” in cell D15.

Then, in cell B16 (for example), enter “�E15/D15”

to determine a f xn .

This displays the mean of the grouped data.

USING A SPREADSHEETDetermining the Mean and Standard Deviation of Grouped DataThis frequency table shows the lengths of Emmanuella’s walks with her golden retriever during one month. To work with this data, you will need to enter it into a spreadsheet and calculate midpoints for the intervals, as shown in Entering Data.


Frequency 1 3 7 10 6 11 8 5 4 2 3



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1. Create the histogram.Select cells D3 to D13 and begin a chart (for example, click on the chart icon). Select a column graph as the type of chart. Click on “Next”.

USING A SPREADSHEETCreating a HistogramThe following frequency table shows the lengths of Emmanuella’s walks with her golden retriever during one month. To work with this data, you will need to enter it into a spreadsheet and calculate midpoints for the intervals, as shown in Entering Data.


Frequency 1 3 7 10 6 11 8 5 4 2 3


3. Finish the chart.Click on the “Titles” tab. Add appropriate titles for the histogram and titles for the axes. Then, click on the “Legend” tab, uncheck the “Show legend” box, and click on “Next”, then “Finish”. The chart will appear in your spreadsheet and you can drag it to any position.

4. Remove the gaps in the histogram (optional).Since a histogram should not contain gaps between bars, you may want to eliminate these from your chart. Double-click on any bar to open the “Format Data Series” dialog box. Click on the “Options” bar and change the gap width to 0, then click “OK”.The histogram will appear as shown below.




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2. Set the horizontal axis labels.Click on the “Series” tab. The “Values” box should already show the range “D3:D13”. Click on the “Category axis labels” box, then use the cursor in the main spreadsheet to select cells C3 to C13 (the midpoints of the intervals). Click on “Next”.

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USING A SPREADSHEETCreating a Frequency PolygonThis frequency table shows the lengths of Emmanuella’s walks with her golden retriever during one month. To work with this data, you will need to enter it into a spreadsheet and calculate midpoints for the intervals, as shown in Entering Data.


Frequency 1 3 7 10 6 11 8 5 4 2 3

1. Create the frequency polygon.Select the block of cells from C3 to D13 and begin a chart (for example, click on the chart icon). Select an XY or scatter graph as the type of chart, showing data points connected with straight lines. Click on “Next”.

2. Finish the chart.Click on the “Titles” tab. Add appropriate titles for the histogram and titles for the axes. Then, click on the “Legend” tab, uncheck the “Show legend” box, and click on “Next”, then “Finish”. The chart will appear in your spreadsheet and you can drag it to any position.

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USING A SPREADSHEET Using the NORMDIST CommandTo determine the proportion of data from 161 cm to 197 cm on a normal distribution of heights of students with mean 177 cm and standard deviation 15 cm, use the normalcdf command.

1. Enter the data.Enter the lower and upper bounds for the data, and the mean and standard deviation of the distribution, into appropriate cells.

2. Determine the proportion of the data between the lower and upper bounds.The NORMDIST function calculates the proportion of data below a given value, as a decimal. Use the difference between the proportions for 161 cm and 197 cm to determine the proportion between the two values. For the cells shown, enter “�NORMDIST(B2,B3,B4,1)-NORMDIST(B1,B3,B4,1)”. The proportion is displayed as a decimal.

3. Display the proportion as a percent (optional).Select the cell showing the proportion. From the Format menu, scroll to “Cells”, click on the “Number” tab, and select “Percentage”. Choose the appropriate number of decimals and click on “OK”.

4. Use the NORMSDIST command with a standard normal distribution.If the data points are z-scores, so that you are using a standard normal distribution with mean 0 and standard deviation 1, you can replace the NORMDIST function with the NORMSDIST function. Omit the mean, standard deviation, and final “1” from the argument, and just enter the z-score.


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USING A SPREADSHEETUsing the NORMINV CommandA brand of running shoes lose their shock absorption after a mean distance of 640 km, with a standard deviation of 160 km. Zack plans to replace his shoes when there is only a 25% chance that they have lost their shock absorption. At what distance should Zack replace his shoes?

1. Enter the data.Enter the given area (as a decimal, 0.25) and the mean and the standard deviation of the distribution into appropriate cells.

2. Determine the data value that represents the given area.The NORMINV function calculates the data value that has a given area below it. For the cells shown, enter “�NORMINV(B1,B2,B3)”. The appropriate distance is displayed.


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3. Use the NORMSINV command with a standard normal distribution.If you are working with a standard normal distribution with mean 0 and standard deviation 1, you can replace the NORMINV function with the NORMSINV function. Omit the mean and standard deviation from the argument, and just enter the area. The z-score representing the given area is displayed.

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USING FATHOMGetting StartedFathom is a purpose-designed statistical software package. The main features of Fathom covered in this tutorial are case tables, summary tables, and graphs.

1. Create a case table.Drag a case table from the object shelf by clicking on the “Table” icon, and drop it in the document. Click and drag the bottom right corner to adjust the size of the case table.

2. Create a summary table.Drag a summary table from the object shelf by clicking on the “Summary” icon, and drop it in the document.

3. Create a graph.Drag a graph from the object shelf by clicking on the “Graph” icon, and drop it in the document.

In other Fathom topics, you can discover how to use these features to work with data.


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USING FATHOMEntering DataThe following frequency table shows the lengths of Emmanuella’s walks with her golden retriever during one month. To work with this data, you will need to enter it into a case table and calculate midpoints for the intervals.


Frequency 1 3 7 10 6 11 8 5 4 2 3

1. Set up attributes.

Variables are called attributes. Create a case table, click on “new” and enter the attributes by entering one attribute in each column.

The key on your keyboard moves the cursor to

the next column:

“lower” “upper” “midpoint” “frequency”

2. Enter the data.

Enter the data from the frequency table under “lower” (lower limits of intervals), “upper” (upper limits of intervals), and “frequency” (frequencies).

Use

Y= WINDOW ZOOM

2nd MODE DEL

ALPHA X, T, U, n STAT

MATH MATRIX PRGM

x–1 SIN COS

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ENTER

CLEAR

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ZDecimalx2

LOG

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TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

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^

to start a new row.

Use or SHIFT to move between columns.

Right-click on “midpoint” and select “Edit Formula”.

Then, type “(lower+upper)/2” and

Y= WINDOW ZOOM

2nd MODE DEL


MATH MATRIX PRGM

x–1 SIN COS

VARS

TAN

ENTER

CLEAR

APPS

ZDecimalx2

LOG

LN

STOR

ON

TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

2

1

^

.

The midpoint of the interval will be calculated in each row.


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USING FATHOMDetermining Mean, Median, Mode, Range, and Standard DeviationDetermine key statistics for the following data.

Unit 1 Test

81 76 73 71 64

80 75 73 71 63

79 75 73 68 61

79 74 73 67 58

78 73 72 66 57

1. Enter the data.

Create a new case table and enter the data under a single attribute, “score”.

2. Create a summary table to display the mean.

Create a new summary table.

Drag the attribute “score” from the case table into

the summary table.

The summary table will begin by showing the

mean as “S1 �mean( )”, with the actual value of

the mean next to the attribute name.

3. Determine the median and standard deviation.

Adjust the size of the summary table to make

room for additional statistics.

Right-click anywhere in the table and

select “Add Formula”.

Type “median()” and

Y= WINDOW ZOOM

2nd MODE DEL


MATH MATRIX PRGM

x–1 SIN COS

VARS

TAN

ENTER

CLEAR

APPS

ZDecimalx2

LOG

LN

STOR

ON

TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

2

1

^

.

The summary table will now show the median

for the scores. Repeat this procedure and type

“popStdDev()”,

Y= WINDOW ZOOM

2nd MODE DEL


MATH MATRIX PRGM

x–1 SIN COS

VARS

TAN

ENTER

CLEAR

APPS

ZDecimalx2

LOG

LN

STOR

ON

TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

2

1

^

to show the standard

deviation for the scores.

4. Determine the range.To determine the range, add a more complex formula in the same way as in step 3: type “max()−min()”,

Y= WINDOW ZOOM

2nd MODE DEL


MATH MATRIX PRGM

x–1 SIN COS

VARS

TAN

ENTER

CLEAR

APPS

ZDecimalx2

LOG

LN

STOR

ON

TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

2

1

^

. The range is displayed as the difference between the maximum and the minimum scores.

5. Determine the mode.To determine the mode, it is helpful to sort the data. Return to the case table, right-click on “score”, and select “Sort Ascending”.Scroll through the data and determine the mode by locating the value(s) that occur most frequently. In this case, the mode is 73.

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USING FATHOMDetermining the Mean and Standard Deviation of Grouped DataThe following frequency table shows the lengths of Emmanuella’s walks with her golden retriever during one month. To work with this data, you will need to enter it into a case table and calculate midpoints for the intervals.


Frequency 1 3 7 10 6 11 8 5 4 2 3

1. Determine the data sums for the grouped data.

Create a new attribute,“fx”, in the case

table for Collection 1.

Right-click on “fx” and select “Edit Formula”.

Then, type “frequency�midpoint” and

Y= WINDOW ZOOM

2nd MODE DEL


MATH MATRIX PRGM

x–1 SIN COS

VARS

TAN

ENTER

CLEAR

APPS

ZDecimalx2

LOG

LN

STOR

ON

TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

2

1

^

.

The data sums for each interval will be

calculated in each row.


2. Determine the sums of the squared deviations for the grouped data.

Create a new attribute,“fsqdev”, in the case

table for Collection 1.

Right-click on “fsqdev” and

select “Edit Formula”.

Then, type “frequency�midpoint”

and

Y= WINDOW ZOOM

2nd MODE DEL


MATH MATRIX PRGM

x–1 SIN COS

VARS

TAN

ENTER

CLEAR

APPS

ZDecimalx2

LOG

LN

STOR

ON

TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

2

1

^

.

The data sums of the squared deviations for

each interval will be calculated in each row.

3. Determine the mean of the grouped data.

Create a new summary table.

Drag the attribute “score” from the case table

into the summary table.

The summary table will begin by showing the

mean as “S1 �mean( )”.

This is not the value you need however.

Right-click on “S1 �mean( )” and

select “Edit Formula”, then type

“sum(fx)/sum(frequency)” and

Y= WINDOW ZOOM

2nd MODE DEL


MATH MATRIX PRGM

x–1 SIN COS

VARS

TAN

ENTER

CLEAR

APPS

ZDecimalx2

LOG

LN

STOR

ON

TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

2

1

^

.

The mean of the grouped data will now be displayed

in the summary table.

4. Determine the standard deviation of the grouped data.

Adjust the size of the summary table to make

room for additional statistics.

Right-click anywhere in the table and

select “Add Formula”.

Type “sqrt(sum(fsqdev)/sum(frequency))” and

Y= WINDOW ZOOM

2nd MODE DEL


MATH MATRIX PRGM

x–1 SIN COS

VARS

TAN

ENTER

CLEAR

APPS

ZDecimalx2

LOG

LN

STOR

ON

TRACE GRAPH

, ( )

7 8 9 C

4 5 6

1 2 3

0 . (2)

4

3

2

1

^

.

The summary table will now show the standard

deviation of the grouped data.


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USING FATHOMCreating a HistogramUse the following data to create a histogram:

Unit 1 Test

81 76 73 71 64

80 75 73 71 63

79 75 73 68 61

79 74 73 67 58

78 73 72 66 57

1. Create the histogram.Create a graph. From the case table for Collection 2, drag “score” onto the horizontal axis of the graph. Click on the graph type in the top right of the graph and change it to “Histogram”.


2. Adjust the interval widths.

Right-click anywhere on the graph and select

“Inspect Graph”.

A dialog box will appear; click on the

“Properties” tab and change binwidth to 5,

then close the dialog box by clicking

the red “×” at the top right corner.

Adjust the vertical axis of the graph, if necessary,

by clicking and dragging the upper part of the axis.

3. Finish the chart.

Double-click on “Collection 2” and change it

to an appropriate title for the graph, such as

“Unit 1 Test Scores”.


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USING FATHOMCreating a Frequency PolygonThe following frequency table shows the lengths of Emmanuella’s walks with her golden retriever during one month. To work with this data, you will need to enter it into a case table and calculate midpoints for the intervals.


Frequency 1 3 7 10 6 11 8 5 4 2 3

1. Create the frequency polygon.

Create a graph.

From the case table for Collection 1,

drag “midpoint” onto the horizontal axis of the graph,

then drag “frequency” onto the vertical axis.

2. Finish the graph.

Click on the graph type in the top right of the graph

and change it to “Line Scatter Plot”.

This connects the data points.

Double-click on “Collection 1” and change this to an appropriate

title for the graph, such as “Emmanuella’s Walks”.

Also double-click on “midpoint” and change this to

“length_of_walk_min”.

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USING THE GEOMETER’S SKETCHPADGetting Started

Sketches and Dynamic Geometry

The ability to change objects dynamically is the most important feature of The Geometer’s Sketchpad. Once you have created an object, you can move it, rotate it, dilate it, reflect it, or hide it. You can also change its label, colour, shade, or line thickness. No matter what changes you make, The Geometer’s Sketchpad maintains the mathematical relationships between your object and other objects it is related to. This is the principle of dynamic geometry and the basis of the power and usefulness of The Geometer’s Sketchpad.

Sketchpad Terminology

Select means move the mouse pointer to the desired location and click the mouse button (left-click for Windows users).

Deselect means select the selection tool and click anywhere in the display area, away from any figures you have drawn.

Drag means move the mouse pointer to the point or figure you would like to move. Click on the point or figure and, while holding down the mouse button, move the point or figure to a new location. Release the mouse button when the point or figure is in the desired position. This can also be done to text and labels.

Select.

Construct a circle.Construct a line.

Label.

Construct a point.

display areatoolbar

menu bar

Custom Tool.


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USING THE GEOMETER’S SKETCHPADUsing the Construct Menu

Command What It Constructs What You Must Select

Point On Object a point on the selected object(s) one or more segments, rays, lines, or circles

Intersection a point where two objects intersect two straight objects, two circles, or a straight object and a circle

Midpoint the midpoint of the segment(s) one or more segments

Segment/Ray/Line the segment(s), ray(s), or line(s) defined by the points

two or more points

Parallel Line the line(s) through the selected point(s), parallel to the selected straight object(s)

one point and one or more straight objects, or one straight object and one or more points

Perpendicular Line the line(s) through the selected point(s), perpendicular to the selected straight object(s)

one point and one or more straight objects, or one straight object and one or more points

Angle Bisector the ray that bisects the angle defined by three points

three points (select the vertex second)

Circle By Centre 1 Point the circle with the given centre and passing through the given point

two points (select the centre first)

Circle By Centre 1 Radius the circle with the given centre and with a radius equal to the length of the given segment

a point and a segment

Arc On Circle the arc that extends counterclockwise from the first point on a circle to the second point

a circle and two points on the circumference of the circle

Arc Through 3 Points the arc that passes through the three given points

three points

Polygon Interior the interior of a polygon defined by using the given points as its vertices

three or more points

Circle Interior the interior of a circle one or more circles

Sector Interior the interior of an arc sector one or more arcs

Arc Segment Interior the interior of an arc segment one or more arcs

Locus the locus of an object one geometric object and one point constructed to lie on a path

Note: At any point in time, your selections determine which menu commands are available at that point. When a command is not available, it is greyed out in its menu. Often this means your current selection is not appropriate for that command.

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USING THE GEOMETER’S SKETCHPADEntering and Graphing a FunctionYou can graph functions on a Cartesian coordinate system in The Geometer’s Sketchpad. For example, use the following steps to graph the function y � 2x � 8.

1. Turn on the grid.

From the Graph menu, choose

“Define Coordinate System”.

2. Enter the function.

From the Graph menu, choose “Plot New Function”.

The New Function calculator should appear.

Use either the calculator keypad or the keyboard

to enter “2 * x � 8”.

3. Graph the function y 5 2x 1 8.

Press “OK” on the calculator keypad. The graph

of y � 2x � 8 should appear on the grid.

4. Adjust the origin and/or the scale.

To adjust the origin, click on the point at the origin to

select it. Then click and drag the origin as desired.

To adjust the scale, click in blank space to deselect.

Then click on the point at (1, 0) to select it. Click and drag this point to change the scale.

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USING THE GEOMETER’S SKETCHPADEditing a Function

1. Edit the function.To change y �2x � 8 to y �2x2 � 8, double-click on the function label. The Edit Function calculator should appear. Move the cursor to the right of the “x”. Use either the calculator keypad or the keyboard to add “^2”.

2. Display the graph of the edited function.Click “OK” to display the modified graph.

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You can also use the Point Tool to plot points without graphing a function. For example, suppose you want to plot (4, 2).


2. Select the Point Tool.

The selection arrow will now look like a dot. This indicates that when you click on the grid, a point will be placed at the location you clicked.

USING THE GEOMETER’S SKETCHPADPlotting PointsSometimes, you may want to plot points without graphing a function. For example, suppose you want to plot (2, 1), (3, 5), and (–2, 0).


2. Enter the coordinates of the points.

• From the Graph menu, select “Plot Points …”.

• For each point you want to plot, enter the x-coordinate followed by the y-coordinate.

• Use the “Tab” key on your keyboard to move from one coordinate entry space to the next.

• Select “Plot” when you have entered both coordinates of a point.

You can continue entering coordinates until you click on “Done”.

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5. Select the Label tool. Use it to double-click on the point you constructed.A label will appear beside the point, as well as a “Properties” box for the point. You can change the label of the point by changing the contents of the label entry in the “Properties” box.

USING THE GEOMETER’S SKETCHPADConstructing and Labelling a Point on a Line, Segment, or Ray


2. Draw a line (or segment or ray).

3. Select the line by clicking on it.

4. From the Construct menu, select “Point On Line”.

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USING THE GEOMETER’S SKETCHPADConstructing a Line, Segment, or Ray through a Given Point


2. Plot the point you want the line (or segment or ray) to pass through.

3. Plot a second point anywhere on the grid.

4. Shift-click to make sure that both points are selected.If you are constructing a ray, make sure that the point where the ray begins is selected first.

5. From the Construct menu, select “Line” (or “Segment” or “Ray”).


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USING THE GEOMETER’S SKETCHPADConstructing a Triangle and Labelling the Vertices

1. Open a new sketch.

2. Use the Point Tool to place three points.If you hold down the “Shift” key on your keyboard while you place the points, all the points will remain selected as you place them.

3. From the Display menu, select “Show Labels”.The order in which you select the points determines the alphabetical order of the labels.

4. From the Construct menu, select “Segments”.

The three sides of the triangle will be displayed.


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USING THE GEOMETER’S SKETCHPADMeasuring an Angle

1. Open a new sketch, and draw a triangle with the vertex labels displayed.

2. Shift-click to select the vertices that form an angle.For example, to measure �ABC, select vertex A, then vertex B, and then vertex C.

3. From the Measure menu, select “Angle”.

4. Repeat steps 2 and 3 for each angle.


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USING THE GEOMETER’S SKETCHPADConstructing and Measuring an Exterior Angle of a Triangle

1. Open a new sketch, and draw a triangle with the vertex labels displayed.

2. Select two vertices.

3. From the Construct menu, select “Ray”.This will extend one side of the triangle to form an exterior angle.

4. While the ray is selected, choose “Point On Ray” from the Construct menu.

5. Drag the point so that it is outside the triangle. Display the label for the point.

6. Select the exterior angle.Select the point, then the vertex for the angle, and then the final vertex. From the Measure menu, select “Angle”.


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USING THE GEOMETER’S SKETCHPADDetermining the Sum of the Interior Angles of a Triangle

1. Open a new sketch, and draw a labelled triangle.

• Measure all three interior angles.

• Shift-click to select all three angle measures.

2. From the Measure menu, select “Calculate”.A New Calculation window will appear.

3. Use the Values pop-up menu to create the formula for the sum of the selected angles.

• Choose an angle from the Values pop-up.

• Then enter “1” and continue entering addends until the formula is complete.

• Click “OK” when you are finished.


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USING THE GEOMETER’S SKETCHPADMeasuring the Length of a Line Segment

1. Open a new sketch, and draw a line segment.

2. While the line segment is selected, choose “Length” from the Measure menu.

The length will be displayed.

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