math ii - fathom 10 coin flips (how many coins would you ... 4-task2.pdffathom can even take it a...

TASK #2 Math II - FATHOM 10 coin Flips (How many coins would you predict land on heads?) • Open a new Fathom Workspace.

• Drag a collection, , from the shelf into the workspace.

• Open the collection by positioning the cursor at the lower

right hand corner of the collection icon (as shown below).

Finally, click and drag when the cursor changes to a

resizing icon. Make the collection larger.

This will effectively open the collection so that

you can see what is inside of it.

• With the open collection selected, choose New Cases…

under the Collection menu (as shown at the right). Choose

10 cases and press OK.

• 10 new gold icons should be created in the collection after

the last step. Double click on one of the icons to open up

the inspector window.

• In the Inspector window under the Tab Cases and the

Column Attribute click on the word <new> and type in the

word “Flip”

• Two cells to the right of the cell you just labeled “Flip”

double click the space under “Formula”

In the calculator window Type

“ ”

Double Click in this space to open the

Calculator/Formula i d

Double Click in this space to open the

Calculator/Formula window.

Double Click

and press OK. This should cause either an “H” or “T” to appear in the value cell.

• Next, at the top of the Inspect Collection 1 window click on the Display Tab. Then, double click on

the cell to the right of caption and under Formula as shown below. When the Formula window opens

up click the next to the word Attributes. Double click on the word “Flip”. Finally, press OK.

• The last step should have caused the title underneath each gold ball

representing a case to change to either “H” or “T” depending on which the

case is representing. Fathom can even take it a step further and have the

icon be a picture of a coin Heads up or Tails up depending on the value of

the “Flip” for each case.

• This time in the Inspect Collection 1 window and under the formula cell for image double click to open

the formula editor. In the formula editor type: . You can select the different Icons

by clicking on the next to Icon Names.

• First click on the “Measures” tab in the Inspect Collection

window. Click on the text <new> and type in

“NumberofHeads”

Double Click in this space to open the

Calculator/Formula window.

Double Click in this space and then double click on the Attribute

“Flip”

Double Click in this space to open the

Calculator/Formula i d

Double Click in this space and then enter

this conditional statement.

Click here and change the title to “NumberofHeads”

Math 2 – Unit 4 M. Winking e-mail: wiseone@mindspring.com p.1

• Double click on the cell to the right of “NumberofHeads”

and under Formula. Then in the formula window type in

and click on OK.

• With the collection highlighted, select

Collect Measures from the Collection

menu.

• The last step will cause Fathom to re-randomize the 10 coin flips and then record the information from

that group in a new collection. Fathom at its default setting will collect 5 sets of coin flips. Open the newly

created measures by resizing the measures box created. Double click on one of the green cases inside.

Double Click in this space to open the

Calculator/Formula i d

Double Click in this space and then enter the count

statement shown.

Double click on the green case to open this

inspector window.

Double click on the green case to open this

inspector window.

Math 2 – Unit 4 M. Winking e-mail: wiseone@mindspring.com p.2

• In the Inspect Measures from Collection window select the Display tab and double click on the Formula cell to the right of caption. This will open the formula window again. Click the next to Attributes and double click the attribute “NumberofHeads”. Finally, click OK .

• The last step will change the title underneath each Measure to the number of Heads flipped in the sample. Currently, we only have 5 sets of 10 coins being flipped. Lets quickly create a 1000 more sets of 10 coin flips. Click on the “Collect Measures” tab in the inspector window.

• First, unselect the “Animations on” and change the number of measures from the default of 5 to as many trials as you would like. Finally, click on .

• Click on the “Cases” tab in the inspector

window and then drag a Graph, , into the workspace.

Double Click in this space to open the

Calculator/Formula i d

Double Click in this space and then double click on

“NumberofHeads”

Any time you are creating large samples of measures it is CRITICAL make sure “Animations on” is NOT checked.

Math 2 – Unit 4 M. Winking e-mail: wiseone@mindspring.com p.3

• Drag the word “NumberofHeads” from the

Inspector window onto the x-axis of the

graph.

• Click on the arrow to the right of word

and change the graph into a histogram

as shown at the right.

• The histogram looks fairly normally

distributed.

• In order to overlay an actual normal curve on

top of the histogram to see how normal the

distribution looks, it will be easier if we look at

the histogram using a relative frequency rather

than just the actual frequency. With the graph

selected, under the Graph menu change the

Math 2 – Unit 4 M. Winking e-mail: wiseone@mindspring.com p.4

Math 2 – Unit 4 M. Winking e-mail: wiseone@mindspring.com 5

Scale to Relative Frequency as shown at the

right.

• While the graph is still highlighted, this time

select Plot Function from the Graph menu.

• In the formula window type in:

and push OK .

• You can experiment with taking new collections in the measure menu and very consistently demonstrate that

this is consistently a very normal distribution.

Math 2 – Unit 4 M. Winking e-mail: wiseone@mindspring.com p.6