Casio Education - Activities - The House That Math Built

Objective: The student will be able to manipulate the distance formula and calculate the scale factor between two given pictures.

Engage: Give students a copy of "The House That Math Built". Ask them to copy the drawing without lifting their pencil.

Equipment
2 Motion Detectors
2 EA-100s
CFX-9850G+
1 picture of " The House That Math Built"
meter sticks - for measuring and pointing
tape
data communication cable

Tape the picture of "The House That Math Built" to a LARGE table.

Set up TWO EA-100 devices with a Motion Detector attached to each one.

Place the motion detectors on the table top as indicated on the picture. Be sure to measure accurately and position the detectors so that the cones of detection are perpendicular to each other. The intersection of the cones must be located over the center of the picture.

Make sure the motion detector is plugged into the SONIC port of the EA-100. DO NOT connect the EA-100 to the calculator.

To collect data points, use a meter stick held over the picture to point to each vertex in the order specified. Note: It is EXTREMELY IMPORTANT that the pointer operator is not inside the cones of detection. This may mean that the student must stand on a chair.

Listen to the ticking sounds emitted from the motion detectors. After pointing to a vertex and hearing the corresponding tick of the detector, move the stick to the next point. Wait for the tick before continuing in like manner. After reaching the final point, wait at that vertex until the EA-100s says DONE.

To operate the EA-100 manually, use the following keystrokes:

Keystroke	Explanation
Press[SHIFT][MODE]	"Set-up"
Press [DATALOG] until "5 Sec" appears "Next"	Press [DATALOG] several times until the sample time you want appears (5 Sec)
Press[TRIGGER]	Chooses the 5 Sec as the time
Press[DATALOG] until "10" appears	Press [DATALOG] several times until the number of sample points you want appears (10)
Press[TRIGGER]	Chooses 10 as the number of samples
Press [DATALOG] until 1 appears "Next"	Press [DATALOG] until you see the time consideration you want. In this case, the time will be collected as data
Press[TRIGGER]	Selects time consideration
Press[TRIGGER]	Begins sampling. This means that it is time to place the pointer on each individual letter on the picture in the following order : A C B D E C D A B

Retrieve the data from the EA-100:

Connect EA-100 to CFX-9850G+ using data communication cable
Turn on CFX-9850G+ and choose Run (1) from the menu
Press SHIFT VARS {PRGM}
Press F6 (>) , then I/O {F4}
Press Recu (F4) {Receive( }
Press OPTN, List {F1}, List {F1} ,1, close Parenthesis { ) }
Press SHIFT EXE {ø }
Press Recu (F4) {Receive( }
Press OPTN, List {F1}, List {F1} ,2, close Parenthesis { ) }
Press EXE

The data should now be listed in List 1 and List 2.

Go to the Main Menu and choose List (4)

Cursor across the top of the screen, highlighting List 3
Press OPTN , List {F1}, List {F1}, 1 , EXE This will copy the data in List 1 to List 3.
Cursor across the top of the screen, highlighting List 4
Press OPTN , List {F1}, List {F1}, 2 , EXE This will copy the data in List 2 to List 4.

Repeat Step 2- ONLY. This will enter the data from the second EA-100 to List 1 and List 2.

For the next part of the procedure you will be operating in the STAT menu.

After entering the STAT menu, you should find List 1 through List 4.
Press GRAPH {F1}
Press SEL {F4}
StatGraph 1 : DrawOn
EXIT
Press SET {F6}
Graph Type: xyline
Xlist : List 2
Ylist : List 4
Frequency : 1
Mark Type : ?
Graph Color: CHOICE
EXIT
GRPH 1 {F1}

Explain: Record the data points from either the tables (List 2, List 4) or the graph. Have the students identify the coordinates for each point A through E. Using the data gathered, have students use the distance formula to determine the lengths of each exterior segment .

Elaborate:Measure the same segments on the actual drawing in cm. After converting the graphed segment lengths to cm, determine the scale factor for the drawing.

Evaluate Give the students a drawing to be redrawn either using an increased or decreased scale factor. Note: An extra project could be to create a 3-D model of the scaled picture.

Lessons / Activities : Lessons EA-100

The House That Math Built