this show is intended for students who were absent from class on the day of the task
TRANSCRIPT
AREA I: MAXIMIZING
AREA WITH A FIXED
PERIMETERThis show is intended for students
who were absent from class on the day of the task.
MAIN MENUClick on a question for assistance.
Question #1
Question #5Question
#2Question
#6Question #3
Question #7aQuestion
#4Question
#7bExit Presentation
READ THE TASK. THEN ANSWER THE FOLLOWING QUESTION.
Which rectangle below has a perimeter of 20 units? Click on the answer of your choice.
CORRECT! GREAT JOB!Now complete problem #1 on your handout by sketching several rectangles with a perimeter of 20 units.
Click here to continue to #2
Main Menu
INCORRECT – YOU HAVE CONFUSED AREA WITH PERIMETER!
You have confused area with perimeter. In order to find the perimeter of a rectangle, do you multiply the base by the height, OR do you add all of the side lengths?
Multiply the base by the height
Add all of the side lengths
INCORRECT – YOU HAVE CONFUSED AREA WITH PERIMETER!
In order to find the perimeter of a rectangle, you add all of the side lengths. Click anywhere on slide to reveal the perimeter of each rectangle.
195
4𝑃=1+9+1+9
units𝑃=4+5+4+5
units
Click to continue
to #2
When you are ready, complete sketches for
#1.
sCORRECT! GREAT JOB!Now complete problem #1 on your handout by sketching several rectangles with a perimeter of 20 units.
Main Menu
Click here to continue to #2
QESTION 2: Look at each of your sketches of a rectangle with a perimeter of 20 units. What do you notice aboutthe relationship between the base and height?
Click here for Hint
Main Menu
QESTION 2: HINT
Try adding, subtracting, multiplying and dividing each base and height. Do you notice a pattern using any of these operations?
Main Menu
Click here to continue to #3
QUESTION 3-TABLENote: You do not need to complete the entire table in order to be able to make a graph. If you are unable to notice anything about the area in the table or graph, you may want to add more data to your table.
Main Menu
Click here to continue to #4
QUESTION 4-GRAPHWhich diagram below looks like your graph?
WATCH!Look at the labels on the graph. Notice that you are graphing how the base is related to the AREA.
You are NOT graphing how the base is related to the HEIGHT.
Redo your graph. Then click continue.
Continue
WHAT HAPPENS AS THE BASE INCREASES?As your base increases, what happens to your area? Yes, it increases.
Will the area continue to increase when the base gets longer than 5 ft? How do you know?
If you are not sure, calculate the areaof rectangles when the base is longerthan 5 ft. Enter this data into your table and plot these points. Then click continue.
Continue
WHAT HAPPENS AS THE BASE DECREASES?As your base decreases, what happens to your area? Yes, it increases.
Will the area continue to increase when the base gets shorter than 5 ft? How do you know?
If you are not sure, calculate the areaof rectangles when the base is shorterthan 5 ft. Enter this data into your table and plot these points. Then click continue.
Continue
EXCELLENT WORK!Your graph is complete. Why does the area increase and then decrease? Is there a logical reason for this?
After you have considered the question above, continue to question #5 or return to MAIN MENU.
MAIN MENU
Click here to continue to #5
TRY QUESTION 4 AGAINWhich diagram below looks like your graph?
QUESTION 5What dimensions (base and height) will enclose the greatest area using 20 ft of fencing?
4 ft by 6 ft
5 ft by 5 ft
INCORRECTIs a square a rectangle?
YES
NO
CORRECT!A square is a rectangle.
On your graph, when the base is 4 ft, the area is 24 sq ft. When the base is 6 ft, the area is 24 sq ft. What happens in between these two points? Is the area larger or smaller than 24 sq ft?
After answering this question, click below to return to Question #5.
Return to Question #5
INCORRECTA rectangle is an equiangular parallelogram.
In other words it has two pairs of parallel sides and all right angles.
Does a square have two pairs of parallel sides and all right angles? If so, then a square is a rectangle.
Return to Question #5
CORRECT! EXCELLENT WORK.Continue to question #6 or go back to the MAIN MENU.
MAIN MENU
Click here to continue to #6
QUESTION 6What kind of rectangle is your result from #5? If your rectangle is not a particular type, you may want to go back to question #5 before continuing.
Click to Continue
Return to Question #5
QUESTION 6 CONTINUED…Do you think that would be the result for any fixed perimeter? In other words, if I gave you a new fixed perimeter (for example: 50 ft), would this same shape give you the maximum area?
NO
YES
CORRECT!When you look at your graph, you will notice that the area increases and then decreases. This happens because the base and height switch. This will always happen when calculating the area of a rectangle, so there will always be a maximum area when the side lengths are the same. Therefore, a square will always give you the maximum area when given a fixed perimeter.
MAIN MENU
Click here to continue to #7a
INCORRECTWhen you look at your graph, you will notice that the area increases and then decreases. This happens because the base and height switch. This will always happen when calculating the area of a rectangle, so there will always be a maximum area when the side lengths are the same. Therefore, a square will always give you the maximum area when given a fixed perimeter.
MAIN MENU
b=4’h=6’
b=6’h=4’
Maximum(dimensions are the
same length)
QUESTION 7AA gardener has 68 ft of fencing. What dimensions would enclose the greatest area?
17 ft by 17 ft
16 ft by 18 ft
CORRECT!Excellent work. Now calculate the maximum area in part b. Click MAIN MENU below.
MAIN MENU
Click here to continue to #7b
INCORRECTWhat kind of rectangle will give you the maximum area if you have a fixed perimeter?
Click below to go back to Question #6. Then try this problem again.
Return to Question #6
QUESTION 7BA gardener has 68 ft of fencing. How much area would your dimensions from #7a enclose?
289 sq ft
288 sq ft
CORRECT!Excellent work. Click MAIN MENU below if you have more questions or exit the presentation if you are finished completing the task.
MAIN MENU
Exit Presentation
INCORRECTWhat kind of rectangle will give you the maximum area if you have a fixed perimeter?
Click below to go back to Question #6. Then try this problem again.
Return to Question #6