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This show is intended for students who were absent from class on the day of the task.

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Click on a question for assistance. Question #1Question #5 Question #2Question #6 Question #3 Question #7a Question #4 Question #7b Exit Presentation

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Which rectangle below has a perimeter of 20 units? Click on the answer of your choice.

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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

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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

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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. 1 9 5 4 Click to continue to #2 When you are ready, complete sketches for #1.

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s 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

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Look at each of your sketches of a rectangle with a perimeter of 20 units. What do you notice about the relationship between the base and height? Click here for Hint Main Menu

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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

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Note: 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

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Which diagram below looks like your graph?

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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

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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 area of rectangles when the base is longer than 5 ft. Enter this data into your table and plot these points. Then click continue. Continue

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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 area of rectangles when the base is shorter than 5 ft. Enter this data into your table and plot these points. Then click continue. Continue

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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

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Which diagram below looks like your graph?

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What dimensions (base and height) will enclose the greatest area using 20 ft of fencing? 4 ft by 6 ft 5 ft by 5 ft

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Is a square a rectangle? YES NO

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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

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A 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

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Continue to question #6 or go back to the MAIN MENU. MAIN MENU Click here to continue to #6

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What 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

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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

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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

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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 b=4’ h=6’ b=6’ h=4’ Maximum (dimensions are the same length)

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A gardener has 68 ft of fencing. What dimensions would enclose the greatest area? 17 ft by 17 ft 16 ft by 18 ft

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Excellent work. Now calculate the maximum area in part b. Click MAIN MENU below. MAIN MENU Click here to continue to #7b

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What 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

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A gardener has 68 ft of fencing. How much area would your dimensions from #7a enclose? 289 sq ft 288 sq ft

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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

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What 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

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