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available parking spaces to 51...

Below is the Sketch of the improved parking lot from 36 available parking spaces to 51 total parking spaces with 15 newly added parking spaces.

The design was 4 rows were made from previously 3 rows. Three of the four rows are composed of 13 parking spaces while one of these four rows has only twelve parking spaces, so a total of 13 + 13 + 13 + 12 = 51 spaces. The length of the single road on top is 12 ft, since it is only designed for a one-way road. While the two-way road at the middle have a width of 24 ft. Each parking space has a width of 9ft then the 12 painted lines that separate each parking spaces in each row, has a total length of 9ft x 13 + 4in x (1 ft / 12 in) x 12 = 121 ft. Then another one-way road with width 12 ft run across from top corner (parking space #13) up to bottom corner (parking space # 51) so the total length of these parking spaces, plus the painted lines, plus the one-way road is;

121ft + 12ft = 133ft. So there is still an extra space 150 ft – 133 ft = 17ft along the length of the parking lot. (Since the length is 50 yards and 1 yard is 3 feet, then the total length in terms of feet is 50 x 3 = 150 feet)For the width, since the total width is 40 yards, and 1 yard is equal to 3 feet, then the total width in terms of feet is 40 x 3 = 120 feet.So based on the design below, the width of the new parking lot, which has 4 one-way roads and four 18-feet long parking spaces, is 4 x 12ft + 4 x 18 ft = 120ft, which correctly fits the width of the parking lot, which is also 120 ft (or 40 yards).

So the new design below is correct and can be used for the plan of adding 15 new units of parking spaces.12 ft

1 2 3 4 5 6 7 8 9 10 11 12 13 18 ft

14 15 16 17 18 19 20 21 22 23 24 25 18 ft

12 ft

12 ft

26 27 28 29 30 31 32 33 34 35 36 37 38 18 ft

39 40 41 42 43 44 45 46 47 48 49 50 51 18 ft

12 ftYou take the above solution and drawing and continue with the assignment below:Assignment: Points, Lines, Planes, and Angles

Many real-world situations require an understanding of measurement and geometry. As you examined in Week 1, for example, measurement, geometry, and estimation are required to create a parking lot. Parking spaces may be parallel, perpendicular, or angled (such as 45, 60, or 75 degrees). But which arrangement will accommodate the most vehicles and maximize the number of parking spaces possible in a parking lot?

In this Assignment, you will reexamine the “Parking Lot Problem” from Week 1 to determine if incorporating angled parking spaces will impact the overall number of the parking spaces in the lot. You also will further develop the mathematical task you created in Week 1 to include concepts of points, lines, planes, and angles.

The Parking Lot Problem Revisited

There has been a change in the parking lot scenario at the CRC. After consulting with city planners, the CRC manager has concluded that angled parking spaces may be easier for drivers to navigate than the 90-degree spaces. Angled parking spaces can only be entered from one direction and drivers must enter these spaces “head-on.”

If each parking space in the CRC lot must maintain the 9 ft. x 18 ft parking areas, but must now be angled at 60 degrees, how will this new requirement impact the overall number of parking spaces possible?

Solve this mathematical task. As you do so:

• Make note of your problem-solving strategies, particularly the estimation and/or approximation strategies you utilize.

• Create a drawing to represent the new angled spaces in the parking lot.

Then, revisit the mathematical task you developed for students in Week 1 and consider how you might expand the task to include the following concepts:

• Points

• Lines (such as perpendicular, parallel, intersecting)

• Planes

• Angles

How might you use one or more of the technology tools introduced in this week’s Discussion to further enhance this task?

The design was 4 rows were made from previously 3 rows. Three of the four rows are composed of 13 parking spaces while one of these four rows has only twelve parking spaces, so a total of 13 + 13 + 13 + 12 = 51 spaces. The length of the single road on top is 12 ft, since it is only designed for a one-way road. While the two-way road at the middle have a width of 24 ft. Each parking space has a width of 9ft then the 12 painted lines that separate each parking spaces in each row, has a total length of 9ft x 13 + 4in x (1 ft / 12 in) x 12 = 121 ft. Then another one-way road with width 12 ft run across from top corner (parking space #13) up to bottom corner (parking space # 51) so the total length of these parking spaces, plus the painted lines, plus the one-way road is;

121ft + 12ft = 133ft. So there is still an extra space 150 ft – 133 ft = 17ft along the length of the parking lot. (Since the length is 50 yards and 1 yard is 3 feet, then the total length in terms of feet is 50 x 3 = 150 feet)For the width, since the total width is 40 yards, and 1 yard is equal to 3 feet, then the total width in terms of feet is 40 x 3 = 120 feet.So based on the design below, the width of the new parking lot, which has 4 one-way roads and four 18-feet long parking spaces, is 4 x 12ft + 4 x 18 ft = 120ft, which correctly fits the width of the parking lot, which is also 120 ft (or 40 yards).

So the new design below is correct and can be used for the plan of adding 15 new units of parking spaces.12 ft

1 2 3 4 5 6 7 8 9 10 11 12 13 18 ft

14 15 16 17 18 19 20 21 22 23 24 25 18 ft

12 ft

12 ft

26 27 28 29 30 31 32 33 34 35 36 37 38 18 ft

39 40 41 42 43 44 45 46 47 48 49 50 51 18 ft

12 ftYou take the above solution and drawing and continue with the assignment below:Assignment: Points, Lines, Planes, and Angles

Many real-world situations require an understanding of measurement and geometry. As you examined in Week 1, for example, measurement, geometry, and estimation are required to create a parking lot. Parking spaces may be parallel, perpendicular, or angled (such as 45, 60, or 75 degrees). But which arrangement will accommodate the most vehicles and maximize the number of parking spaces possible in a parking lot?

In this Assignment, you will reexamine the “Parking Lot Problem” from Week 1 to determine if incorporating angled parking spaces will impact the overall number of the parking spaces in the lot. You also will further develop the mathematical task you created in Week 1 to include concepts of points, lines, planes, and angles.

The Parking Lot Problem Revisited

There has been a change in the parking lot scenario at the CRC. After consulting with city planners, the CRC manager has concluded that angled parking spaces may be easier for drivers to navigate than the 90-degree spaces. Angled parking spaces can only be entered from one direction and drivers must enter these spaces “head-on.”

If each parking space in the CRC lot must maintain the 9 ft. x 18 ft parking areas, but must now be angled at 60 degrees, how will this new requirement impact the overall number of parking spaces possible?

Solve this mathematical task. As you do so:

• Make note of your problem-solving strategies, particularly the estimation and/or approximation strategies you utilize.

• Create a drawing to represent the new angled spaces in the parking lot.

Then, revisit the mathematical task you developed for students in Week 1 and consider how you might expand the task to include the following concepts:

• Points

• Lines (such as perpendicular, parallel, intersecting)

• Planes

• Angles

How might you use one or more of the technology tools introduced in this week’s Discussion to further enhance this task?

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