Math Help
Car Park Maths Project
Do you have problems setting an interesting and new maths project, that all the students in your class, whatever their level of ability is, can take part in? This project to plan a new car park layout, gained the interest of the students and provided many lines of investigation that stretched the more able, while allowing the others to utilise their basic maths. I used it with GCSE students but it can easily be adapted to other levels.
This idea was thought up when the college car park was being extended and changed and it certainly engaged the students and provided for some novel and interesting ideas from the students.
Drawing a Scale Plan
The students will need to measure the car park, paths and buildings. They will need to calculate the angles to ensure the lines meet up correctly. Encourage a legend to be added to the plan to show trees, bushes, paths, doors etc
Set a scale that the plan should be drawn to, this will enable you to easily check the results at the start against a master plan. This will involve the use of ratios to calculate the length of the lines of the paper.
Alternatively, this could be a combined exercise for the whole class, producing a single scale plan that can be copied and provided as the starting point of the project.
Data Gathering
The students will need to obtain data to decide how big to make their car park spaces. There are various types of data gathering and surveys that can be undertaken and used in the project. Some examples are given below, but don’t let this list limit your imagination.
- The size of spaces in a number of car parks in the local area.
- The size of various types of cars
- The popularity of the different size cars
- The room need to open car doors
Presenting Data
There are various standard ways to present the data, for the car park spaces and the car park sizes. Some examples are specified below for the car data, but there are many more possibilities. The students can take this as far as their capabilities allow.
- Group the car data in to a frequency table. Calculate the percentages to show the most popular sizing groups.
- Visually present the grouped data in bar charts
- Use a scatter plot to show the relationship between length and width. There should be a strong correlation.
- The popularity of cars sizes could be presented as a ratio.
Calculating Statistics
Everyone should be able to attempt to calculate the median, mode and mean averages for the length and width of the spaces and the cars. A good extension is to calculate further measures such as the standard deviation and percentiles.
Making Decisions from Data
The point of the data gathering is to determine what size the car park space needs to be. They are trying to fit in the maximum number of spaces, while still allowing the car park to be used effectively. This is the interesting part to see what the students will think of.
- do the students remember that you need to open and close the doors
- have they allowed room to drive in and out of spaces
- what inventive ideas have they come up with. One report handed in had three recommended car space sizes, one for large cars, one for small cars and one for disabled drivers who need to open their doors wide.
Extension Study
There are many further directions that this study can be taken to. A few ideas are below, but encourage your students use their imagination
- Usage Surveys: Surveying the car use in the area to determine the usage to ensure the car park has enough spaces.
- Financial: Would it be possible to charge for the use of the car park, how much you would expect to make, how much it would cost to operate, would people pay.
- Trigonometry: One student measured the turning circle of a few cars and use trigonometry to calculate the optimum turning space needed to get in and out of a car park space
Marking
You are really marking this project on the accuracy, applicability and the difficulty employed in the various techniques, but do allow a portion for the finished result.
- Are there a reasonable number of spaces?
- Is it possible to get in and out of you space and car without scraping the car next to it.
This study was very popular with the students and the reports varied from fairly basic to some advanced maths according to the ability of the student. While they had some guidance and ideas, they were encouraged to think up more for themselves and they certainly did this.
Car Park Maths
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