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Question

Context In 1933, Head Teacher James Dempsey, stated that the Junction Park Swimming Pool, Queensland’s first state school swimming pool, started the movement that spread not only across schools in Queensland, but also in New South Wales. With the very first on-site state school swimming program, came the first dedicated swimming teachers. The pool was opened by the Minister of Education, Walter H. Barnes, on Saturday afternoon, 5 February 1910. The concrete structure of the pool cost about £175 and was built by Messrs. Wells and Bennett, of Woolloongabba. The pool is 43ft. long by 16ft. wide, with a maximum depth of water varying from 30in. to 50in. when full. When it first opened the daily average in the pool was 100 swimmers, in four sessions during the day. (Mapping Brisbane History, 2024)

Today across the Sunshine State, only about 200 of about 1200 public schools have their own swimming pool, meaning more than 80 per cent of schools are forced to transport their students to access swimming lessons. (The Courier Mail, Jan 2024).

Narangba Valley State High School has requested you, a Brisbane-based pool designer, to design a fenced composite-shaped pool, surrounding paved areas and shade sail areas. You have also been asked to consider and calculate some of the costs involved in its construction.

Task Write a mathematical report to demonstrate that you can:
• Use appropriate metric units when solving measurement problems involving perimeter and area of composite shapes.
- In the creation of:
o Pool Fencing
o Composite pool shape
o Pool Paving

• Use appropriate metric units when solving measurement problems for volume of right prisms.
- In the creation of pool volume

• Use formulas to solve problems involving the area and circumference of circles.
- In the creation of paved circular areas

• Use Pythagoras to solve measurement problems.
- In the creation of right - angled shade sails

• Use modelling to solve practical problems in relation to the building and costs of the construction
- Involving labour rates, material costs, inflation and pool prep.
Conditions Duration – 8 weeks
Mode/length – Written Report
Individual/group - Individual
Resources – Scientific calculators and computers will be used for research and presentation
Checkpoints Checkpoint 1 – Week 4
Checkpoint 2 – Week 6
Checkpoint 3 – Week 8
Due Week 9 – Last common-day lesson
Stimulus • The completed design is to be contained within a 16 by 24 metre land space.
• Display the one designs on grid paper using the scale 1cm represents 1 metre – teacher support can be given for knowledge of scale.
• Design border paving and fencing around each of the pools with a maximum 2 metre of border paving around the outside
• For the design, circular paved areas should have one area which has a diameter larger than 1m and less than 6m and the other having an area between 18 and 25 square metres.

Write A short paragraph that outlines the context of the problem.

Answer 1

The context of the problem is that Narangba Valley State High School has requested a Brisbane-based pool designer to design a fenced composite-shaped pool, surrounding paved areas, and shade sail areas. The school is looking to have a new swimming pool constructed on their premises, and the designer is tasked with considering and calculating the costs involved in its construction. This project stems from the historical significance of the Junction Park Swimming Pool, which was Queensland's first state school swimming pool and started a movement that spread across schools in Queensland and New South Wales. Today, only about 200 out of 1200 public schools in Queensland have their own swimming pool, prompting schools without pools to transport their students for swimming lessons. The designer is expected to use mathematical calculations to determine the appropriate measurements, volumes, and costs associated with designing and constructing the new pool.

Answer 2

now write a short paragraph that identifies the task and the problem that is to be solved.

Answer 3

The task at hand is for the Brisbane-based pool designer to create a mathematical report demonstrating their ability to design a fenced composite-shaped pool, surrounding paved areas, and shade sail areas for Narangba Valley State High School. The designer must use appropriate metric units to solve measurement problems involving perimeter, area, volume, and circumference of various shapes within a specified land space. Furthermore, the designer is required to utilize Pythagoras' theorem and modeling techniques to address practical problems related to construction costs, labor rates, material costs, and inflation. The ultimate goal is to provide a comprehensive design plan that meets the school's requirements within a specific timeframe and budget.