Problem Solving with Areas - can you solve real life scenarios
Problem solving, as far as GCSE Mathematics is concerned, usually has two key features:
A question is given as a real-life scenario (eg. Bob is painting a bedroom in her house …)
There is normally more than one topic of maths you will need in order to answer the question (eg. Area and Percentages)
Understand the problem: Read the problem carefully and make sure you understand what is being asked. Identify the key information and the goal of the problem.
Break down the problem: Divide the problem into smaller, manageable parts. Identify the steps needed to solve the problem.
Identify the unknowns: Determine what information is missing and what needs to be found.
Gather information: Use any relevant information or data that is provided to help solve the problem.
Explore possible solutions: Brainstorm different ways to solve the problem. Consider different approaches and evaluate their potential effectiveness.
Select the best solution: Choose the solution that is most likely to be effective and that is most feasible given the constraints of the problem.
Test your solution: Try out your solution and see if it works. Make adjustments as needed.
Evaluate the results: Analyze the results of your solution and consider how it could be improved.
Communicate your solution: Clearly explain your solution and the steps you took to solve the problem.
Area is a commonly used topic of maths in the real world
Laying a carpet,
painting a house,
designing a sports field,
Also, doing each of these things has a cost – so a lot of area problems also involve calculations with money
building a patio or
decking all involve area
Also, doing each of these things has a cost – so a lot of area problems also involve calculations with money
Once upon a time, there was a man named Mr. Weaver who had a beautiful garden in the shape of a rectangle. In the middle of the garden, there was a patio also in the shape of a rectangle and there were two ponds in the shape of circles with diameter 3.8 m. The rest of the garden was covered with lush green grass.
Mr. Weaver was determined to make his garden even more beautiful, so he decided to spread fertiliser over all the grass in his garden. He knew that one box of fertiliser would cover 25 m² of grass, so he needed to figure out how many boxes of fertiliser he needed to buy.
The garden measured 9.5 m in length and 17 m in width and a patio with the length 9.5 m and width 2.8m
He started by calculating the area of the grass by subtracting the area of the patio and the two ponds from the total area of the garden.
The total area of the garden was 9.5 m x 17 m = 161.5 m².
The area of the patio was 9.5 m x 2.8 m = 26.6 m².
The area of each pond was π x (3.8/2)^2 = 11.31 m². So, the total area of the two ponds was 11.31 m² x 2 = 22.62 m².
The area of the grass = Total area of the garden - area of the patio - area of the ponds = 161.5 m² - 26.6 m² - 22.62 m² = 112.28 m²
Next, Mr. Weaver divided the area of the grass by the area that one box of fertiliser can cover, which is 25 m². So, he needed:
112.28 m² / 25 m²/box = 4.491 boxes ≈ 4.5 boxes of fertiliser.
So, Mr. Weaver went to the store and bought 5 boxes of fertiliser to the nearest round number. He spread it evenly over the grass in his garden and watched as his garden became even more beautiful and lush.
He was pleased with the results and was proud of his beautiful garden. The end.