MATH REPORT
By Angelina Charalambous
Mansfield State High School
Draft Submission: 08/03/21
0
Contents
1.
Introduction ................................................................................................................................ 1
2.
Formulation of the Task .............................................................................................................. 1
2.1
Procedures and Methods........................................................................................................ 1
2.2
Assumptions and Observations .............................................................................................. 2
3.0 Solution of the task ....................................................................................................................... 2
Formula Table: .................................................................................................................................... 2
Overall comment: good effort Ange, i can see you have tried to present your findings in a logical
ways....but it would be much better if you can focus more on your reasoning of every decision
you made of the garden design.....it is mainly in your results section...(maths report is very
different from english writing. it doesnt need fancy language but elaborate your thinking is the
key. )
To improve your report, i suggest you need to show more thinking and reasoning behind each
decision you made. e.g. why you choose the layout of the house, why you put the house at the
front, why you put the pool where it is designed...why you choose certain materials?.e.g fence
material...why is it colour bond not wood....etc...if you haven't thought about it...you need to
come up with an explanation to show you can demonstrate a COMPLEX procedure as per the
marking criteria.
1
1. Introduction
This report is based on a backyard bonanza competition entered by partners. In order
to decide if the renovation can be done with a budget of $50,000. Calculations need
to be made and research conducted to work out whether this renovation is possible.
A budget was set up that included all expenses, such as main features including; above
ground swimming pool with compliant fencing, fencing around perimeter of block,
covered entertainment area, clothesline, shed, three raised garden beds, turf, plants,
trees and a pathway. A diagram was drawn to ensure that all compulsory features fit
into the backyard with a key of one square= 2 metres. This investigation will also
provide detailed explanations of strengths and weaknesses/ limitations that were
found. Procedures and methods will be included that provide written steps in order to
complete this task. Images taken will also be employed as evidence of working out.
2. Formulation of the Task
Important variables identified in this investigation include fixed and discretionary
variables. Fixed variables include the size of the land, house size, $50,000 budget,
above ground swimming pool, covered entertainment area, three raised garden beds,
garden shed, turf, plants, clothesline, pathway and fencing. Discretionary variables
include labour cost, driving distance,
Mathematical concepts include finding areas, perimeters, volumes of regular and
composite shapes and budgets. Techniques discussed include hand drawn scale
drawings, using excel for a budget and using google for websites.
2.1 Procedures and Methods
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Read and analyse task (understand the task and highlight key concepts)
Understand important concepts
Write down observations, assumptions and variables
Search for appliances and costs (research materials and all costs of the
renovation)
Create budget and insert any information required
Solve equations that need to be done
Analyse data (interpret findings)
Evaluate the reasonableness of solutions ( justify whether or not the
renovation is within budget)
Consider strengths and limitations
Justify and explain all procedures
Consider the original task
Conclude investigation ( summarise and restate key concepts of the
investigation)
1
2.2 Assumptions and Observations
Assumptions
A number of assumptions have been made regarding this investigation. These
assumptions include; a fence must be installed around the perimeter of the land
separating other houses, the land is levelled meaning there are no slopes or hills,
partner has skills to do some DIY’s in the renovation, cannot exceed $50,000 limit,
other competitors have the same budget, other competitors have same choice of
houses and size of land, tools are provided for the construction, the size of the family
is for four people, hire workers and pay labour for some projects.
Observations
A number of observations have been made during this investigation such as the pool
must be isolated by an approved pool fence, the lands dimensions are exactly 27m
wide and 28.5m long, only three online stores can be used to buy resources from. It is
observed that sheds are to be placed on concrete slabs, this is going to increase the
costs of the budget. The clothesline will be held down and set with cement so that no
strong winds will blow the clothesline away.
3.0 Solution of the task
(Insert graph)
Formula Table:
SHAPE
Patio
Garden bed L shape
FORMULA
Length x Width
6.0x4.9
= 29.4m^2 x 200
= 5880
V= 150-155
=95
95 x 55 x 41
214.225cm^3 ÷ 1000
= 338.25L
2.14.225 + 338.25
= 552.475 L
552.475 + 300 + 410
= 1262.475L
= 1.6791 tonnes
Garden bed rectangle
Volume= L x W x H
= 50 x 200 x 41
410 000cm^3 ÷ 1000
= 410 L
Garden bed Square
Volume= L x W x H
100 x 100 x 30
300 000 ÷ 1000
= 3000L
2
Cement Filling
20 Kg
20 x 1.47
= 29.4 Kg
Therefore I need 200 bags of
cement
Results:
The results of this renovation will talk about the required components, scale drawing, the formulas
used to conduct calculations, budget, cost breakdown and technology used and how it was utilized.
The required components in order to complete this backyard renovation were as follows; above
ground pool with approved pool fencing, compliant fencing around perimeter of the house, three
garden beds but one at least composite, garden shed, clothesline, pathway to main features, turf, and
a covered entertainment area. These components are essential as they meet the minimum
requirements for renovating a backyard. A hand drawn scale drawing is a great way of visualising and
planning a backyard renovation. This is due to seeing whether the layout and design would fit in the
back yard submissive to the house. Having a budget is a great organisation technique that lists and
keeps track of costs. It also helps keep visual whether the budget of $50,000 is being exceeded.
Formulas used to conduct calculations are as follows; permitter and volume of a rectangular patio,
composite garden bed shape to calculate volume and perimeter, volume and perimeter of a
rectangular and square garden bed, the radius of the pool to decide how big of a fence is needed,
calculations to decide how much concrete is needed for concrete slabs under patio, pool and shed,
also for filling and placing poles for fence. Lastly, technology used when conducting research were
using Bunnings website, Clark rubber website and centenary landscaping. Excel was also used for
conducting budget. Reasons as to why these technologies were used is because it is a well-used lay
out and easy to use/ read.
Discussion:
The viability and reasonableness of the backyard bonanza renovation, is that there were many
strengths and limitations. Strengths that were fund in this investigation was the $50,000 budget. This
budget provided a wide spending range that covered all expenses. The overall money spent on the
renovation was $35,081.23. This left $14,918.77 in the budget. However, limitations that affected the
renovation was that resources were only aloud to be bought from three retailers such as Bunnings
Warehouse, Clark rubber and Centenary Landscaping. Although these websites provided products/
materials needed, variety and quality of products could be found cheaper.
Conclusion:
This report has explored many budget outcomes of the backyard bonanza renovation. These include
research across three well know retailers providing different prices and materials, labour cost and
added expenses, assumptions and observations, procedures and methods, results and discussion.
3
Material Links:
Patio: https://www.bunnings.com.au/softwoods-6-0-x-4-9m-colorbond-patiogable-roof-kit_p3310571
Synthetic Turf: https://centenarylandscaping.com.au/shop-products/syntheticturf
Garden shed: https://www.bunnings.com.au/lifetime-2-1-x-2-1-x-2-27mpolyethylene-garden-shed_p3318106
Clothesline: https://www.bunnings.com.au/daytek-22m-a-frame-portableclothesline_p0202382
Plants: https://www.bunnings.com.au/plant-spathiphyllum-250mmchico_p0170092
4