Design a Garden
Design a Garden
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Design a Garden
Open the lesson as a mathematics investigation, not a gardening lesson. The central idea is using area, perimeter, volume, scale and budget calculations to satisfy fixed design constraints.
Learning goal
I can design a garden plan that meets area, perimeter, percentage, volume, scale and budget requirements.
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What maths ideas will help when designing a garden?
Use this to surface prior knowledge such as area, perimeter, percentage, budget, scale and volume. Invite students to notice which ideas appear most often.
Project rules
Your garden design must follow these conditions:
total area between 130 m² and 200 m²
grass covers exactly 50% of the garden
paving covers exactly 25% of the garden
include fencing, a raised veggie patch, a cylindrical water tank and a scale diagram
total cost must be no more than $10,000
Stress the word exactly for the grass and paving percentages. Students often treat these as approximate, but the task requires precise proportions.
Introduction
The investigation begins by stating:
what you are designing: an outdoor garden area
the budget limit: $10,000
the area range: 130 m² to 200 m²
the aim: create a design that is practical and mathematically correct
This slide matches the report introduction section. Keep the focus on setting up the mathematical purpose clearly.
Introduction
Your method should explain the order of your work:
choose garden dimensions
calculate total area and perimeter
find grass and paved areas
calculate veggie bed soil volume
include the tank and other features
build a full budget
draw a scale plan
Point out that a clear method helps the report read like a planned investigation rather than random calculations.
Resources and assumptions
Useful resources include:
spreadsheet or word processor
price lists or shop catalogues
grid paper and drawing tools
area, perimeter and volume formulae
Typical assumptions:
ground is level
labour costs are not included
retail prices already include tax
You can also mention limitations such as fixed fence panel widths, fixed paver pack sizes or soil sold in standard bag amounts.
Choosing garden dimensions
First choose dimensions that make the total area valid.
For a rectangular garden:
Area = length × width
Examples:
10 m × 14 m = 140 m² ✓
12 m × 15 m = 180 m² ✓
9 m × 12 m = 108 m² ✗ too small
A rectangle is a sensible default because it makes area, perimeter and scaling easier, but students may choose another shape if they can justify the mathematics.
Which garden size is valid for the task?
9 m × 12 m
10 m × 14 m
8 m × 15 m
10 m × 20 m
Valid area must be between 130 m² and 200 m². 10 × 14 = 140 m² is the only option in range.
Start of the investigation
In the introduction, you state the budget limit of $10,000 and the area range of 130 m² to 200 m². A clear method then begins by choosing garden dimensions before calculating area and perimeter.
This checks the key constraints and the order of the method from the introduction block.
Fence Perimeter
The fence goes around the outside edge of the garden.
For a rectangular garden:
Perimeter = 2 × length + 2 × width
Example:
If the garden is 10 m by 14 m,
Perimeter = 2(10) + 2(14) = 48 m
Reinforce the difference between area and perimeter. Students often confuse square metres with metres when costing fencing.
Fence panels and cost
After finding the perimeter, choose a fence product.
Use:
Number of panels = perimeter ÷ panel width
Total fence cost = number of panels × unit price
Example:
48 m ÷ 2.4 m = 20 panels
20 × $45 = $900
In a real purchase, students may need to round up to a whole panel if the division is not exact. That practical detail is worth discussing.
Checking the fencing choice
A good fencing calculation should show:
garden dimensions
total perimeter in metres
panel size used
number of panels needed
final fence cost
This slide helps students see what evidence should appear in their report section, not just the final answer.
For a 10 m by 14 m garden, what is the perimeter?
24 m
48 m²
140 m
48 m
Distractors target common errors: adding once, using area, or using the wrong unit. Perimeter is measured in metres, not square metres.
Why might you need to round up fence panels?
Expected elements: perimeter in metres, panel width, dividing perimeter by panel width, rounding up if needed, then multiplying by unit price. Students may mention garden dimensions too.
Grass Area
Grass must cover exactly half of the total garden area.
Use:
Area of grass = 0.50 × total area
Example:
If the total garden area is 140 m²,
Grass area = 0.50 × 140 = 70 m²
Connect 50%, 0.5 and one half so students see these as equivalent forms.
Grass layout
The grass area must fit the design and match the calculation.
Possible layouts:
one large rectangle
a circular lawn
two smaller sections
Whatever shape you choose, the total grass area must still equal the required amount.
If students choose non-rectangular grass shapes, remind them they must use the correct area formula and label the plan clearly.
Turf cost
Once the grass area is known, calculate the price.
Use:
Grass cost = grass area × price per m²
Example:
70 m² × $8.50 = $595.00
Keep units visible: square metres for area and dollars per square metre for price.
Grass section summary
This part of the report should include:
the total garden area
the required 50% calculation
the grass shape and position
the turf price used
the total turf cost
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If the total area is 140 m², how much must be grass?
35 m²
70 m²
90 m²
140 m²
Grass must be exactly 50% of the total area.
Grass rules
Grass must cover exactly half of the total garden area. If the garden is 140 m², the grass area is 70 m². After that, the turf cost is found using price per m².
This reinforces equivalent meanings and units: half, 50% and square metres.
Paved Area
Paving must cover exactly one quarter of the total garden area.
Use:
Area of pavers = 0.25 × total area
Example:
If the total garden area is 140 m²,
Paved area = 0.25 × 140 = 35 m²
Connect one quarter, 25% and 0.25 as equivalent representations.
Paving layout
Pavers might be used for:
a patio
a pathway
a courtyard area
The design should explain where the paved section goes and why that shape suits the garden plan.
Students should describe the paved region clearly enough that another person could identify it on the scale plan.
Counting pavers
If each paver has known dimensions, you can estimate how many are needed.
Example:
A 400 mm × 400 mm paver has area
0.4 × 0.4 = 0.16 m²
For 35 m² of paving:
35 ÷ 0.16 = 218.75
So you would need 219 pavers if sold individually.
This is a good place to discuss unit conversion from millimetres to metres before finding area.
Paver cost
After finding the number of pavers, multiply by the unit or pack price.
Example:
219 pavers × $6 = $1,314
If pavers are sold in packs, round to a whole pack and recalculate the cost.
Real-life pricing often forces rounding, which can affect whether the budget still works.
A 400 mm by 400 mm paver has area of
0.16 m²
0.4 m²
160 m²
0.04 m²
Students must convert 400 mm to 0.4 m before finding area: 0.4 × 0.4 = 0.16 m².
Paving calculations
Paving must cover exactly one quarter of the total area. For a 140 m² garden, that is 35 m². If each paver covers 0.16 m², divide to estimate the number of pavers needed.
This echoes the sequence taught: percentage of area first, then number of pavers.
Veggie Patch Raised Garden Bed
The raised veggie patch is a three-dimensional object.
A simple model is a rectangular prism with:
length
width
depth or height
This means you must calculate volume, not just area.
This subtopic is the transition from 2D measurement to 3D measurement.
Soil volume
For a rectangular prism:
Volume = length × width × depth
Example:
2 m × 1 m × 0.4 m = 0.8 m³
This tells you how much soil the bed needs.
Emphasise cubic metres as a new unit. Students often write m² by mistake when moving from area to volume.
Soil and bed costs
The veggie patch cost may include:
the raised bed kit
soil
optional seeds or plants
Example soil cost:
0.8 m³ × $75 per m³ = $60
If soil is sold in bags, students may need to convert total volume into a number of bags and round up.
Veggie patch summary
This section should show:
the bed dimensions
the volume formula used
the total soil required
the chosen product prices
the final cost
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Which measurement is needed for soil in the veggie bed?
Perimeter
Scale
Volume
Radius
The veggie patch is a 3D object, so students need volume in cubic metres.
Veggie bed volume
A raised veggie bed can be modelled as a rectangular prism. Its soil volume is found by length × width × depth. The answer is measured in m³, not square metres.
Use this to emphasise the move from 2D to 3D measurement.
Cylindrical Water Tank & Garden Features
A cylindrical water tank uses circle measurements.
You need to state:
radius r
height h
the area covered on the ground
the tank cost
Clarify radius versus diameter if needed. Students may know one but use the other incorrectly in the formula.
Tank area and capacity
For a cylinder:
Base area = πr²
Volume = πr²h
The base area shows how much ground space the tank uses.
The volume shows its water capacity.
The task treats volume as an extension, so the main required idea is recognising the tank as a cylinder and using the circle formula correctly.
Other garden features
Extra features may include:
trees or hedges
a bird bath
lighting
decorative items
These features are optional, but their prices must still be included in the full budget.
Keep the mathematical focus on cost and space, rather than on decoration choices alone.
Fitting features into the design
Every feature should fit within the plan without breaking the rules on:
total area
grass percentage
paved percentage
overall budget
This is a useful place to highlight trade-offs: adding one feature may force changes elsewhere.
What does πr² show for a water tank?
Tank cost
Base area
Fence length
Full budget
The required idea is that πr² gives the ground area covered by the cylindrical tank.
What rules can extra features never break?
Expected elements: extra features must still fit within total area, grass percentage, paved percentage and budget. Good answers may mention trade-offs or changing other parts of the plan.
Complete Budget Summary Table
A budget table gathers all costs in one place.
Include columns for:
category
item description
quantity or units
unit price
total price
Finish with one total cost for the whole design.
Students should see the budget table as evidence of mathematical organisation, not just bookkeeping.
Using the budget limit
The final cost must be $10,000 or less.
A strong design:
stays under budget
spends close to the limit
shows realistic prices
explains where most money was used
The brief says to aim close to the budget, so a very low total may still need explanation.
Reading a sample total
Example total from the scaffold:
$4,097.50
This is under the budget, but it is far from $10,000.
A student could improve the design by adding more features or choosing higher-cost materials while still staying within the limit.
Use this as analysis, not as the only correct answer. Students should create their own budget values.
What makes the sample total of $4,097.50 weak?
It is over budget
It lacks a fence
It is too close to $10,000
It is far below $10,000
A strong design should stay under budget but aim close to the limit, not leave a very large unused amount.
Which part of the budget table is most useful first?
Category
Quantity
Unit price
Total cost
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Garden Diagram & Scale Guidelines
The garden plan must be drawn neatly on grid paper.
A scale is needed so the diagram matches real measurements.
Examples:
1 square = 1 m
1 cm = 1 m
Explain that a scale drawing keeps shapes proportional, so the plan is not just a sketch.
What the scale diagram must show
Label the diagram clearly with:
perimeter lengths
total garden area
grass zone
paved zone
veggie bed
water tank
other features
A mathematically useful diagram is labelled. An unlabelled drawing cannot support the report properly.
Why scale matters
Scale helps you:
keep the layout accurate
fit all features into the space
compare measurements easily
connect the drawing to your calculations
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Why is a scale important on the garden diagram?
It adds colour
It keeps size accurate
It lowers the cost
It changes the area
Scale links the drawing to real measurements and keeps the layout proportional.
Scale drawing
A garden plan should be drawn on grid paper using a clear scale, such as 1 square = 1 m. The diagram must include clear labels for zones and lengths.
This checks the practical requirements for the final labelled scale diagram.
Discussion
In the discussion section, summarise the final measurements:
total area
perimeter
grass area
paved area
This is where you bring the main results together.
Students should not introduce new calculations here; they should summarise and interpret earlier results.
Discussion
Analyse the budget by explaining:
whether the design stayed under $10,000
which items cost the most
how changes in dimensions would affect area and cost
how materials could be changed to save money
This subtopic develops mathematical reasoning about how one design change can affect several calculations.
Discussion
A strong discussion also reflects on:
future additions with more money or space
challenges in measurement or modelling
design trade-offs you had to make
This shows how the mathematics guided the final design.
Encourage clear links between reflection points and the numbers already calculated.
Conclusion
The conclusion compares the first cost prediction with the final budget.
It should also summarise what the investigation showed about designing a garden that fits both mathematical rules and practical limits.
The conclusion is brief: compare prediction and result, then state the main learning from the task.
How can bigger dimensions change the budget?
Expected elements: changing dimensions changes total area, then changes grass and paved areas, perimeter, material quantities and overall cost. Strong answers mention more than one linked effect.
What part of this lesson helped you most?
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What is one maths idea you will remember?
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Which part of the garden task still feels hardest?
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Glossary
area - the amount of surface a shape covers, measured in square units
perimeter - the distance around the outside of a shape
percentage - a part out of 100
scale - the ratio between a drawing and the real object
budget - the total amount of money available
unit price - the cost for one item or one measurement unit
volume - the amount of space inside a three-dimensional object
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Glossary
rectangular prism - a box-shaped solid with rectangular faces
cylinder - a solid with two equal circular ends and one curved surface
radius - the distance from the centre of a circle to its edge
capacity - the amount a container can hold
assumption - something accepted as true to simplify a model
constraint - a rule or limit that the design must follow
proportion - the size of one part compared with the whole
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