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Sustainable school garden project - Mathematics Year 6

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Introduction

Can you present a garden proposal that another person can check? Combine a scale plan, area allocation, estimated material quantities, a transparent budget and a small statistical enquiry. Justify choices using evidence and acknowledge what the model leaves out.

Success criteria. Produce a dimensioned plan and complete budget, use a chart or statistic responsibly, justify three design decisions and complete a sixteen-item transition review spanning eight major KS2 mathematical areas.

This is an original enrichment project linked to Year 6 mathematics, not a statutory requirement to build a garden. Work with fictional prices and data. It does not certify actual site safety, accessibility compliance, structural suitability, horticultural needs or observed practical measuring skill.

Design a scale layout and account for every area

Separate the real photograph from the mathematical model. The unchanged Commons photograph shows raised beds, paths, containers, a picnic table and a board. It gives ideas about uses and routes. It has no reliable scale for our dimensions; it is not evidence that its beds have our lengths or that its water containers meet a particular standard.

Our fictional site. Model a rectangular plot twelve metres long and eight metres wide. Ignore any wall thickness for this first calculation and state that simplification:

$12 \times 8 = 96$

The model covers 96 m². At a scale of 1:100, one centimetre on the plan represents one hundred centimetres, or one metre, on the site. Draw a twelve-centimetre by eight-centimetre rectangle. Do not confuse drawing centimetres with real metres.

Allocate thirty percent to paths. We choose a single full-width horizontal path across the middle. Its real width is 2.4 m and its length 12 m. It runs between y = 2.8 m and y = 5.2 m if the lower-left corner is (0, 0). The lower planting band is 2.8 m high; the upper band is also 2.8 m high.

$0.30 \times 96 = 28.8, 12 \times 2.4 = 28.8$

Path area is 28.8 m². Planting receives the remaining 67.2 m². Each planting band covers 33.6 m²:

$96 - 28.8 = 67.2, 12 \times 2.8 = 33.6$

At 1:100 the path is 2.4 cm wide and each planting band 2.8 cm wide. Adding these widths reconstructs the eight-centimetre plan height. The conceptual layout below is NOT drawn to scale; the numerical dimensions and your scaled drawing determine the geometry.

             real length 12 m
+--------------------------------+
| Upper planting band: 2.8 m high |
+--------------------------------+
| Central path: 2.4 m wide        |
+--------------------------------+
| Lower planting band: 2.8 m high |
+--------------------------------+
             real height 8 m

Why not just make the path two metres wide? A twelve-by-two strip covers 24 m², which is 25% of the site, not 30%. This comparison reveals a plausible but inconsistent plan. A stated percentage is a constraint to check, rather than a label to paste onto a convenient sketch.

A second check. Two planting bands of 33.6 m² total 67.2 m². Adding 28.8 m² of path recovers 96 m². On the drawing, the outer area is 96 cm²; that numerical coincidence occurs because one drawing centimetre represents one real metre. The units are still different and the actual area scale factor is ten thousand when both areas use square centimetres.

What the first model omits. Real designs need gates, access routes, edging thickness, drainage and local review. Two broad planting bands do not automatically give access to every plant. A good mathematical proposal identifies that limitation rather than claiming a build-ready accessible plan.

Estimate quantities and build a budget with a reserve

Volume needs depth as well as area. Suppose the fictional plan covers all 67.2 m² of planting area with a uniform layer 0.15 m deep. This is a quantity-estimation assumption, not advice about soil depth for a real plant.

$67.2 \times 0.15 = 10.08$

The ideal layer requires 10.08 m³. A supplier sells fictional bags containing 0.75 m³ each. Dividing gives 13.44 bags:

$10.08 \div 0.75 = 13.44$

We cannot order a fraction of a bag in this model. Round UP to fourteen, not to the nearest whole number. Fourteen supply 10.5 m³; thirteen supply only 9.75 m³ and would be short. The model surplus is 0.42 m³. Actual compaction, handling and delivered quantities remain separate uncertainties.

Use the declared fictional price list. Every value includes any tax assumed in this exercise; delivery is charged once. These are not current offers.

Item	Quantity	Fictional unit price	Cost
Soil bags	14	£28.00 per bag	£392.00	Seed packs	8	£3.50 per pack	£28.00	Path surface allowance	28.8 m²	£9.00 per m²	£259.20	Delivery	1	£35.00 per delivery	£35.00

$392 + 28 + 259.20 + 35 = 714.20$

The subtotal is £714.20. Add a ten-percent contingency on that subtotal, meaning an unspent reserve for uncertainty rather than a guaranteed extra purchase:

$0.10 \times 714.20 = 71.42, 714.20 + 71.42 = 785.62$

Against an £800 budget, the plan including reserve leaves £14.38. Keep pence in the calculation and state the reserve basis. Ten percent of the budget would be £80, which is a different policy and must not be substituted silently.

Compare suppliers fairly. A second fictional bag contains 0.5 m³ and costs £20. Its unit cost is £40 per m³. The 0.75 m³ bag at £28 costs about £37.33 per m³. For our required quantity, twenty-one smaller bags supply 10.5 m³ and cost £420; fourteen larger bags supply the same 10.5 m³ for £392. The larger-bag option saves £28 before any other differences. Compare delivered usable quantity and price, not bag price alone.

The original corbettmaths Maps and Scales - Corbettmaths supports the scale-conversion method. Its map distances are a separate example; our site has a declared 1:100 scale, not the map's own numerical scale.

Unfamiliar cost change. If path price rises from £9 to £10 per square metre, the increase is £28.80. The new subtotal is £743.00 and its ten-percent reserve £74.30. The revised total is £817.30, exceeding £800 by £17.30. A good response proposes a justified revision or reports the shortfall; it does not quietly omit the reserve.

Check and communicate. Keep units beside each quantity, show why bags round upward, list all cost assumptions and reconstruct subtotal plus reserve. An attractive plan with an impossible purchasing quantity is not a complete mathematical solution.

Use data to justify three decisions without overstating it

A fictional consultation. Twelve volunteers choose exactly one preferred focus. Six choose vegetables, three flowers and three herbs. Counts total twelve. This describes those twelve volunteers; their self-selection means we cannot automatically claim it represents the entire school.

Preferred focus	Count	Percentage	Pie angle
Vegetables	6	50%	180°
Flowers	3	25%	90°
Herbs	3	25%	90°

A three-sector pie chart can show those proportions. Alternatively use three labelled bars for direct count comparison. Do not label the four equal source pieces as three unequal categories without explaining that vegetables combine two quarters.

From preference to one tentative design. Assign half the 67.2 m² planting area to vegetables and a quarter each to flowers and herbs:

$67.2 \div 2 = 33.6, 67.2 \div 4 = 16.8$

One lower band could hold vegetables, while the upper band is split into two equal six-by-2.8-metre rectangles for flowers and herbs. These areas total 67.2 m². This is a mathematical allocation inspired by the volunteer responses, not evidence that those sizes are horticulturally optimal.

A numerical summary with units. In a separate fictional four-plot trial, water amounts are 2, 3, 4 and 3 litres under the same stated conditions. The total is twelve litres and the mean three:

$(2 + 3 + 4 + 3) \div 4 = 3$

That is a summary of this trial, not a recommended watering amount per plot, day or plant. A real recommendation would need species, weather, soil and measured conditions. Keep statistical description separate from practical advice.

Write three justified decisions. Decision one: choose the 2.4-metre path because its 28.8 m² satisfies the chosen thirty-percent constraint and leaves a checkable 67.2 m². Decision two: choose fourteen of the 0.75 m³ bags because thirteen are insufficient and the given supplier comparison saves £28 at equal ordered volume. Decision three: propose the half-quarter-quarter planting split because it reflects the twelve volunteers' counts, while explicitly asking for a more representative consultation before final allocation.

Each decision links a choice to actual arithmetic AND a limitation. 'It looks nice' alone is not a data-informed explanation. Equally, a precise percentage does not remove bias in the consultation.

Compare methods rather than only answers. For path area use either thirty percent of the whole or twelve times the declared width. For ordering use either division with upward rounding or a check of thirteen and fourteen bags. For a mean use total divided by count and reconstruct total by multiplying back. Agreement of two independent routes is stronger than repeating the same unexplained calculator entry.

Your proposal dossier. Include the scaled plan, area conservation, material estimate, full budget with contingency, a labelled chart or the trial mean, three decisions and a statement of assumptions. Then complete the transition review. The project combines topics but does not replace reviewing every required source course.

Review eight KS2 strands with fluency and reasoning

One fluency task and one reasoning task per strand. Attempt all sixteen before checking the worked guidance in Learning Check. Explain the first wrong step in a mistaken method. The garden context is useful, but this review deliberately tests transfer beyond that single model.

Strand	Fluency item	Reasoning item
Number and place value	N1: What value does the digit 7 have in 4,782,106?	N2: Round 12,499 directly to the nearest 1000. Compare rounding first to the nearest 100 and then to the nearest 1000. Use the convention that exact halves round upward.
Operations	O1: Calculate 48 × 25.	O2: Compare 120 ÷ (3 + 2) with 120 ÷ 3 + 2. Explain the different operation orders.
Fractions decimals percentages	F1: Find three quarters of 28.	F2: Explain why one half plus one third is five sixths rather than two fifths. Use a common whole.
Ratio and proportion	R1: Divide 25 counters in the ratio red:blue = 2:3.	R2: A square has side 3 cm on a 1:100 plan. Find its real side and real area; explain why an area conversion cannot use a single length factor.
Algebra	A1: Evaluate 3n + 2 for n = 5.	A2: Find all nonnegative integer pairs a,b satisfying 2a + b = 12. Explain why the list is complete.
Measurement	M1: Convert 1.25 litres to millilitres.	M2: A learner says 2.5 m plus 35 cm is 37.5 m. Correct the first error and give the length in metres.
Geometry	G1: Find a triangle's area with base 8 cm and perpendicular height 5 cm.	G2: Translate (−2, 3) four right and one down. State the new coordinates and explain a distance invariant for a whole translated shape.
Statistics	S1: Find the mean of 4, 5 and 9.	S2: Explain why the twelve self-selected garden volunteers cannot automatically stand for every pupil's preference.

Scaffold without removing reasoning. For N1, mark each place-value column. For O1, use twenty-five as one quarter of one hundred. For F1, find one quarter before three. For R1, find the total number of ratio parts. For A2, use a table with a starting at zero. For M2, first put both lengths in the same unit. For G2, change each coordinate separately. For S1, identify both total and count.

Useful checks. Multiplication can be checked by division or a different decomposition. An equivalent-fraction answer should fit a common denominator model. A scale result should carry the correct length or square unit. For the algebra pairs, substituting one pair is not a completeness proof: use the nonnegative bound on a to limit every possible row.

Select a representation for an unfamiliar extension. Suppose a proposed design changes the path percentage but retains the twelve-metre length. Choose a rectangle model and solve width as path area divided by twelve. If the proposal instead changes supplier bag capacity, use a quantity table and an upward whole-bag check. The right representation follows the mathematical structure, not a keyword.

Reflect on evidence. Mark each fluency item secure, developing or revisit; do the same separately for its reasoning partner. Set three specific next-step targets, such as 'check the denominator counts recorded zeros' rather than 'be better at maths'. Reattempt a changed example after an interval. Sixteen completed items are a diagnostic sample, not proof of every KS2 objective or practical skill.

Interactive Tasks

Quiz: Test Your Knowledge

What is the area of the fictional twelve-by-eight-metre site? (Ninety-six square metres) (!Forty square metres) (!Twenty square metres) (!Ninety-six metres)

At scale one to one hundred, what plan represents the site? (Twelve centimetres by eight centimetres) (!Twelve metres by eight metres) (!One hundred and twenty centimetres by eighty centimetres) (!One point two centimetres by zero point eight centimetres)

What area does the chosen central path occupy? (Twenty-eight point eight square metres) (!Twenty-four square metres) (!Thirty square metres) (!Sixty-seven point two square metres)

Why order fourteen soil bags instead of thirteen? (Thirteen provide less than the required volume) (!Thirteen point four four must round to the nearest whole number) (!The photograph proves fourteen bags are present) (!Every garden always needs fourteen bags)

What is the fictional subtotal before contingency? (Seven hundred and fourteen pounds twenty pence) (!Seven hundred and eighty-five pounds sixty-two pence) (!Eight hundred pounds) (!Three hundred and ninety-two pounds)

What does the ten-percent contingency apply to in this budget? (The stated subtotal of seven hundred and fourteen pounds twenty pence) (!The total school budget without explanation) (!Only the seed packs) (!The number of soil bags)

What can be concluded from the volunteer survey? (Six of these twelve volunteers chose vegetables) (!Every pupil in the school chose vegetables) (!Exactly half of every school prefers vegetables) (!The survey removes all uncertainty about planting)

What is the mean of the fictional two three four three litre amounts? (Three litres) (!Twelve litres) (!Four litres) (!Three litres per day recommended for all plants)

Which change makes the revised plan exceed the budget? (Raising the path rate to ten pounds per square metre while retaining the stated reserve policy) (!Checking the same plan by a second method) (!Labelling plan dimensions) (!Keeping the original prices unchanged)

What makes a design decision mathematically justified? (Linking a choice to checked data and stating assumptions and limits) (!Choosing the most colourful diagram) (!Omitting costs that make the total too high) (!Treating photo pixels as measured metres)

Memory Game

Scale	The relationship between drawing and actual lengths in the same unit
Area	Coverage measured in square units
Volume	Three-dimensional quantity measured in cubic units
Unit price	Cost per stated comparable quantity
Contingency	A declared reserve for uncertainty
Sample	The observations actually collected
Assumption	A stated condition used to simplify a model

Drag and Drop

Path check	Multiply length by perpendicular width and compare with the percentage constraint
Bag order	Round a positive fractional required bag count upward
Budget check	Add each cost and the explicitly based reserve
Survey limitation	Volunteer preferences need not represent the whole school
Proposal evidence	Provide a plan budget statistic and justified decisions

Crossword Puzzle

GARDEN	The setting for the fictional integrated project
SCALE	Drawing-length relationship to the real site
BUDGET	The amount available for the proposal
VOLUME	Quantity needed for a layer with depth
SAMPLE	The volunteers actually included in the survey
RESERVE	Money kept for uncertainty

LearningApps

Optional extra practice. Choose an appropriate activity with your teacher. If the external collection is unavailable, use the native activities and independent tasks in this course.

Cloze Text

Open Tasks

Easy

Dimensioned plan: Draw the twelve-by-eight-centimetre plan with a 2.4-centimetre central path and two 2.8-centimetre planting bands. Label real and drawing units.
Area conservation: Check path area, both planting-band areas and their sum. Explain why a two-metre path would give a different percentage.
Soil quantity: Find the ideal layer volume and test thirteen and fourteen bags. State the whole-bag assumption.
Four-plot mean: Calculate total and mean of the fictional water amounts. Explain why this is not a universal watering instruction.

Standard

Complete budget: Recalculate every cost, subtotal, ten-percent reserve and balance against eight hundred pounds. Retain pence.
Consultation chart: Construct the three-category survey display with counts and a total. Use labels and explain the volunteer limitation.
Supplier comparison: Compare both bag sizes at equal ordered volume. Show unit rates and the total saving under the given fictional conditions.
Three decisions: Write the three evidence-based decisions in your own words, with a check and limitation for each.

Advanced

Price-change response: Recalculate the full proposal if path rate becomes ten pounds per square metre. Report the shortfall and a transparent possible revision.
Sixteen-item transition review: Complete fluency and reasoning items in all eight strands. Explain methods and independent checks rather than giving a score alone.
New area constraint: Change the path allocation to one quarter while retaining its full twelve-metre length. Find width and compare planting area and path cost at the original rate.
Complete unfamiliar proposal: Produce a different dimensioned model with quantities, complete budget, statistic, three decisions and limitations. Check conservation of area and money and set three next-step learning targets.

Learning Check

Plan and area audit: Submit the scaled plan and check the original thirty-percent layout.
Quantities and budget: Submit materials, supplier comparison, reserve and changed-price result.
Data and three decisions: Submit a chart or statistic and three justified decisions with limitations.
Transition number operations fractions ratio: Complete N1–N2, O1–O2, F1–F2 and R1–R2.
Transition algebra measurement geometry statistics: Complete A1–A2, M1–M2, G1–G2 and S1–S2.
Unfamiliar revision and next steps: Check the quarter-path variant and evaluate the complete dossier.

Worked checks and assessment guidance

At 1:100, draw 12 cm by 8 cm. The 12 m by 2.4 m path covers 28.8 m², thirty percent of 96 m². Each 12 m by 2.8 m planting band covers 33.6 m²; together 67.2 m². Widths 2.8 + 2.4 + 2.8 recover 8 m. A 2 m strip would cover 24 m², twenty-five percent.
Soil layer 10.08 m³ requires 14 bags of 0.75 m³: ordered 10.5 m³, model surplus 0.42 m³; 13 bags supply only 9.75 m³. Costs £392, £28, £259.20 and £35 sum to £714.20. Reserve £71.42 gives £785.62 and £14.38 remaining. Alternative 21 half-cubic-metre bags cost £420 at equal volume, £28 more. New path rate £10 gives subtotal £743, reserve £74.30, total £817.30 and £17.30 shortfall.
Survey counts 6, 3, 3 out of 12 give 50%, 25%, 25% and 180°, 90°, 90°. Tentative planting areas 33.6, 16.8, 16.8 m² conserve 67.2 m². Trial amounts 2, 3, 4, 3 litres total 12 and mean 3 litres. Require one area, one purchasing and one consultation decision tied to these data; distinguish self-selected preference evidence and fictional quantities from practical recommendations.
N1: 700000. N2: direct nearest thousand 12000; nearest hundred first gives 12500, then half-up to 13000, so double rounding changes the result. O1: 1200. O2: 24 versus 42; brackets alter order. F1: 21. F2: three sixths plus two sixths gives five sixths of the same whole, not two fifths. R1: red 10, blue 15. R2: real side 3 m and area 9 m²; in centimetres the side factor is 100 and the area factor 10000.
A1: 17. A2: pairs (0,12), (1,10), (2,8), (3,6), (4,4), (5,2), (6,0); nonnegative b bounds a from zero to six, proving completeness. M1: 1250 mL. M2: convert 35 cm to 0.35 m, giving 2.85 m. G1: 20 cm². G2: (2,2); translating every vertex equally preserves distances. S1: total 18, count 3, mean 6. S2: self-selection and small coverage do not establish whole-school preference.
Quarter allocation gives path 24 m², width 2 m, planting 72 m² and path cost £216 at £9 per m². Keep a changed proposal internally consistent rather than mixing old and new quantities. Require units, area and money conservation, source/data limitations, three justified decisions and three specific next-step targets. Completing this project is not a claim of complete annual coverage or observed site-design competence.

Learning evidence

Keep the dimensioned scale plan, area audit, purchasing and budget calculations, labelled chart or statistic, three justified design decisions and all sixteen diagnostic responses with corrections. Record three next-step targets separately from marks. This original project is evidence of mathematical modelling and reasoning; real construction requires appropriate adult and site-specific review.

OER and Wikipedia

Checked 11 November 2026. Department for Education: mathematics programmes of study, upper KS2 measurement, ratio, algebra, geometry and statistics, informs this cross-topic enrichment project. The fictional project and eight-strand diagnostic are an editorial learning design, not a claim that a garden project is itself statutory.

All dimensions, purchasing rules, prices, survey counts, water observations and worked feedback are original fictional examples. The photograph is an existing school garden, not a measured or safety-approved plan for the fictional site.

Original embedded Maps and Scales - Corbettmaths, corbettmaths, illustrates scale conversion using a separate map example. Source media is unchanged; no video is falsely labelled Commons-licensed. No construction, legal accessibility, watering or horticultural approval is inferred from the mathematical model.

Clay Elementary School Garden.jpg, EWood45, CC BY-SA 4.0. Unchanged.

PieChartFractionFourthsSplit.svg, Ezra Katz, CC BY-SA 3.0. Unchanged.