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Practice sheet · Gardening & Farming Path · Lens 1: Math

Area & growing days

Practice for The Math of Gardening & Farming: beds, spacing, labels, seeds, rain, the frost-free season, farm scale and GDD (pp.8–15), plus Algebra A1–A2 (pp.17–18).
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Volume = length × width × depth; 1 m³ = 1,000 L. 1 mm of rain on 1 m² = 1 L. N-P-K numbers are percents of the bag’s mass. Buy and sow whole numbers: round up.

Germination rate = sprouted ÷ sown. Seeds to sow = plants wanted ÷ rate. GDD = (high + low) ÷ 2 − 5, or 0 if that is negative (p.15).

Warm-up

One step

Area, volume, percent and rain.
1

A new bed

A raised bed is 1 m wide and 3 m long. Find its area and its perimeter.

2

Fill it

Fill the bed 25 cm deep. How many m³ and litres of soil? Soil comes in 40 L bags: how many bags?

3

Read the bag

A 5 kg bag is labelled 12-4-8. How many grams of nitrogen, phosphate and potash does it hold?

4

Rain

It rains 15 mm on the 3 m² bed. How many litres of water fell on it?

Core

Two or three steps

Sketch the bed and label the units.
5

Square planting

A bed is 0.9 m × 2.4 m, split into 30 cm squares (p.9). How many squares? Plant half with lettuce (4 a square) and half with carrots (16 a square). How many plants?

6

Seed test

You sow 50 seeds and 42 sprout. What is the germination rate? How many seeds should you sow to get 21 plants?

Garden Maths Practice · Gardening & Farming Path · Unizon1/2
Gardening & Farming Path · Unizon · PracticeArea, percent & growing days
7

Beat the frost

Edmonton’s average last frost is about May 14 and first frost about Sept 23. How many frost-free days? What is the latest sowing date for a 100-day crop?

8

Count the heat

Five days (high, low in °C): (22, 8), (26, 12), (15, 3), (9, −1), (28, 14). Find each day’s GDD with base 5 °C and the total.

9

Top up the rain

The 3 m² bed needs 25 mm of water a week. It rained 10 mm. How many litres must you add? How many 9 L cans?

10

Quarter section

A quarter section (160 acres) of canola yields 45 bushels an acre. A bushel of canola is about 22.7 kg. How many tonnes is the harvest?

Level Up

Equations

A1–A2 (pp.17–18).
11

Sunflower

A sunflower is 12 cm tall and grows 3 cm a day: h = 12 + 3d. On which day is it 1.5 m tall?

12

Seedling plans

Plan A: C = 25 + 1.5n. Plan B: C = 10 + 3n. When do they cost the same? Which is cheaper for 16 seedlings?

13

Fence by a wall

You have 24 m of fence for a garden against a wall. A = x(24 − 2x). Which x gives 64 m²? What is the biggest area?

14

Gravel path

A 3 m × 1 m bed gets a path w m wide all round. Path area = (3 + 2w)(1 + 2w) − 3. How wide is the path if its area is 5 m²?

Make your own problem

Your turn to be the garden planner

  1. Measure a real or pretend bed, pot or field.
  2. Write a question about its soil, plants, water or harvest.
  3. Solve it, round up for anything you buy or sow, and check the units.

My problem, and my worked answer:

Garden Maths Practice · Gardening & Farming Path · Unizon2/2
Gardening & Farming Path · Unizon · PracticeArea, percent & growing days

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. Frost dates and yields are averages (book pp.13–14).

Warm-up
1
3 m² · 8 m 1 × 3 = 3 m². 2 × (1 + 3) = 8 m of boards.
2
0.75 m³ = 750 L · 19 bags 25 cm = 0.25 m. 1 × 3 × 0.25 = 0.75 m³ × 1,000 = 750 L. 750 ÷ 40 = 18.75, so 19 bags.
3
N 600 g · P 200 g · K 400 g 12% of 5,000 g = 600 g; 4% = 200 g; 8% = 400 g.
4
45 L 15 mm × 3 m² = 45 L.
Core
5
24 squares · 240 plants 90 ÷ 30 = 3 across, 240 ÷ 30 = 8 along: 24. 12 × 4 + 12 × 16 = 48 + 192 = 240.
6
84% · 25 seeds 42 ÷ 50 = 0.84. 21 ÷ 0.84 = 25.
7
132 days · June 15 May 14 → Sept 23: 17 + 30 + 31 + 31 + 23 = 132. Count back 100 days from Sept 23: June 15. Frost dates are averages; half of years are later (p.13).
8
10 · 14 · 4 · 0 · 16 → 44 GDD (22 + 8) ÷ 2 − 5 = 10; 19 − 5 = 14; 9 − 5 = 4; 4 − 5 < 0, so 0; 21 − 5 = 16.
9
45 L · 5 cans 25 − 10 = 15 mm. 15 × 3 = 45 L. 45 ÷ 9 = 5.
10
≈ 163.4 tonnes 160 × 45 = 7,200 bushels. 7,200 × 22.7 = 163,440 kg ≈ 163.4 t.
Level Up
11
day 46 1.5 m = 150 cm. 12 + 3d = 150 → 3d = 138 → d = 46.
12
10 seedlings · Plan A ($49 vs $58) 25 + 1.5n = 10 + 3n → 15 = 1.5n → n = 10. At 16: A = 25 + 24 = 49; B = 10 + 48 = 58.
13
x = 4 m or 8 m · biggest 72 m² x(24 − 2x) = 64 → x² − 12x + 32 = 0 → (x − 4)(x − 8) = 0. Halfway, x = 6: 6 × 12 = 72 m².
14
w = 0.5 m (3 + 2w)(1 + 2w) = 8 → 4w² + 8w − 5 = 0 → (2w − 1)(2w + 5) = 0 → w = 0.5 (not −2.5).
Make your own: change cm to m before you multiply, write L or m³ on every line, and round up seeds, bags and cans.
Garden Maths Practice · Gardening & Farming Path · UnizonAnswer key