Wednesday, December 2, 2009

Garden Math

by Phoebe Green and Beth Koennicke

Gardens are a source full of fresh fruits, vegetables, and flowers that provide for and sustain life. But did you know a garden, from its creation to harvest, is rich in mathematical concepts and connections as well? From finding area and perimeter to observing shapes and symmetry, gardens are truly authentic models of mathematical concepts. Whether you are an educator looking for new ways to teach math or someone interested in the mathematics required to create your own garden, you’ve come to the right place!
But enough introductions; welcome and enjoy!

Planning a Garden

Planning a Garden

The first step when planning a garden is to determine its layout. The layout will include the shape and dimensions of the garden. For example, this picture shows a 15’x12’ rectangular garden layout.

Next, a gardener would determine what types of vegetables to grow in order to figure out how they will be planted. For example, lettuce is not usually planted in a square or rectangular bed, but in rows or columns, depending on the shape and dimensions of the garden. The example garden has been broken up into 4 planting rows, 4 walking rows (brown), a bed of carrots, a column of tomatoes, and a column of pumpkins.

Mathematics is also involved in figuring out the dimensions of each part of the garden. If we knew each planting row is to be 2’ wide by 10’ long, then the rest of the dimension of the garden can be figured out easily using simple mathematics:

Planting Rows:

4 planting rows x 2’ wide = 8’ in planting rows

12’width of garden - 8’ in planting rows = 4’ left over

4’ feet left over / 4 walking rows = 1’ per walking row.

Bed of Carrots:

15’ lengths of garden – 10’ length of planting rows = 5’ left over for bed

Width of bed is 2 planting rows and 2 walking rows: 2’ + 2’ + 1’ + 1’ = 6’ width of bed

Column of Tomatoes and Column of Pumpkins (equal size):

5’ / 2 columns = 2.5’ per column

12’-6’= 6’ long

(Geometery, Measurement, Numbers and Operations)

Determining the area of the garden is essential, especially when buying fertilizer. Fertilizer can be expensive, so it is important to only buy as many bags as necessary. Each bag of fertilizer tells the surface area it will cover, so the easiest way to ensure you will have enough fertilizer without over buying is to use the mathematical equation: Area of garden/Area of 1 bag fertilizer = # of fertilizer bags needed.

 The area of a garden is found by multiplying the length by the width (l x w = A). In our sample garden, the area is 180 sq ft.:

15’ x 12’ = 180 sq ft

If each bag of fertilizer covers 20 sq ft, the sample garden would need 9 bags of fertilizer.

180 sq ft/20 sq ft per bag = 9 bags

(Geometry, Measurement)



  Once a garden has been planned, constructed, and fertilized, a fence is normally built around it to keep animals out. Once again mathematics must be used in figuring out the perimeter of the garden in order to know how many feet of fence is needed. Perimeter is calculated by adding up the measurement of each side. Our sample garden would need 54’ of fence to go all the way around. 12’+15’+12’+15’= 54’

(Geometry, Measurement)


       Seed packets are loaded with mathematical information. These packets tell a gardener how far apart to plant seeds (distance measurement), the likelihood the seeds will germinate (probability), how long they will take to reach full maturity, as well as the cost per packet!

         This gives gardeners the opportunity to estimate planting expenses and predict the likelihood of the plants growing.

Example 1: Estimating Planting Expenses

            Say we wish to estimate how much it would cost us to plant a row of green beans in our garden. First   we must look at the information on the green beans packet. The packet says each bean (seed) should be planted 2” apart.

     Using our example garden, we know we will need 60 beans for our row of green beans.

       (10 feet in the row x 12” per foot = 120” in the row; 120” in the row / 2” per bean = 60 beans per row)

        Now, looking back at the packet, it says there are 20 beans per package. We now know we need 3 packets of beans, and, if each packet costs $2.00 we can expect to spend $6.00 planting our green beans!

Example 2: Prediction of Germination

              Using our earlier calculations we also have the ability to predict how many beans will actually grow into plants using the “Germination Rate” found on the back of our packet.

           Say the germination rate of these particular green beans is 95%. Knowing this rate, and that we are planting 60 beans, we can expect that 57 of these beans will grow into plants. (60 x .95 = 57).

Wow! Who ever thought gardening could be so mathematical?

           (Measurement, Numbers and Operations, Probability and Statistics)

*photo taken by: Phoebe Green


Once the plants begin to grow gardeners can measure the growth of vegetables through graphs. You can measure and graph height, the number of leaves, and later, the amount of blossoms and fruit.


*graph pictures:


Gardens and plants are full of mathematical concepts once they begin to grow; all you have to do is look!
Once vegetables and plants start growing students can observe the shapes of the plants and garden.
Students can also find symmetry and angles in plants and leaves.
Rational counting skills can also be exercised while young children enjoy counting the leaves and fruit on plants.

(Geometry, Numbers and Operations)

Tuesday, December 1, 2009


Once your plants start producing vegetables, you can measure and record your daily yields.

For cucumbers you could measure and record the length of the fruit, as well as weight.

For example:

  • Count how many cucumbers you harvest each day and make a chart to record your results.
  • For green beans you could weigh your harvest each day you pick and record it on a chart.
  • At the end of the season, make a graph to find out when the peak yield was, what was the average yield, and how much you harvested total.

(Measurement, Numbers and Operations, Probability and Statistics)


Now What? Using the Harvest

You can practice fractions when you cut up your tomatoes and pumpkins to cook them. Each individual fruit or vegetable is its own whole. Practice finding halves, quarters, and any other fractional piece you can safely cut. Name what shapes the fruits and fractional pieces are.

Cooking and preserving are good ways to practice conversions. When making a batch of mashed potatoes determine how many pounds of potatoes you will need to feed the whole class.

Ratios and measurement conversions are important when making pickles.

For example, when making dill beans it is important determine how many pounds of green beans you will need to make 7 quarts of dill beans.

(Geometry, Measurement, Numbers and Operations)