# Design, Grow, and Ponder in a Garden

## A garden can inspire students to make mathematical connections.

Spring has sprung, and one of the greatest joys of pleasant weather is to putter around in a garden. But do you know how gardening relates to math? Flower petals, seed heads, soil, borders, and fences--along with other aspects of gardening--are all mathematical. So why not start a garden with your students? You can use algebra, geometry, advanced algebra, and even pre-calculus and allow students to enjoy the fresh air while they ponder petals. Your colleagues will be eager to collaborate across disciplines as well, since they can have students examine the art and science of gardening.

### Petals and Spirals and the Fibonacci Sequence

When I taught an advanced algebra class at a charter school, we analyzed the existing flowers in a garden on school property. We then went into more detail about the recursive nature of the Fibonacci sequence. Students may either inspect existing plants or begin their own garden. In this way, they may categorically research flower types that are vital in a Fibonacci garden.

This year I am spotlighting flowers in my garden that relate to Fibonacci numbers. A Fibonacci number is one of the integers of the sequence in which each subsequent number is the sum of the previous two, starting with the numbers 0 and 1. Thus it begins, 0, 1, 1, 2, 3, 5, 8 ... Did you know that the number of petals in a flower is often one of the following numbers: 3, 5, 8, 13, 21, 34, 55? For instance, lilies, irises, and trilliums each have three petals. Hundreds of species of flowers have five petals, such as columbine and buttercup. The number eight is not as common, but exists, in such flowers as bloodroot and delphiniums. My favorite thirteen-petaled flower is the Black-eyed Susan. Further, 21, 34, and 55 petals are also quite common. For instance, the hearty daisy which returns every year often has 13, 21, 34, 55, or 89 petals. The coneflower, whose Latin name is “echinacea purpura” is also a favorite perennial in my garden and has a center with orange spirals that number 34 and 55.

Of particular interest might also be the tiny florets in the core of certain flowers’ blossoms, particularly that of a daisy, echinacea, and sunflower. For instance, in the heads of a sunflower the number of spirals--one in one direction and one in an alternate direction--come in Fibonacci pairs, such as 21 and 34, or 34 and 55, or 55 and 89, or 89 and 144.

Counting petals and examining spirals may seem rather elementary at its start, but it can be a fascinating pretext to a mathematical examination of the Fibonacci sequence more generally. Further, mathematics that may stem from this activity might include how the Golden Ratio relates to the Fibonacci sequence or an examination of recursive functions more broadly.

### The Dirt on Data

A math teacher might want to team up with a science teacher to do soil testing and examine various data. One of the most basic soil tests is a measure of pH level. Different plants prefer different acidy. One way to introduce students to acidity or base measures is to have them look at the pH levels of some common household substances, such as lemon juice, milk, coffee, bleach, etc. Students can then explain the pH ratings as logarithmic and exponential equations. Gathering more data means more mathematical analysis as well. For instance, growth rates might be charted and modeled.

### Math and Garden Design

At a basic level, students can compute the area that their garden will be or its perimeter to plan specific garden-bed designs or fences. At a more complex level, students can create an investigation when given a certain perimeter as a constraint (due to, for example, a limited amount of fencing materials). Given such a perimeter constraint they might determine the maximum area for the garden. Furthermore, one might use graphs and equations to minimize a perimeter for a particular set area.

Now that we have already explored some scientific applications, how can the study of gardens connect to language arts curriculum? When I was teaching English classes for the Birmingham public school system in suburban Michigan, we also created a “poetry garden.” Students wrote poems about a particular flower or seed that they planted. They laminated their poems and posted them next to their flowers. They might try to integrate scientific or mathematical concepts and descriptions in their writing, such as the manner in which poet and naturalist Diane Ackerman does in A "Natural History of the Senses." This can be further developed into an “art meets science” unit by discovering how creative writing and scientific inquiries can tackle our complex natural environment more generally. Additional authors such as C.P. Snow, Annie Dillard, Oliver Sacks, Stephen Jay Gould, and Richard Feynman may also bridge the divide between art and science across the curriculum. Here are additional methods to mix mathematics and gardening.

## Math and Gardening Activities and Lessons:

Students discuss ways in which mathematics applies to the real world, such as in the case of a garden. They then plan and plant a garden employing mathematics.

Planning a Naturalized Garden

Students develop a plan to design and construct a naturalized garden on a plot of land. Students examine the mathematical and scientific benefits to humans and the environment in planting a naturalized garden.

Rectangular Gardens within a Given Perimeter

Given the parameters of a certain perimeter for a garden, students are challenged to design a garden with a maximum area. Students may further analyze the relationships between the dimension of length, perimeter, area, surface area, and volume.

Building a Garden Fence

Students use algebra and geometry to find the appropriate dimensions needed to construct a fence for a garden. Students also use a graphing calculator in the process to integrate technology.

Launching Laudable Landscapes

Students explore various kinds of garden designs and then employ a certain plan or create their own garden plan. Students are then encouraged to implement one of the student designs in a school or community environment.