In this lesson we will be exploring the wide world of trees and trying to utilize some simple mathematics to determine the height of these majestic organisms. Slap on the thinking caps and join me in the rain as we investigate trees!

Let's talk trees!

As you look out your window or walk around your neighborhood, chances are you see trees! In fact, nearly 30% of the entire Earth is covered in trees! And this is a good thing! But sometimes we can forget or take for granted all of the things these silent workhorses do. The Arbor Day Foundation provided us a short list of some beneficial aspects of having trees in and around the places we live, and even in the places we will never visit:

Trees help clean our air.

• Global forests removed about one-third of fossil fuel emissions annually.

• Trees remove pollution from the atmosphere, improving air quality and human health.

• Roadside trees reduce nearby indoor air pollution by more than 50%.

Trees contribute to our health.

• A study of 10 cities found community forests save an average of one life each year. In New York City, trees save an average of eight lives every year.

• Office workers with a view of trees report significantly less stress and more satisfaction.

Trees help clean our drinking water.

• Forested watersheds provide quality drinking water to more than 180 million Americans.

• In 1997, New York City spent $1.5 billion to preserve the forested watershed that supplies New York City’s drinking water by purchasing thousands of upstate acres of forested watershed. A filtration plant large enough to clean New York City’s water supply would have cost more than $6 billion dollars. Today, New Yorkers enjoy some of the cleanest drinking water in the world, and New York City has won regional water taste competitions.

Trees provide much-needed cooling.

• Trees lower surface and air temperatures by providing shade. Shaded surfaces may be 20–45°F cooler than the peak temperatures of unshaded materials.

• Evaporation of water from trees has a cooling influence.

Trees benefit wildlife.

• Trees provide vital wildlife habitat.

• Trees and forests provide important species range. Many animals have a range of hundreds of square miles. The mountain lion of North America, for instance, has a range of nearly 400 square miles.

Trees help us save energy.

• Trees properly placed around buildings can reduce air conditioning needs by 30% and can save 20–50% in energy used for heating.

• For instance, the average Cincinnati, Ohio community tree saves the average household $56 annually in cooling costs by reducing electricity use. More than 85,000 Cincinnati community trees save residents $4.8 million.

• Carefully positioned trees can reduce a household’s energy consumption for heating and cooling by up to 25%. Computer models devised by the U.S. Department of Energy predict that the proper placement of only three trees can save an average household between $100 and $250 in energy costs annually.

What's a tree's favorite subject in school?

Geometree.

Trees + Mathematics = Tons of Fun Outside!

Today we are going to be using a few different mathematical concepts to figure out how tall the trees around us are. We are going to use a few different methods to double check our work - these methods will get more difficult, but I know you can do it!

How can you identify a dogwood tree?

By its bark.

Outdoor Adventure Challenge

OK, enough sitting! Let's get outside and see how big these trees are! Today you will be using four different methods to determine the height of two different trees. We will then compare our data to see how accurate we were in our readings.

Materials

To take part in today's challenge you will need the following:

• To have watched the videos above. I have instructions for you, but having seen things before you go outside will make the instructions all the more clear.

• A printout of the Tree Height Measurement paper below. We will use this to collect our data.

• Your homemade inclinometer.

• Something to write with.

• Something to write on.

• A 12'' ruler. I have a special surprise method that I included on the sheet that will use this tool.

• Someone from your home. They will help you look out for obstacles and will play a very important role in the Ratio Method.

What to Do

1. Once outside, you need to determine how long your stride (normal step size) is in feet and inches. You will be using this distance to measure the distance between you and the tree numerous times. To do this, measure from the heel of your back foot to the toe of your front foot after you have taken a normal step. You can mark the distance on the ground and then measure with your ruler.

2. Select two trees to measure.

3. Using the four methods on the Tree Height Measurement sheet, measure and record your data for both Tree 1 and Tree 2.

4. When you're finished, come back inside and we can chat!

Reflection

What an amazing day staring at trees! As the biggest plants on the planet, they give us oxygen, store carbon, stabilize the soil, and give life to the world’s wildlife. They also provide us with the materials for tools and shelter. Not only are trees essential for life, but as the longest living species on earth, they give us a link between the past, present and future. Majestic indeed. Since you spent so much time working with these leafy/needly beasts, we have a few questions to ask:

• Did you have a prediction as to which method was the most accurate? Were you correct? How did you know?

• What are some other methods we could use to measure trees? How would a shadow help?

• What other properties of trees could we measure beyond just height?

• Why is measuring trees important from an ecological perspective and not just as a fun mathematics activity?

Quick Quiz

On your mark...get set...go! Let's see what you remember from today. Don't forget, you can measure tons of things with your new found mathematical skills. Good luck!