Maple Trees, Syrup and Sugarbush Math

Based on Ininatig's Gift of Sugar The Tradition of Native Sugarmaking by Laura Wittstock

1. Examine Growth Rate

"Sugar maple trees average about 1 foot of height growth and 0.2 inch of diameter growth annually for the first 30 to 40 years. Hence a 30-year-old tree might be 6 to 8 inches in diameter and 30 to 35 feet in height.

After about 140 to 150 years, height growth ceases and radial growth slows greatly. Although rare, old-growth sugar maple stands can average 300 to 400 years in age; individual trees range from 70 to 110 feet tall with diameters at breast height of 20 to 36 inches." 1

Your school is planting 3 Acer saccharum. They will use them to teach about sugarbush.
The trees are 3 inches in diameter. A tree must be 10 inches in diameter to tap. When
will the trees be large enough to tap?

2. Review this chart regarding Maple Syrup production.

How many gallons of syrup were produced in 2005?   Which state had the largest production?

(Click on the graph to see a larger view)

What percentage of the total production did that state have?

Imagine you are planning to develop a business that produces maple candy.
In which state should you establish it? Why?

Vocabulary Geometry - the circle: diameter, radius, circumference

3. In order to know how many taps to place in a tree, you need to know the diameter of the trunk of the tree. How would you determine this without cutting down the tree?

4. Use the information at Make Your Own Maple Syrup! to answer these questions.

How much maple syrup is made from a gallon of maple sap?

You intend to give each 4 neighbors a quart of homemade maple syrup.
How many gallons of sap will you need to collect?

You determine that you will tap 4 trees. One is 11 inches in diameter. One is 24 inches in diameter. One is 19 inches in diameter. The last has a diameter of 27 inches.

How many taps do you need?

According to Hobby Maple Syrup Production what is the average season yield per tap?

Will you have an adequate yield to make the four gifts above?

5. In your town's park there is a massive maple tree. In fact, the park was established to protect the beautiful, old tree. For the upcoming bicentennial celebration the mayor has asked you to see if it qualifies as a Big Tree. This requires some measuring. Another measurement resource.

What measurements must be obtained?

Describe how to make one of the measurements.

The mayor wants to know for her speech, who was in charge of the government in your region, when the tree began to grow.

You measure the tree with a long piece of rope and find a circumference of 4.3 yards.
Use the growth information in question 1. How old do you estimate the tree to be?

Use a spreadsheet, with labels, to show how you work this out.

Answer the mayor's question.

6. The people in the story are members of the Anishinaabe or Chippewa people.
According to the Minnesota Compass , how many Native Americans live in Minnesota?

What percentage of Minnesota's Native Americans are Chippewa?

Challenges:

What species is the largest tree (Champion) in your state?

Calculate the diameter of a tree located near your school or home.

Finished? Excellent! Harness these resources to extend your know how.

Maple Syrup - A Taste of Nature

What tree is it?

Sugar Maple and sugaring facts

Why Plant Trees / Nature Conservation & Biodiversity

Learn more about circle geometry video

Developed & posted 11/2007 Cynthia J. O'Hora Released to public domain for non profits

Save a tree use a digital answer format - Highlight the text. Copy it. Paste it in a word processing document. Save the document in your folder. Answer on the word processing document in a contrasting color (not yellow) or font (avoid fancy ones like , ). Or perhaps you have the resources to record verbal answers. If you do, be sure to first read / record the question. Then record the answer immediately after it.