The Maple Tree

The Sugar House

The Double Samara Seed

The seed of the maple tree (Acer saccharum) is symmetrical about a plane of symmetry. The shape of the seed helps it to fly away from the parent tree so that the seedling has space to grow.


From Seedling to Sapling to Sugar Maker

From Seedling to Sapling to Sugar Maker

The maple tree grows about 1 foot per year for the first 30 to 40 years of life. The following chart shows the classification of a maple tree as it grows:

A sugar maple is ready to be tapped once the diameter reaches 10-12 inches. (Circumference = π × diameter. Therefore, the circumference should be at least 31.4 inches.)


Maple Fractals

Maple Tree Fractals

Did you know that maple trees exhibit approximate fractal patterns?

A maple leaf is an approximate fractal (the pattern is finite).

A computer rendering of a fractal maple leaf

Photo credit: Paul Bourke

Branches of a maple tree grow in a fractal pattern

Photo credit: Mark Charles Langdon, Waterloo, Ontario, Canada

How Old is This Tree?

How Old is This Tree?

The age of a tree can be measured by counting the number of tree rings. (Unfortunately, you would have to cut down the tree which would prevent you from sugaring...) This tree was 31 years old. Maple trees are usually about 30 years old when they are ready to be tapped.


Sap's Runnin'! Time to Go Sugarin'!


PhotoCredit: http://commons.wikimedia.org/wiki/File:Tree_rings.jpg

Sap's Runnin'! Time to go Sugarin'!

The sap in a maple tree starts flowing up and down the tree when nights are freezing (below 32°F or 0°C) and days are consistently warm (around 40°F or 4.4°C). A bigger swing in temperature usually leads to a better sap run. In Vermont, the sap usually starts running around the time of Town Meeting Day. A good Sugarer analyzes the weather reports and forecasts to decide when to tap the trees.

Buckets or Tubing?

Buckets or Tubing?

A 16 quart bucket of sap, half full, weighs over 15 pounds. One person can be expected to gather between 750-1,000 buckets per day. That's between 11,250 pounds and 15,000 pounds per day or 1,500 to 2,000 gallons of sap! For a large operation with 12,000 taps, you would need at least 12 gatherers who would move over 180,000 pounds of sap in a day or 24,000 gallons of sap. 

The same sugarbush with 12,000 taps would need approximately 80 miles of plastic pipeline! All of the sap moves directly to the collection tank at the bottom of the hill. 

This tank holds 210 gallons of sap. That's the same as 480 quarts or 60 half-full buckets.

The tractor is used to gather the tanks and take them to the sugarhouse. Only two workers are needed to collect a collection tank. 

Pipelines are credited with saving the sugaring industry in the 1970s when the cost of labor increased. 


To the Sugar House!

The Evaporator

The evaporator heats the sap, which is usually only 2-4% sugar. The water in the sap evaporates and leaves syrup behind. It takes 40 gallons of sap (or 20 half-full buckets) to make one gallon of syrup:

(gallons of sap/40) = gallons of syrup

Is It Syrup Yet?

Is It Syrup Yet?

Maple sugarers need to be aware of several measurements when making syrup: 

When all these requirements are met, a sugarer knows they have syrup! Don't forget to filter the niter out...

A hydrometer is used to measure the density of liquids.






If It Isn't Syrup It Might Be... 

If It Isn't Syrup It Might Be.....

Burnt? Or it could be one of these other maple treats:

Is it the Grade A Fancy Kind?

Is it the Grade A Fancy Kind?

From left to right: Vermont Fancy, Vermont Grade A Medium Amber, Vermont Grade A Dark Amber, Vermont Grade B, Commercial Grade

Sugarers use a standard grading kit, such as the one above, to classify maple sugar. The lighter syrup is generally thought to be the best, although it is a matter of taste preference. The grading kit is like a ruler for sugarers. 

Ain't Nothin' Like the Real Thing

Ain't Nothin' Like the Real Thing

If it's not pure maple syrup, you might as well be tapping telephone poles....An analysis of this data shows that maple-flavored syrups have little to no maple syrup content. These imitation syrups are much less expensive than pure maple syrup.


How Much Is This Going to Cost Me?

How Much is This Going to Cost Me?

The following is a chart listing the average price of maple syrup in Vermont in 2008 based on the amount purchased. These are the retail prices you may encounter at the store: 

                                                                       www.usda.gov

The following graph of the average price of maple sryrup based on the amount purchased indicates that there is nearly a linear relationship between price and volume.  

This graph shows that purchasing more maple syrup at once saves the consumer money.

Who Wins the Maple Syrup Production Race? 

Who Wins the Maple Syrup Production Race?

Quebec is the winner with 5,337,000 gallons of maple syrup produced in 2008. The chart below shows how much syrup was produced by other states and provinces in 2008: 

                                                                                           www.usda.gov

It is easier to interpret the date by making pie graphs. As you can see, Vermont produces the most syrup in the United States (38%): 

Canada produced 76% of all maple syrup in 2008!

Conclusion: The Math of Maple Syrup

The Math of Maple Syrup

The world around us is filled with many exciting math phenomena. Maple sugaring is just one example here in Vermont. Algebra, Data Analysis, Geometry, Measurement, and Numbers and Operations are all part of sugaring:

Algebra: A sugarer is concerned with the rate of change in tree growth, the rate of the sap drip (determined by the pressure of the sap in the tree), and the amount of sap needed to produce syrup. 




Data Analysis: There are so many numbers and patterns to discover in maples sugaring. Extensive data can and has been collected and analyzed on growth of trees, perfect weather conditions for sugaring, the right conditions for making syrup from sap, product comparisons, pricing of syrup, and the patterns of production. 

Temperature fluctuations in Burlington, VT during March 2010

Geometry: Many maple 
trees appear symmetrical to the eye. That is why so many children love to draw the maple sugar tree. This symmetry is also found in the seeds of sugar maples. Fractals abound in the structure of the leaves and branches. A sugarer uses geometry to determine which trees to tap and how many taps to use by analyzing diameters and circumferences. 
Photo Credit: www.cirrusimage.com/tree_maple_sugar.htm

Measurement: Sugaring is rich with measurements. You can measure the growth of a tree, the age of a tree, the outside temperature, the amount of sap produced, the time it takes to make syrup from sap, the cooking temperature of syrup and other maple treats, the density of syrup, the weight of syrup, the sugar content of syrup, and the grade of syrup. 

Numbers and Operations: A sugarer counts the number of trees, the number of taps, and the number of buckets in the sugarbush. The rings of a tree can be counted to determine the age of a fallen tree. Sugarers use calculations to determine the number of workers needed, the amount of sap collected, and to estimate profits. 



Any More Questions? Check Out These Great Resources About Maple Sugaring