Sweet Signs of Spring: An Adventure in Math

Clear sap dripping into a metal bucket from a metal spile tapped into a maple tree
Educational Activity from Indiana Dunes National Park
Intended Age: Grades 4-6

By Lynda Lancaster
April 9, 2020
Objectives--Students will be able to:
  • Discuss how maple sap is transformed into maple syrup.
  • Calculate the amount of syrup that can be acquired from a certain amount of sap.
  • Understand the effect of weather on maple syrup production and hence the life cycle of the tree.
Background and Science behind maple trees and maple syrup:
A man leans in to listen for the tap of the maple sap as it drips into a metal bucket hanging from a maple tree.
Are you outside? Listen, can you hear the drip, drip of the sap just starting to move in the trees? Remember last summer when the leaves were on the trees and they were busy making sugar? That sugar was stored in the tree’s roots. When it started getting cold, the leaves shut down their factories, and fell off the trees. As the days get warmer in the spring, the water in the trees starts to flow, bringing the sugar from the roots called sap.

Now the sugar they stored in the roots is once again traveling through the xylem and phloem to get to the leaves to give them the burst of energy they need to open and get started making sugar for the tree again.

But WAIT! One of the sweetest things about living in Indiana is that some of the sweetest sap is in our Maple Sugar trees. If you know how to do it, you can collect some of that sap and turn it into maple syrup!
A few things you need to know:
Maple sap dripping out of a spile into a bucket.
Maple sap - maple sap looks like water when it flows from the trees; it contains water, amino acids and traces of vitamins and minerals; sap is 2 - 3% sugar; it takes 40 gallons of sap that is 2.2% sugar (the sugar content of an average maple tree) to make one gallon of pure maple syrup; sap weighs 8.34 pounds per gallon, the same as water.
Golden sap or syrup boiling in a pan on a stove.
Maple syrup - pure maple syrup is maple sap which has been boiled to 7 degrees F above the boiling point of water (the boiling point of water changes every day with the weather and barometric pressure); the proper density of pure maple syrup is 32 degrees F Baume (a standard scale used to measure sugar concentration in syrup, measures specific gravity, this is what our hydrometer measures) at the boiling point; pure maple syrup is 67% sugar and weighs 11.0 pounds per gallon at 60 degrees F.
A glass jar filled with light tan maple sugar
Granulated maple sugar - made by heating pure maple syrup to 252 degrees F, removing it from the heat and stirring until maple sugar granules form.
Park staff and partner collect data from blue bags filled with maple sap for a research project.
Science Brief: Dr. Joshua Rapp, an Associate at Harvard Forest in Massachusetts, and an international consortium of scientists known as ACERnet, are monitoring sap flow across the range of sugar maple trees. They are conducting research to understand how climate effects sap flow, sugar content, and chemical composition, which together influence the quality and quantity of maple syrup produced.
A sugarbush is an area of land with sugar maple trees which are tapped to make maple syrup or maple sugar. Dr. Rapp and the ACERnet team are utilizing data from sugarbushes in Quebec, New Hampshire, Massachusetts, Virginia, and Indiana in their project. They look at the amount of sugar in the sap, the amount of sap collected from each tap, and the secondary chemistry (non-sugar compounds) and compare these data with weather data from each location.
Volunteer citizen scientists at Indiana Dunes National Lakeshore have been collecting data for Dr. Rapp for the past four years. At the beginning of each season, they tap 24 trees, and hang bags from spiles inserted into each tap to collect the sap. Each afternoon during the season (roughly the beginning of February through mid to late March), if enough sap is flowing they weigh the sap that was collected from each tap. They also determine the sugar concentration of the sap that flows from each spile using a tool called a refractometer. The refractometer measures the amount of sugar in Brix (basically the percentage of sugar in the sap). In addition to that data, they also record the date, the time, and the amount of snow cover. At the end of the season, it is all sent to Dr. Rapp. Prior to 2020, they also collected small vials of sap to send to the lab for secondary chemistry analysis. This year there was not enough funding to have the samples from Indiana Dunes analyzed.
The volunteers really enjoy meeting in the sugarbush. It’s just fun to be outside in the woods, to realize you’re helping produce maple syrup, and you’re helping scientists answer important research questions!
Four glass bottles of maple syrup in varying shades of amber color.
This information will help you with the math exercises:

Sap= % sugar as it comes out of the tree
Syrup= 67% sugar per gallon
Maple Sugar= 67% sugar heated to 252 degrees F.

A gallon of sap weights 8.34 lbs
A gallon of syrup weighs 11 lbs

1 kg=.2642 gallons of water

Jones Rule of 86:
For this formula, do not convert % to decimals.
86/% sap Sugar Content= Number of gallons of sap for 1 gallon of syrup

*At 2.2% it takes about 40 gallons of sap to make one gallon of syrup

This is the data collected for the research project at the park this spring. We will use this data for this project.
Date Daily High Temp
INDU in green
Daily Low Temp
INDU in green
Weather Channel High/low for Chesterton Sap collected.
In Kg
% Sugar
Feb 4 32 24 38/31
Feb 5 35 27 32/25 5.75 3.55
Feb 6 32 24 29/25
Feb 7 31 24 38/27
Feb 8 37 26 22.7 2.57
Feb 9 36 25
Feb 10 36 27 32.5 2.74
Feb 11 33 26 38/25
Feb 12 35 21 35/23 37.5 2.61
Feb 13 32 12
Feb 14 19 3
Feb 15 34 5
Feb 16 37 17
Feb 17 39 25 33 2.46
Feb 18 39 28 64.95 2.48
Feb 19 38 21
Feb 20 27 11 28/22
Feb 21 22 10 37/12
Feb 22 49 25 39.55 2.38
Feb 23 56 33 111.4 2.45
Feb 24 40 36 40.65 2.38
Feb 25 40 34 37/32
Feb 26 32 27
Feb 27 31 25
Feb 28 31 20
Feb 29 36 21
March 1 2020 53 27 75.85 2.48
March 2 52 32 206.2 2.27
March 3 41 20 50/31 54.5 2.41
March 4 51 25 44/28
March 5 44 27 53/28 76.8 2.43
March 6 53 32 36/30
March 7 50 22 56.25 2.38
March 8 67 37 66.55 2.46
March 9 61 49
March 10 62 34 53/28
March 11 42 30
March 12 56 34 30.5 2.28
March 13 57 35 49/35
March 14 40 33
March 15 39 30
March 16 40 29
March 17 39 31 41/33 39.5 2.34
March 18 41 33 44/34
March 19 44 38 62/40
March 20 63 38 61/30
March 21 30 27
March 22 36 24
March 23 38 29 59.2 2.12
Total 1052.65
Average % sugar content 2.36
A row of containers holding Indiana maple syrup.
Do you have any ideas why there are not measurements for everyday? Imagine what happens to water when it gets to be 32 degrees F. Yes, there was no flow of sap on the days there is no data.

Scientists measure the amount of sap, or volume of sap, in kilograms, but when was the last time you bought a kilogram of syrup?

Convert the sap to gallons using a multiplier of .2642. Round your answers to two decimal points
Date Volume in Kg Volume in gallons (show your work)
Feb 5 5.75
March 2 206.2
March 7 56.25
Glass gallon jars filled with dark, maple syrup.
How do we know how many gallons of sap needed to make one gallon of maple syrup? You could just start boiling what you have to remove the water until the sap is 67% sugar, but how would you know how may gallon jugs you would need?

The Jones Rule of 86 is a mathematical way to determine how much sap you will need per gallon of syrup. The Jones rule uses the percentage of sugar in the sap. That percentage of sugar in the sap varies by tree and by region and scientists use a variety of tools to measure the percentage of sugar in the sap.

Using the Jones Rule of 86 determine how many gallons of sap you will need to get one gallon of syrup. For example when the sap is 2.2% sugar, it will take about 40 gallons of sap for one gallon of syrup.

86/ % sugar sap= gallons of sap to get one gallon of syrup (note, when you divide, do not convert the % to decimals)
Date % sugar in sap Show your work No. of gallons needed
Feb 5 3.55 86/3.55% 24.23 gallons
Feb 23 2.45
March 1 2.48
March 2 2.27
Three glass, gallon sized bottles filled with a clear liquid.
The average % sugar for the season was 2.36%. There were 1052.65 Kg collected for the season. How many gallon jugs should you have on hand to collect all your yummy syrup?

Show your work:

Two boys with yolks carrying sap buckets.
As a busy 5th grader, you may not have all that much time to go out every day to check the bags collecting the sap. Make a graph and pick which days you would want to go out to collect sap.

Use these data points to create a bar chart that compares temperature and the amount of sap collected.

Daily High Temp Sap collected
INDU in green In Kg
35 5.75
37 22.7
36 32.5
35 37.5
39 33
39 64.95
49 39.55
56 111.4
40 40.65
53 75.85
52 206.2
41 54.5
44 76.8
50 56.25
67 66.55
56 30.5
39 39.5
38 59.2

Two park volunteers tend syrup making in the Sugar Shack at the Chellberg Farm
Use this data set to create a graph of the % sugar. Do you notice a trend in the % sugar as the maple sugar season goes on?
% Sugar

When I looked at the data, I noticed:

I could find out if my hypothesis is true by:
A yellow-rumped warbler on a maple twig with opened, red buds.
Once the leaves start to bud on the trees, the sap turns bitter so it’s time to stop collecting sap and go out and enjoy the flowers blooming and the birds coming back.
Please contact Ranger Kim Swift for the answers or the file version of the activity.

Indiana Math Standards covered in this program.

5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem).
5.AT.6: Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
5.AT.7: Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
5.AT.8: Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values
5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems.

5.DS.1: Formulate questions that can be addressed with data and make predictions about the data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, bar graphs, and line graphs. Recognize the differences in representing categorical and numerical data.

Last updated: April 30, 2020

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