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Tracking Math in the Wild

Nature has an endless supply of things to count, measure, categorize and sort; of patterns to puzzle out; and of data to record and graph. Check out these activities for using this variety and abundance to build math skills and to deepen ecological understanding.

Below is list of activities for collecting data and/or doing operations on numbers from nature. For all of the activities students will need pencil and paper to collect data or do calculations. You will also need to decide in advance whether to take measurements in metric or English units (keeping in mind that conversions are another kind of operation).

The activity description will also list the math skills used, the grades the activity can work with, the requirements (tools, supplies, or skills), the best season(s) for the activity, how long it should take (not counting moving between indoors and outdoors), and the steps for doing the activity.

This is a work in progress. Suggestions to improve an activity or new activities are greatly appreciated.

Mostly or All Outdoors Mostly or All Indoors


Citizen Science Project Websites

Other Outdoor Math Websites



Ant Feeding Station

Math Skills: counting, measuring distance, counting by categories, counting over time, graphing data over time

Grades: K and above

Requirements: grassy protected areas outside, small pieces of cardboard or plastic lids, cookies, honey/molasses, meat, optional - flags to mark location of feeding stations

Season: late spring, fall

Time: 30 minutes to set up, 5 to 10 minutes several times per day or week

What kind of bait attracts ants? Do different species of ants like different baits?

Pick several spots outside in protected grassy areas (near a fence for example). Leave small piles of cookie crumbs, or drops of honey or molasses, and/or bits of meat on a small square of cardboard or on top of a plastic lid. Check back several times during the day to see if the ants have found it.

Once the ants have found your bait, count how many ants come to the bait in a 5 or 10 minute period. Repeat counts several times to see how it changes over a day or over a week. See if you can follow the ants back to their nest. Measure the distance to the nest.



Math Skills: counting, counting by categories, graphing counts

Grades: 2nd and above

Requirements: outdoor space with a diversity of plants and habitats

Season: late spring, fall

Time: 30 minutes to 3 hours

How many different kinds of plants and animals (and fungi) live at our school?

A bioblitz is rapid survey of all the species in particular area. Formal bioblitzes go for a 24 hour period, and involve multiple ways of sampling plants, insects, fungi, fish, mammals and other organisms. Often, there are taxonomic experts on-hand to give scientific names to what students find. The goal is to make a list of everything that lives in an area.

However, any school can do a simple bioblitz by having the students cover a defined area and writing down the name or a short description of everything they see. For example: red bird, black bird, yellow flowers, grass, tree with pointy leaves. At the end of 15 minutes, students share the results and tally up the total number of species. Species can be put into broad categories, plants and animals at least, and students can make a bar graph of the categories.

Extensions: (1) Repeat the activity every week or so. Students will be able to see how species change over time. The total number or categories can be graphed over a period of time. (2) Partner each student with a younger child. (3) Extend the time period to 90 minutes and engage local experts who may be able to provide some special equipment and knowledge for sampling.


Bird Feeder Counts

Math Skills: counting, counting categories, addition, graphing daily counts

Grades: K and above

Requirements: bird feeder(s), bird seed

Season: any time of year

Time: 30 minutes to an hour to set up, 5 to 10 minutes of observing several times per day or week

How many birds and species of birds live at our school?

Purchase or make bird feeders. There are models that attach to a window with suction cups, or that hang from or sit on a stand. Work with your facilities staff to find an ok place to put the feeder. Things to consider are the mess (spilled seed and bird poop), minor damage at the attachment site, long term maintenance and removal when the project is done and squirrels. Make sure that the feeder is in a place where it is easy to add birdseed.

After the birds find the feeder, establish a time when students can take turns counting the number of birds at the feeder. Record birds at different times of day and over multiple days.


Branch Angles

Math Skills: measuring angles with a protractor, categorizing and comparing measurements, graphing measurements for different species

Grades: 4th and above

Requirements: accessible twigs and branching stems (herbaceous plants, shrubs, small trees), protractor

Season: any time of year

Time: 30 minutes

Do all the twigs/stems on a plant have similar angles? Do different plants have different angles?

Go outside. Pick a branching plant to measure angles on. It can be a herbaceous plant like goldenrod, a shrub, or a small tree. Line up the base line of the protractor with the main stem or branch so the twig/stem you want to measure is pointing up, with the origin over the place where the twig/stem and branch meet. Find the angle on the protractor (inner scale if there is one). Repeat on other twigs/stems.


Branch Rings

Math Skills: counting

Grades: K and above

Requirements: branch that is several years old, tree saw, magnifying glasses (optional), rulers (optional)

Seasons: any time of year

Time: preparation time 30 minutes, counting rings 10 minutes

How old is the branch?

Prepare sections of branches by sawing a small branch (3/4" to 1 1/2" in diameter) into 1" to 2" pieces.

The outermost layer is the bark. Just underneath it is a thin layer of phloem-cambium-sapwood. The phloem carries sugars down to the roots. The cambium produces the phloem cells on one side and sapwood on the other. The sapwood carries water and mineral nutrients up to the leaves. Just inside the sapwood is the layer of woody cells laid down the previous year, dark summer wood on the outside and lighter spring wood on the inside. Summer and spring rings alternate into the center, forming the heartwood. In the very center is the pith or central core of the tree.

Have students count rings from the inside out or outside in to estimate the age of the branch, remembering that a pair of light and dark rings (light ring on the inside) makes up one year. Try measuring the width of each ring to see which was the best year for the branch (a magnifying glass may help with measuring).

Extension: Take a branch with branches coming off it. Take sections of the branch, and of each of the branches comeing off of it down to the twigs. See if you can reconstruct when branching occurred over time.



Butterfly Feeding Station

Math Skills: count, count categories if different kinds of butterflies can be recognized, adding categories, fractions of kinds of butterflies, if done over time, graph numbers vs date on a coordinate plane

Grades: K and above

Materials: trees to nail oranges to, aluminum nails*, oranges

Season: late spring, fall

Time: prep - 30 minutes, activity - 5 or 10 minutes at a time

What kind of butterflies live at our school?

Cut the oranges in sections (halves, quarters, slices). Nail them to a tree. Check back frequently to see if butterflies are visiting the oranges. Count the number of butterflies that visit at set times. If there are different kinds of butterflies, count them by species.

You can also make butterfly baits with the recipe at

*if the nail is forgotten and left in the tree, and the tree ever has to be cut down, aluminum won't ruin the saw.


Counting Colors

Math Skills: category counts, picture graphs or t-charts, bar graphs (draw conclusions), fractions and decimals of category counts, if data collected over time, graphing on a coordinate plane

Grades: K and above

Requirements: a variety of flowering plants on the school grounds

Season: late spring, fall

Time: 30 minutes

What is the most common flower color? Does it change over time?

Have the students go outside and count as many different colors of flowers as they can see. They can also count the different kinds of flowers of each color, for example 3 kinds of yellow flowers, 2 kinds of blue flowers, or the total number of flowers of one color and one kind.

Extension: Repeat this activity weekly over a season so that students can track bloom time of plants. For older students, consider participating in the Citizen Science "Project Bud Burst" which tracks the stages of plant bloom each spring over multiple years to see if plants are blooming earlier each year.


Honeybees and Hexagons

Math Skills: calculating perimeter and area for self-tesselating polygons (triangles, squares, hexagons) and comparing ratios of area to perimeter

Grades: 6th and above

Requirements: rulers, calculator

Season: NA

Time: 30 minutes

Why do bees build their honeycombs out of hexagons instead of squares or triangles?

Have students draw a triangle, a square and a hexagon. Then have them calculate the perimeter and the area of each shape.

Assume the perimeter represents the amount of wax required to build a cell in a honeycomb, and the area represents the amount of honey that can be stored in the cell. Students should then determine which cell design, triangle, square or hexagon, can store the most honey per amount of wax used by calculating the ratio of area/perimeter.

Optional - Show this animation explaining the math behind the honeycomb -

Caution! - While the hexagon does indeed beat the square and triangle in the efficient use of materials, another reason for the choice of shape is that the bee larvae are raised in the same kind of cells that honey is stored in. The cross section of larvae is round, not square or triangular, so the hexagon design holds the larvae better than the other shapes. Since other social insects also use a hexagon for their larval cells, bees might have just adopted the shape for honey, and kept it because it worked better than the other shapes.


Insect Feeding Signs

Math Skills: graph the number of feeding signs on each leaf on a number line or a bar graph, add all the signs of feeding together and divide by the number of leaves to get the average, if students had different kinds of leaves, categorize the feeding signs by kind of leaf

Grades: 2nd and above

Requirements: leaves from trees on school grounds or your yard, newspaper

Season: late spring, fall

Time: prep - 1 hour, activity 1 - hour

How many leaves are insects munching on?

Spring: In late spring, collect leaves from trees on school grounds or from your yard. Pick five to ten leaves from one or two branches on one kind of tree for each student and place in a folded sheet of newspaper (so you will need 100 to 200 leaves total). In class give each student a folded sheet. Have them spread their leaves out on the newspaper and look for insect feeding signs on each leaf (see below). They should count each instance of insect feeding, and categorize them if they can. If leaves were picked from different trees, that can also be noted.

Fall: In fall, collect fallen leaves from school grounds or from your yard. Grab a small handful for each student and place each handful in a folded sheet of newspaper. In class give each student a folded sheet. Have them spread their leaves out on the newspaper and look for insect feeding signs on each leaf (see below). They should count each instance of insect feeding, and categorize them if they can. If leaves were collected from different trees, that can also be noted.

Insect Feeding Signs: small round holes, scalloping along the edges, pale squiggles on the surface, places where the top or bottom of the leaf has been scraped off leaving a network of small veins, or places where there is nothing left but the big veins.


Leaf Area Estimate

Math Skills: calculating the area of polygons, using ratios of leaf length to area to estimat leaf area from length

Grades: 6th and above

Requirements: leaves from school grounds or other locations, sissors, rulers

Season: spring, fall

Time: 1 hour

What is the area of a leaf? Can the area be estimated from a leaf's length?

Have students pick four or five leaves from trees on school grounds. Be sure this is ok with your facilities staff. If there are no trees that can be sampled, get some from your own yard, or a neighbor's yard or a park.

Students should cut their leaves into sections resembling squares, rectangles or triangles over a sheet of paper. All of the leaf should be cut up. Where possible, combine smaller shapes into larger ones. Carefully trace around the leaf shapes. Discard the bits of leaf. Measure the dimensions of each outline and use the appropriate formula to determine the area of each outline. Add up the areas to get the total area of the leaf. Compare with measurements made by other students.

Extension: Measure the length of the leaf (but not its stem) before cutting it up. After measuring the area, find the ratio between the leaf length and the leaf area. Compare ratios of similar and differently shaped leaves. If ratios for similar shaped leaves are similar, then leaf length can be used to estimat leaf area using the ratio.


Leaf Litter Depth

Math Skills: measuring, categorizing litter depth by tree or kind of tree, graphing litter depths

Grades: 2nd and above

Requirements: natural accumulations of leaf litter in undisturbed wooded areas or under trees, rulers

Season: fall (but can be repeated in the spring to see if depth changes)

Time: 30 minutes outside to collect data, 30 minutes for calcuations

Do different trees have different depths of leaf litter (and possibly different amounts of leaves)?

Spread students out on the edge of the area where measurements will be made. They should step carefully into the leaf litter, kneel down and gently slide the ruler into the leaf litter until it won't go any further. Then they should lean down so one of their eyes is level with where the ruler disappears into the litter and record the measurement.

If space allows, have them move forward two steps and repeat the measurement two or three more times.

If students measured litter under different trees, the measurements can be categorized by tree and compared.

Extension: Delineate a sample area 1 ft/25 cm by 1ft/25 cm. Measure the litter depth in the middle of the sample area (make sure the area was not disturbed before measuring). Collect all the leaves in the sample area and count them. Repeat twice. Calculate the ratio of leaves/sq ft to litter depth for all three samples and average them. Use this to estimate the number of leaves produced by a tree for which you have measured an average litter depth and area covered by leaves.


Soil Particle Distribution

Math: measurement, categorization of layers, comparing layers, fractions, scale drawings

Grades: 2nd and above

Requirements: places to dig up soil on school grounds, trowels for digging, tub or bucket for mixing soil samples, peanut butter jars (or similar) for each student, markers for labeling jars, scoop for measuring (1/2 cup or similar), water, rulers

Season: any time of year the ground is not frozen

Time: 30 minutes to collect soil, 30 minutes to process and set up soil samples, day to let soil settle, 30 minutes to collect data and make drawings

How many kinds of soil (sand, silt and clay) are in the school yard?

In a spot where it is ok to dig, use a trowel to remove any plants from circle about twice the width of your trowel . Shake any soil on the plants into a tub or bucket. Dig out the soil to about the length of your trowel and put it in the tub. Repeat in another place as needed to get enough soil so that each student will have about 1 cup of soil. (If possible, have each student participate in collecting soil samples). (Alternatively, have each student bring a soil sample from home in their jars)

Back in the classroom, mix the soil thorougly. Have each student put 1 cup of soil into their clean, labled jar. Fill jars 3/4 up with water, screw on the lid tightly and shake 3 minutes to mix the water and soil. Then set the jars someplace out of the way to let the soil settle without disturbance. This should be someplace students can take measurements without moving their jars, so the edge of a window sill or counter is a good idea.

Sand particles will settle in a few minutes, silt may take an hour and clay particles will take a day. Have the students check their jars at different times to see if they can see layers settling. After a day, have them measure each layer from the bottom to the top. They should make a scale drawing showing each layer, coloring it in to match the sample color and drawing in dots if they can see particles in a layer.

Categorize and compare the measurements. Calculate the fraction of each kind of soil in the schoolyard soil.

Extension: Collect soil sample from different depths in the school yard (again, get permission!) or from different places to add to your soil data bank.


Tree Bark Patterns (any time of year)

Math Skills: measuring, comparing measurements, graphing measurements

Grades: 3rd and above

Requirements: trees, sheets of white copy paper, dark-colored crayons, a ruler (inches or cm),

Go outside. Pick a tree. Hold the paper against the tree's bark at about chest height so that the long side of the paper wraps around the tree. Rub the crayon over the bark. Use sideways strokes (with the circumference of the tree). Strokes should be hard enough to pick up the ridges in the bark, but not hard enough to tear the paper. Cover most of the paper with strokes. Repeat until the bark ridges are easy to see (ridges will show up as short, dark strokes stacked on top of each other running up and down the paper). NOTE: A tree with really smooth bark won't have ridges. When you are done, write the name of the tree at the top of the paper (oak, maple, walnut, etc.). If you don't know the name assign a number to the tree.

Either in the field or back in the classroom, use the crayon to connect the short strokes of the ridges. Use a ruler to measure the distance between ridges in 5 to 10 places. Record the measurements. Each student should have a set of measurements for their tree.

Depending on the students' ages, record the measurements on a number line, line plot or bar graph, categorize the measurements by tree species, even determine the average.



Tree Height Using Similar Triangles

Math Skills: measuring

Grades: 3rd and above

Requirements: yard stick, meter stick or just a long stick, and a journal and pencil, optional a 30 m/ 100 ft tape measure

Season: any time of year

Time: 15 minutes

How tall is the tree?

Pick a tree to measure. It should be straight and have a main trunk. Position yourself facing the tree, but out from under its branches.

Hold one arm in front of you at shoulder height. Make a fist. Lay the stick on your arm with one end touching your chin. Grasp the stick where it lays on your fist and rotate it so that it is upright (careful not to poke yourself in the nose!). Once upright it should be lined up with the tree, with your fist covering the tree's base. Carefully step backwards until the top of the stick lines up with the top of the tree.

NOTE: If your fist does not line up with the base of the tree, squat, kneel or lay down on the ground so that it does.

Mark where you are standing once the stick is lined up with the tree. Measure the distance between your mark and the tree using a tape measure or by pacing it off. This is the distance to the tree.


Tree Height Using Your Own Height

Math Skills: measuring

Grades: 3rd and above

Requirements: students should know their own height and their pace length, light colored chalk

Season: any time of year

Time: 15 minutes

How tall is the tree?

Measure your own height in inches or cm.

Pick a tree. It should be straight with one main trunk. Position yourself with your back to the tree. Use the chalk to mark a line over your head. Step away and check the mark to make sure it will be visible from a distance. If not, make the mark stronger.

Step back from the tree far enough so you can see the top easily and still see the mark you made. Estimate how many sections of the tree marked by your height could fit into the length of the whole tree (count the part marked by your height). For the top of the tree you may only be able to fit in a fraction of the section. Estimate the fraction.

Multiply the number of sections you can fit in by your height. This is the height of the tree.


Tree Canopy Circumference

Math Skills: measuring, calculating the area of a circle

Grades: 3rd and above

Requirements: students should know their pace length

Season: any time of year

Time: 5 minutes to measure, 10 minutes for calculations

How big is the tree canopy?

Starting at the edge of the tree canopy or drip line. This is where the leaves and branches stop and rain, if it fell would reach the ground instead of being intercepted by leaves.

Walk towards the trunk of the tree, counting paces as you go until you reach the base of the tree. Estimat how many paces would take you to the center of the trunk and add this to the number of paces you walked.

Multiply the number of paces by your pace length to get the radius of the canopy. Use the radius to estimate the area of the circle formed by the canopy.


Tree Trunk Circumferemce

Math Skills: measuring

Grades: 3rd and above

Requirements: tape measure

Season: any time of year

Time: 5 minutes.

Pick a tree. Measure from the base of the tree up 4 1/2 feet. At that height, wrap the tape measure around the tree and measure around the trunk. this is the circumference.





Citizen Science Projects

Backyard Bark Beetles -

Instructions for designing a bark beetle trap and sending samples to the scientists.

Project BudBurst -

Pick a plant and learn how to observe and record stages of budburst in your plant.

E-Butterfly -

Report, organize and access information on butterflies in North America.

Great Backyard Bird Count -

Every February, birders across US count the birds in their backyards

Missouri Honeysuckle Project -


Other Outdoor Math Websites

Honeycomb -

Bee Life Span -

Monarch Math Activities -

The Tiny Seed -

Pumpkin Seeds -

Designing Math Trails for the Elementary School -

Common Core in Dirt -