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Springtime Math




In springtime, you and your students might like to explore math in the great outdoors. Here are some ideas.




Look at a tree and try to estimate its circumference and its diameter, and then figure out how to measure it.

Estimate the height of a tree using shadows
  • Measure the shadow of a tree and measure the shadow of a 12" ruler rising straight up at a 90 degree angle from the ground.
  • Divide the length of the tree's shadow by the length of the ruler's shadow. If, for example, the tree's shadow is 20 times longer than the ruler's shadow, then the tree would be around 20 feet tall.
  • Or, if you compare the ruler's actual length to its shadow's length, then you can assume that the tree's height compared to its shadow will be the same ratio.

About the Author

Wendy Petti is the creator of the award-winning Math Cats Web site, author of Exploring Math with MicroWorlds EX (LCSI, 2005), and a frequent presenter at regional and national math and technology conferences. She teaches grade 4 math at Washington International School.

(These estimates might be inaccurate if the shadow measurements are taken near the middle of the day when the sun is overhead, or if the tree's crown is very broad and dense.)

What is the ratio of a trees height to its circumference? Does it vary for different species of trees or for trees of different ages?

Guess how many blades of grass might be encircled by a large rubber band dropped casually on a playing field, and then get down on your hands and knees and start counting!

Lie on your back and watch a cloud moving past, and try to predict how long it will take to finish passing a treetop... then start a stopwatch!

Measure your shadow at different times of day.

Try to locate the largest and smallest blooms on a flowering bush or in a garden bed, estimate their dimensions, and then measure and compare them.


Children as young as kindergarten can learn to enter data in spreadsheets (or record daily numbers in a list). You can help your students set up a spreadsheet to record data and display it with a simple graph that automatically will reflect changes when you update the data. What sorts of data? Here are just a few ideas from an endless supply of possibilities:

  • daily temperature highs and lows
  • daily changes in pollen count
  • the time of sunrise and sunset each day
  • the daily growth of newly-planted indoor or outdoor plants from seeds or seedlings
  • daily changes in the length of time it takes to run from here to there
  • a comparison of the height of bouncing balls on pavement, dry soil, moist soil, and/or grass


Does your school yard have any space for a new playground? The opportunities for using math abound as students design a possible playground to fit the space.

  • Make a diagram of the playground, drawn to scale (perhaps one foot = one inch or one meter = 5 cm).
  • What mathematical shapes are used?
  • What quantity of wood chips or other cushioning material will be needed around the playground equipment?
  • What will the materials cost?


Your students can be math detectives as your class takes a walk around the school yard or through the neighborhood.

  • Where can you find math in nature? Can you find leaf or petal clusters in groups of 3, 4, 5, 6? Can you find spirals?
  • What geometric shapes can you find, manmade or natural? Keep an eye out for rectangles, circles, triangles, trapezoids, cylinders, cones, rhombi (diamonds), and more.
  • Can you guess the angles formed by branches or leaves? Check your guesses with a protractor or angle wedges that you have measured and cut ahead of time.
  • Draw and label your discoveries, or bring along a digital camera to record the highlights of your hike.
  • Collect leaves from trees, bushes, or flowers. Look for leaves that are symmetrical.
  • Make a record of the leafs shape by placing a piece of paper over it and rubbing it with the side of a crayon, or press the leaf into modeling clay and lift it out carefully.
  • Flip the leaf over and lay it on top of the crayon rubbing or clay imprint. How well does it fit? Give a prize to the most symmetrical leaf!


  • Collect flowers with different numbers of petals. Remove the stems and press the flower heads between several layers of paper towels. It takes about three weeks to press them under heavy books, but you can press them in 1-4 minutes in a microwave oven, sandwiched in paper towels between two stacked plates. Set the microwave on medium and check after each minute. They should feel rigid, not limp.
  • Make a geometric picture frame for each flower head. Depending on the number of petals on the flower, the frame might be in the shape of a square, pentagon, hexagon, or circle. Use a protractor to measure the angles:
    • square -- 90 degrees
    • pentagon --108 degrees
    • hexagon --120 degrees
    • Or use a compass to draw a circle.
  • As an option, draw the shape in several sizes on paper of different colors, cut out, and glue the shapes together to make a nested frame.
  • Glue each flower head into its own geometric frame. Hang them from loops of thread or yarn to turn them into ornaments or a flower mobile.

Additional Resources

Math in Nature
* Fibonacci Numbers and Nature: This award-winning, well-illustrated resource has a wealth of information on how Fibonacci numbers can be found in nature, including the spirals of pinecones and some edible plants.

Spring-Themed Math Lesson Plans
* Spring Time Flowers: A math lesson plan on collecting and graphing data about students favorite flowers
* Egg Hunt Reinforces Math, Language Skills: Use plastic egg halves for math matching activities.
* Springtime Online!: See the math activity for grades 3 and up on identifying and graphing bird species.

Spring-Themed Math Crafts from Math Cats
* Symmetrical Butterflies
* Rotating Shapes: Think math flowers!"

* Spring Into Math and Science (grades K-1)
* Sensational Springtime (grades K-2): Hands-on math and science investigations with a spring theme