How do you know what time it is or what the weather will be? Can you figure out how old a tree is by looking at it? In this badge, you’ll do all of these things! Math can be used to tell us all kinds of things about nature, from how tall or old a tree is to the weather, season, or time.

**Steps**

- Tell time with nature
- Track the weather
- Explore the circumference of trees
- Search for shadows
- Find the area and perimeter of plants

**Purpose**

When I've earned this badge, I'll know how to use math to tell time, predict the weather, and learn about trees. I'll know how to measure shadows, perimeter, and area.

This badge is part of the Math in Nature series of three badges.

### Step 1: Tell time with nature[]

Clocks help us know what time it is. We have clocks in our homes, cars, and public buildings, like schools and airports. Many of these are modern clocks that need electricity to work. Other clocks use water, sand, weights and springs, or even the sun and moon. Sundials are one of the oldest tools used to tell time. They’re a circle with each hour of the day marked. As the sun travels across the daytime sky, a shadow is cast which marks the time. The shadow is like the hand on the clock.

Most sundials are made out of stone, metal, or pottery. Cultures all over the world have used sundials to tell time. The Maya and Inca peoples had buildings with sundial features. Like people from long ago, you can make a sundial. You can even measure the passage of time with just your hands!

Stonehenge was built about 5,000 years ago in what is now England. It may have been used to celebrate the longest and shortest days of the year.

Choices—do one:

- Make a sundial. First, draw a straight line down the center of a paper plate and another to create quadrants, or four equal parts of the circle. Write, 3, 6, 9, and 12 at the top of the lines, like the face of a clock, and add in the remaining numbers. Then poke a hole in the center for a straw or chopstick so it’s standing up. Then find a sunny area or flashlight to test your sundial. Use a clock to check the actual time and rotate your sundial so the shadow matches the current time. Then wait a few minutes to observe how the shadow moves. What is the new time on your sundial and the actual time? How accurate is your sundial?
- Make a life-sized sundial. If you have a sunny day, a friend, some rocks, and ribbon, you can make a sundial with people! First, place a rock in the center of an imaginary circle on the ground. Stand by it and cast a shadow. Have your partner extend a piece of ribbon from your foot to the end of your shadow, cut it, and pin it down with another rock. Check the actual time and write it down. Repeat several times throughout the day. Each time, look at the shadow: is it long or short? Wide or narrow? How did it move or change? How does the time of day affect the shadow? Can you use your sundial to tell time without a clock?
- Use the sun and your hands to tell time. You can measure how much time is left before the sun goes down with just your hands and a clear view of the sun, without any trees or tall objects blocking the horizon (be careful when looking at the sun!). Put your arms out in front of you with your palms facing in. Line your index finger up to the bottom of the sun. If your pinky is below the horizon, the sun will set within the hour. If you still have space, place the index finger from your other hand below your pinky. Continue moving and counting how many times you move your hands down until you reach the horizon. That’s about the number of daylight hours until the sun sets.

For more fun: Count the number of fingers between the bottom of the sun and the horizon. How many did you count? Each finger is about 15 minutes of daylight. How much time is left before the sun sets?

### Step 2: Track the weather[]

Have you ever forgotten to wear a coat on a rainy day? Or gone outside without boots when it’s snowing? Knowing what the weather is like can help you dress for the outdoors. This can help whether you’re walking to school or wondering if it’s a good day for a hike! Meteorologists are scientists who study weather. They use tools, or instruments, to help them measure, track, and predict the weather.

Choices—do one:

- Make your own weather station. A weather station is a collection of instruments to track the weather. Set up your own weather station with a jar to collect rainwater. Add streamers and windmills to see how fast and in what direction the wind blows. Then track what you see in a weather journal. What do you observe each day? What do you think the weather will be later in the day or tomorrow? Then, compare the weather conditions you tracked with an app, a newspaper, or a TV or online weather report.
- Track nature’s clues. From animals and plants to changing seasons and even coming storms, you can track the weather just by looking around. Search for changes in plants, how animals act, or what is happening in the sky. Write down and tally what you see. Research what each clue might mean, make a guess of your own, and then wait to see what happens with the weather. Were you right?
- Build a barometer. A barometer traps air in a container and measures the outside air pressure pushing against it. If the air pressure outside and inside is different, the gauge will move up (if the pressure is high) or down (if the air pressure is low). High air pressure means the weather will be clear and sunny. Low air pressure means it will be rainy or snowy. To make your own, stretch a balloon over the mouth of a jar (like the top of a drum) and secure it with a rubber band. Tape a straw to the center of the balloon. Stand a piece of cardboard next to it and mark the spot where the straw points. This is your barometer’s home position. It’s neutral—it’s not high or low. Then draw a picture of sunshine and good weather above the neutral line and rain, snow, and storms below. Place your barometer in a sheltered outdoor space. Wait a minute or two. What happens? Mark your gauge and write the date, time, and weather.

### Step 3: Explore the circumference of trees[]

Trees are nature’s superheroes! They take out pollution and carbon dioxide from the air we breathe and release oxygen. They keep our drinking water clean and protect our homes from the heat and cold. They protect soil and provide us fruit and nuts. They lower our stress, make us happy, and create space for wildlife to live, eat, and play.

So what can a tree tell you about itself? Well, by measuring just around the outside of a tree trunk, you can find out a lot about the tree. Circumference is the distance around the outside edge of a circle. For the most accurate measurement, wrap a string or tape measure around the tree about 4.5 feet from the ground.

Choices—do one:

- Measure circumference to find the age of a tree. You can find out how old a tree was by looking at the number of rings in its trunk. But if the tree is still alive, you can estimate its age by measuring its circumference in inches. If the tree’s circumference in inches is its approximate age in years, how old is the tree? Measure the circumference and estimate the age of other trees in the area.
- Measure circumference to understand tree health. Sometimes you can look at a tree and know it isn’t healthy, like if it’s missing leaves or even rotting. The tree’s trunk circumference can also tell you how healthy a tree is—a big trunk can more easily move water and nutrients than a small trunk. To find out how healthy a tree is, measure its circumference in inches. Then, measure the tree pit or area where the roots grow. Most trees need about 5x5 feet to properly grow. How big is the tree trunk? How big is the tree pit? Measure different trees to compare how healthy they are.
- Measure circumference to find the amount of carbon stored by a tree. How much carbon a tree can store depends on its size, age, and species. Over the course of its life, a single tree can capture and store one ton of carbon dioxide. This helps clean our air! To find out how much carbon a tree has stored, measure the circumference of its trunk in centimeters. Then use the table to convert the circumference to dry weight in kilograms. Divide this by 2 to find the amount of carbon stored by the tree. Measure different trees to explore which trees have stored the most carbon.

### Step 4: Search for shadows[]

Shadows are mysterious. They move, change, and disappear. A shadow is created, or cast, when something blocks light. If you understand how shadows change with the sun, you can tell time or figure out how tall a tree or an object is. A shadow’s size is similar to the size of the actual person or object. It’s a proportion. A proportion is the relationship between the size, number, or amount of two things. A shadow and the object that casts it are proportional.

Choices—do one:

- Find a tree’s height using shadows. On a sunny day, you can use a tree’s shadow and proportions to calculate its height. Choose a tree to measure that is on level ground—ground that’s flat, not on a hill or slope. Then stand near the tree and have a partner measure your height and shadow height in inches. Then measure the tree’s shadow in inches. Use proportions to find the approximate height of the tree in inches.
- Go on a shadow adventure. Go outside and look for shadows. Notice where the light is coming from and how big each shadow is. Can you change its size or shape? Try to block or change the light and notice what happens. Trace and measure your own shadow. Trace and measure shadows you see. How do they compare to one another? If you can measure the objects, are they proportional to their shadows? If you can’t measure the height of something (like a tree) you can find its approximate height with proportions.
- Measure the power of shadows. When the sun moves, a shadow’s size changes. It disappears completely at noon. Make shadow puppets to discover the relationship between the light source and size of the shadow. Use your hands or cast shadows with your body. Measure both the shadow and you. Do they have the same proportion? What light position casts the longest shadow? Which casts a short one without disappearing? Does the shadow keep its shape or get distorted? Try other objects and light positions.

### Step 5: Find the area and perimeter of plants[]

Plants are lifesavers! They turn the sun’s energy into food, fresh air, and other useful things. When they make food for themselves with their leaves, they make fresh air for us. They also provide food in gardens, farms, and orchards. So, how much fresh air can a plant produce? And how much space do you need for plants to grow in a garden?

You can find the answer to these questions using area and perimeter. Perimeter is the distance around the outside of a two-dimensional (2D) object. A 2D object is flat, like a leaf or sheet of paper. You can also find the area, or space inside, of a flat object. The area of irregular shapes, or shapes without equal sides or angles, like a leaf, can be hard to calculate, but you can estimate and guess a number close to the correct or actual answer using what you know.

Choices—do one:

- Find the perimeter and area of leaves. First, trace around a leaf on graph paper. Then place some yarn along the outline and cut it to that length. Measure the yarn. How long is it? That’s the leaf’s perimeter! To calculate the area, count and write down the number of full squares inside the leaf outline. Then, count each partial square that is at least half covered by the leaf. Do not count the squares with the stem. Add the two numbers together to estimate the area of your leaf. Then measure other leaves. Which has the largest area?
- Find the perimeter and area to plan a garden. Plants need different amounts of space and sunlight to grow. Gardeners and farmers plan their plantings carefully to make the most of their space. First, draw the shape of your garden on graph paper. Then imagine you want to add a fence. Can you find the garden’s perimeter and area? Then decide what to grow. How much area does each plant need? Add in your plants. How many of each can you grow? Add in benches, paths, and anything else. Make sure to find the area and perimeter of each plant or object you add.
- Find the perimeter and area of a natural landscape. How big is the nearby lake? How much tree canopy is there in the woods? How big is the climbing structure in the park? There’s no tape measure big enough to check! Instead, use a map or aerial photos (pictures taken from above) to measure perimeter and area. Trace the outline of the area you want to measure with yarn and cut it to that length. Measure the yarn and use the scale to calculate the perimeter. For area, use the scale to create a grid on the landscape. Then, count and write down the number of full squares inside the outline. Next, count each partial square that is at least half covered. Add the two numbers together to estimate the area.

### Words to Know (Glossary)[]

Anemometer: A scientific instrument used to measure wind speed.

Area: The space inside of a flat shape.

Barometer: A scientific instrument used to measure the air pressure.

Circumference: The distance around the outside edge of a circle.

Estimate: To guess a number close to the correct or actual answer using what you know.

Gauge: A scientific instrument that measures changes in amounts.

Instruments: Tools used by scientists during their research.

Irregular shapes: Shapes without equal sides or angles.

Level ground: Flat area that’s not on a hill or slope.

Line of symmetry: An imaginary line where something could be folded and both sides would be reflections.

Meteorologist: A scientist who studies and forecasts the weather.

Neutral: Not high or low.

Perimeter: The distance around the outside of a two- or three-dimensional object.

Proportion: The relationship between the size, number, or amount of two things.

Quadrant: One of four equal parts created when a horizontal and vertical line cross.

Shadow: The dark shape created, or cast, when something blocks light.

Standard units of measure: A unit of measure that everyone agrees on and use to measure things, like inches, feet, and degrees Fahrenheit.

Sundial: An instrument that tells the time using the sun and shadows.

Thermometer: An instrument that measures the temperature or how hot or cold it is.

Tree pit: The area around the tree where roots can grow.

Weather station: A collection of instruments to track the weather.