Can you imagine the perfect hike and campout? Beautiful hiking trails, interesting sights, a cozy campground, and a delicious meal? Enjoying time in nature often requires planning. You might decide where you'll go, how long you'll be gone for, and what you'll bring. In this badge, you'll use math to help you plan and organize a hike and campout. You'll think about all these things as you get ready for your hiking adventure.

When I've earned this badge, I'll know about different types of maps. I'll know how to calculate distance, pace, elevation changes, and area.

**Words To Know**

- Adjacent: Touching or next to.
- Area: The space inside a flat shape, found by multiplying length by width. Contour interval: The distance, or elevation change, between each contour line on a topographic map.
- Contour line: A line on a topographic map that shows elevation change. Coordinate plane: A graph with x- and y-axes.
- Decline: Sloping down.
- Elevation: The height above sea level. Incline: Sloping up.
- Index line: A thick contour line on a topographic map, typically every fifth line, that notes the elevation.
- Sea level: Zero elevation, or the point where the ocean meets land.
- Segment: A part of a whole. Terrain: The physical features of a piece of land.
- Topographic map: A map that shows a terrain's elevation, or height, above sea level.
- Walking pace: How fast people usually walk.
- x-axis: The horizontal, or side-to-side, part of a graph.
- y-axis: The vertical, or up-and-down, part of a graph.

Types of Hikes

A loop hike is when you never retrace your steps but still end up right back where you started. The route is a circle.An out-and-back hike is when you hike to a point, turn around, and hike back on the same trail. When planning an out-and-back hike, count each segment twice.A lollipop hike is an out-and-back hike with a loop at the end of the "out" segment. You'd hike out on a trail, do a loop, and then hike back.A point-to-point or through hike is like out-and-back, except you only go one way. Someone would pick you up at the end.

## Step 1: Find your hiking pace[]

Animals walk and run at different speeds. A tortoise moves along slowly. A cheetah races past the other animals. What are the benefits and drawbacks of moving fast? What about the benefits and drawbacks of moving slow?

As animals, humans also move at different paces. A person's walking pace is how fast they usually walk. It takes some people about 5 minutes to walk a quarter mile, but everyone is different.

When you're planning a hike, it can be helpful to figure out your pace. With others, this can also help your group to move at a speed that's comfortable for everyone.

**Choices-do one:**

Calculate your pace. Find somewhere safe to walk. Then start a stopwatch and move a quarter mile along the route at your usual pace. Stop the stopwatch: how long did it take you to go a quarter mile? Multiply that time by 4 to find how long it would take for you to go a mile. If there are 60 minutes in an hour, how many miles could you go in 1 hour? How many could you go in 3 hours?

OR

Compare human and animal paces. Imagine you're hosting the first all-species Olympics, where animals of all kinds can show off their speed! Choose some favorite animals and find out their normal pace, walking, running, or moving in any way. How fast is an elephant? What about a snail or a leopard? Compare what you find to the average walking pace for a human. You may find that some animals are very fast for short distances. Others can maintain a good speed for a longer time. If you had a marathon, who would win? The tortoise or the hare? What about a 400-meter sprint?

OR

Calculate and compare different paces. Some people run on hiking trails. How long would it take if you wanted to skip or walk backwards? Find somewhere safe to find out! First, find your normal pace. Start a stopwatch and move a quarter mile along the route. Stop the stopwatch: How long did it take you? Do it again, this time running, skipping, or doing something else. Repeat as many times as you want in as many different ways. Then multiply each time by 4 to find your pace for a mile. If there are 60 minutes in an hour, how many miles could you go moving each way? How many miles could you go in 3 hours?

## Step 2: Choose a hiking trail[]

Choosing where to go may be the most important part of planning your hiking adventure. Maps can help as they show all different kinds of information, from the weather to the location of forests and the height of mountains.

If you know where you want to explore, you can usually get a map of trails to help plan your trip. Hiking maps show landmarks and may even show how difficult a hike might be. They show different trails and the lengths of each segment. A segment is a part of a whole.

**Choices-do one:**

Choose a trail on a sample map. Look at the sample map on page 5. Identify landmarks to visit. Can you find a route that's about the same number of miles long as the distance you can move in 3 hours? Look for different types of hikes, like a loop, out-and-back, lollipop, or point-to-point hike.

OR

Choose a trail on a map of your local area. Hiking near home lets you see your local area in a new way. You don't have to be in the woods to go for a hike! Use maps of your neighborhood and identify local landmarks or places to visit. Then investigate different routes. Can you find a route that's about the same number of miles long as the distance you can move in 3 hours? Then you can share your map with others and go on a hike!

OR

Choose a trail on any map. If you could go hiking anywhere in the world, where would you go? A rain forest? A desert canyon? The Andes mountains? Find a hiking map from anywhere in the world. Identify and learn about important cultural, natural, or historical landmarks to visit. Then investigate different routes. Can you find a route that's about the same number of miles long as the distance you can move in 3 hours?

How To Choose a Hiking Trail

Identify any landmarks on the map. What do you want to see on your hike? How much time do you want to spend hiking?Choose a starting point and find a route that is about the same number of miles long as the distance you move at your normal pace in that time. What will you visit? What direction will you go?Add the lengths of adjacent, or touching, trail segments to calculate the hike's length. 4. Once you find a hike that's the same distance as you can hike in the time, trace it with a marker.

## Step 3: Find changes in elevation on a map[]

Do you hike faster going uphill or down? What if the trail is rocky? The type of terrain you're on affects how fast you move. Terrain is the physical features of a piece of land, like flat, steep, rocky, rolling, or wooded.

A topographic map shows the terrain's elevation. Elevation is how high a place is above sea level. Sea level is where the ocean meets land. Mountains have a high elevation. Beaches have a low elevation. A topographic map includes landmarks, like a regular map, but also has little lines called contour lines that each show elevation. The closer the lines are together, the steeper the elevation changes. The wider the lines are apart, the flatter the land. One side of the line is uphill; the other side of the line is downhill.

Elevation changes are important to know about when planning a trip. If your trail is very steep, it may take longer to hike it. Elevation changes can also cause changes in temperature and wind-both things you'd want to know!

**Choices-do one:**

Calculate elevation changes on a sample topographic map. Choose three points on the map on page 7. Write down each point's elevation and add them to the coordinate plane. Then, find the elevation change between each point.

OR

Calculate elevation changes on a topographic map of your area. Find a topographic map with the route you chose in Step 2. Choose three points, find their elevations, graph them on a coordinate plane, and find the elevation change between each point.

OR

Calculate elevation changes on any topographic map. Find a topographic map of anywhere in the world. Where will you go? What will you see? This could be the same place as Step 2 or somewhere new! Choose three points on the map and find their elevations. Graph them on a coordinate plane. Find the elevation change between each point.

For more fun: Calculate your pace moving from different elevations.

## Step 4: Decide how much food to bring[]

Girl Scouts make sure to always be prepared! It's a good idea to take food with you, even on a short hike.

Foods like trail mix can help keep you energized on the hike. Trail mix is a combination of dried fruits, seeds, nuts, cereal, and anything else. If you're hiking all day, you may want lunch. And if you're camping, you might want a special treat like s'mores.

**Choices-do one:**

Make a snack for your hike. Use a trail mix recipe to figure out how many batches you'll need for the whole troop. Look at how many servings the recipe makes. Then calculate how much of each ingredient you'll need to feed everyone joining your adventure!

OR

Pack lunch. For a full day of hiking, you'll need lunch. How about a sandwich and some fruit? How many loaves of bread will you need? List all the ingredients for your sandwiches. How much will you need of each ingredient? Now think about the fruit. If you choose fruit that doesn't come in an easy, single serving format like an apple, how much will you need? If you want to include something else in your menu, calculate how much of it you will need for everyone.

OR

Enjoy your trip with a treat. As you relax around a campfire, you may want a yummy treat for yourself and the troop. Choose a recipe. How many servings does the recipe make? Figure out how many batches of the recipe and how much of each ingredient you'll need to make one portion for each person.

Important note:Check for any food allergies and avoid those ingredients for all activity choices.For more fun:Make the snack, lunch, or treat with your troop and enjoy!

## Step 5: Pack for your adventure[]

If you were going camping, you'd need a tent and sleeping bags. The number of tents would depend on how big they were and how many people they could fit. Each person would need a sleeping bag. You'd also need supplies like food, water, and flashlights.

You can figure out how big your campsite needs to be by calculating the area. Area is the space inside of a flat object. You can calculate the area by multiplying length and width.

Area = length x width

To make sure there's enough space in your bags or vehicle, you can find their volume. Volume is the amount of space something takes up in three dimensions. You can calculate the volume by multiplying length and width and height.

Volume = length x width x height

**Choices-do one:**

Pack your equipment. If you're carrying supplies, will your backpacks be big enough to fit them all? Calculate the volume of your backpack and gear to find out. First, measure and calculate the volume of your backpack. Then find the volume of each supply in the same unit of measure. Will everything fit? Pack it to see if your calculations are correct.

OR

Load your vehicle. If you're riding in a vehicle to the start of your adventure, find how many vehicles you'll need to transport people. Then, calculate the volume of each vehicle's trunk to see how much cargo it can hold. First, measure and calculate the trunk's volume. Then calculate the volume of each supply in the same unit of measure. Will all the equipment fit?

OR

Plan your campsite. Figure out how big your campsite needs to be by calculating the area of your tents and sleeping bags. How many people will fit in a tent? Measure and calculate the area of the bottom of a tent. Then find the area of a sleeping bag and pillow in the same unit of measure. Use graph paper to plan your campsite. How many tents will you need? Draw, cut out, and place rectangles to see how many tents and sleeping bags fit. Then build your campsite by pitching your tent (or outline it with masking tape), unrolling your sleeping bags (or towels!), and moving them to see if your plan works!

How Much Water Will You Need?

To stay hydrated, it's recommended that each person drink 2 cups of water every hour during average weather conditions. Can you calculate how much water you'll need for your hike and how heavy it will be? If the hike is planned for three hours...

How many cups of water will each person need?How many ounces of water will each person need?How many quarts of water would each person need?How much would each person's water weigh in pounds?If you have a water bottle, would it hold enough water for your hike? How long would it be before you ran out of water?

Tip: If the water bottle doesn't say how many ounces or cups it can hold, pour water in it from a measuring cup.