Geometry extends way beyond our bodies, our classrooms, and our yards. Geometry is present in the community, too. It does not matter if you live in a busy city or a rural area. There is evidence of geometry all around you!
What do you see when you take a walk through your neighborhood? You might notice roads and sidewalks. There could be fences and walls. Do you have local restaurants and diners in your neighborhood? Are there many trees and fields?
INVESTIGATE!
Why is it important to know the area, perimeter, or volume of a space or object?
cylinder: a solid figure with straight parallel sides shaped into a circle or an oval, like a can of soup or a paper towel roll.
sphere: a round shape that looks like a ball.
hemisphere: half of a sphere.
Most buildings are rectangular prisms, which are 3-D shapes with a rectangle for a base. They are tall structures with six flat faces, just like a cube. It also has right angles like a cube. And it has eight points, or vertices, like a cube!
What is the difference between a cube and a rectangular prism? The length, width, and depth of a rectangular prism are not all equal the way they are in a cube.
Look for more polyhedrons in your neighborhood. Take a stroll to the playground. There are lots of shapes there! Perhaps the slide is a cylinder tube. A bridge is made of rectangular prisms. A half of a sphere might peek out from the top of the playset. A half of a sphere is called a hemisphere.
perimeter: the boundary of a shape.
area: the surface of an object.
PERIMETER AND AREA
In the last chapter, we discussed measuring smaller items, such as tables and doorways. How do we measure large areas? How do we measure an entire park? For that, we need to use perimeter and area!
The perimeter of a shape is when the measurements of all the sides of a shape are added together. For example, let’s say there is a table at your neighborhood park. The top of the table is a rectangle. The two short sides of the rectangle tabletop each measure 40 inches. And the two long sides of the rectangle tabletop each measure 60 inches. Add all the sides up!
40 inches + 40 inches + 60 inches + 60 inches = 200 inches
The perimeter of the table is 200 inches. The perimeter is the total number of inches measured around the shape and added together. This is the length of all the sides of the shape.
square inch: a unit of area that measures length times width, in inches.
The area of the table in the neighborhood park is a little different. To find the area of the tabletop, the length and width must be multiplied. The length of the tabletop is 60 inches. This is the long part of the picnic table. The width of the table is 40 inches. This shows how wide the tabletop is. To find the area of the table, multiply the length and the width.
60 inches x 40 inches = 240 square inches
The area of the table is 240 square inches.
Square inches! Why not use regular inches? The rectangle’s area shows how many square units can be contained in that shape, or how many 1-inch squares could fit onto the tabletop. If you were planning on painting the top of the table, you’d know that you needed 240 square inches of paint to have enough to cover the whole tabletop.
This method would work if you wanted to paint the outside of the houses and other buildings in your neighborhood. Measuring the outside can tell a painter how many cans of paint they need. It can tell a construction worker how many boards they need. Knowing the area will help a window installer get the right amount of glass for windows and doors in a building.
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DID YOU KNOW? The Kansas City Public Library in Missouri has a parking garage that looks like a book shelf! Each book on this pretend shelf is about 25 feet tall and 9 feet wide! |
The pavers who pave the parking lots have to know how much tar is needed. The workers making sidewalks must know how much concrete they need. How wide are the sidewalks? How long are they? This is true for roads as well. And even highways! That is a lot of tar to measure for.
Perimeter and area are important things to know about indoor spaces, too. People need to know the area of a room if they want to buy carpet or put in wooden floors. They need to know the area of each wall so they can buy the right amount of wallpaper.
There are important questions that need to be asked and answered ... even when just measuring that table at the park!
RIDE THE ROADS
The geometric designs of roads are handled by engineers. There are three main parts that make up road design. There is alignment, which is how the road will be made horizontally and what curves the road will have. There is also the profile. The profile is how high or low a road goes. Last, there is the cross section. This allows engineers to understand where the drains should be, how wide bike lanes need to be, and how many cars can go on the road. Roads must be constructed in a safe way for neighborhoods everywhere. Engineers help!
engineer: someone who uses science, math, and creativity to design and build things.
volume: the amount of space inside a shape.
cubic feet: a unit of volume that measures length times width times depth (or height), in feet.
THE COMMUNITY POOL NEEDS WATER!
If there was a community pool at your local recreation center, the workers at the community pool would need to keep it filled with water. A truck might come and fill up the pool the first time. How do the workers know how much water should go in the pool? They need to find out the volume of the pool to know how much water to bring.
The pool has length, width, and depth (or height). Maybe it is 4 feet deep. The length of the sides are 10 feet each. The width is 9 feet on each of the shorter sides. To find the volume, multiply the length times the width times the depth.
4 feet x 10 feet x 9 feet = 360 cubic feet
DESIGN A SIDEWALK
Sidewalk design is a job for an engineer! It’s important that engineers plan safe sidewalks for people who want to walk, bike ride, and do other activities on sidewalks. When a sidewalk is designed, engineers decide how long and wide it will be. They also consider the material they will use, such as concrete. And they want to be sure the sidewalks are not too steep, or else they will be hard to climb!
Watch a video of artists using sidewalks as a place to make art!
KEYWORD PROMPTS
3D sidewalk chalk art 
This is the volume of the pool! That is the total amount of water the pool can hold. And it is measured in cubic feet, which means feet cubed, because the length, width, and depth make it 3-D.
What happens on a really hot day when everyone in your town goes swimming at the pool? The water rises! What happens if too many people go into the pool at once? The water will overflow!
Your body has volume, too. Workers can never fill the community pool all the way to the tippy top and then have 50 people hop in, or there will be a big flood of water leaving the pool! When considering how much water to put in the pool, workers keep the volume of bodies in mind so that flood doesn’t happen.
glacier: a slowly moving mass of ice and snow.
A community pool can hold a large volume of water, but the entire planet can hold even more. The volume of water on Earth is tremendous! The surface of Earth is about 71 percent covered in water. The oceans hold about 97 percent of that water. Water is also in the form of a gas in the air, in the form of liquid in rivers and lakes, and in the form of ice in glaciers. The water volume of all the oceans, seas, and bays on Earth is measured in cubic miles—321,000,000 cubic miles! There is also water in the soil. On Earth, the water volume of soil moisture is 3,959 cubic miles.
Now that you know how to spot examples of geometry in your neighborhood, let’s venture farther afield and see what shapes and patterns we can find in nature!
CONSIDER AND DISCUSS
It’s time to consider and discuss: Why is it important to know the area, perimeter, or volume of a space or object?
CIRCLE IT!
Circles are another shape you’ll find in the neighborhood! Circles are special, because the distance between the center point and any point on the circle is the same—this is called the radius. If you drew a straight line from a point on the circle through the center point to a point on the other side of the circle, you’d be drawing the diameter. Circumference is the measure of the circle all the way around. And pi, or π, is the circumference divided by the diameter of the circle, which is always about 3.14, no matter how big or small the circle is!
RUB A DUB DUB ... WALL?
SUPPLIES
* tracing paper
* crayons with the outer wrapping removed or colored chalk
Rubbings can be made of carvings that we may find in the community. There are markers along streets where important events have occurred. There are engravings in walls and benches and on plaques. What do you see on manhole covers? Get ready to make a rubbing!
•What are these surfaces made of?
•What patterns can you find?
•Can you spot geometric shapes?
•Do certain surfaces use the same patterns?
•Are all sidewalks the same?
•Are all walls the same?
•How are they different?
TRY THIS! Create your own patterns to rub. Using a small amount of clay, you can create patterns on cardboard. Try rolling the clay into long strands or small balls. What other shapes can you make that will create a pattern? Compare your rubbing of the homemade pattern to the rubbings you made of other surfaces. How are they different?
SUPPLIES
* math journal
* large piece of graph paper
* markers, crayons, pencils
* ruler
Mapmakers design maps for books, as well as for phone apps and the Internet. They show the world where the streets and buildings—and even our homes—are! You can be a mapmaker, too, with a few supplies and observant eyes.
1Make a list of things in your neighborhood! What are the parts of your neighborhood? What buildings are in your neighborhood? Are there parks, woods, and highways?
2Once you have a complete list, assign a number of graph paper blocks to each thing according to how big it is. A school might be a nine while a front yard might be a two.
3Start drawing streets, roads, walkways, and buildings. Don’t forget your own home! Include fields, woods, and streams as much as you can. Think about the number of graphing blocks that you first decided on for each building. You might find you change your number as you draw! How are the streets angled to each other? Where do the houses and other buildings go? How much distance is between each building?
4When your map is done, find the parallel and perpendicular lines. Go over these in different colors.
5What shapes can you find? Can you find different polygons and polyhedrons? Color them in different colors. What is the most popular shape in your neighborhood?
TRY THIS! Make another map, but this time, make it of your dream city or town. What buildings do you wish were along the streets and roads? The map can be as fantastical as you want!
MODEL MAKERS
Architects are people who design buildings and structures. Architects need to use models. These small mini-buildings are versions of the big buildings they plan to build. By using a model, architects can show others what their design is and how they plan to build a building. One of the smallest building models was made with just one toothpick! It was a tiny model of the Empire State Building. It holds the Guinness World Record as the “smallest toothpick sculpture.” Have you made models before? What are some important things to remember when making a model?
SUPPLIES
* magnifying glass
* binoculars
* paper
* clipboard
* pencil
Your eyes can be enhanced with magnifying glasses and binoculars. They are extensions of our sight. We can see up close. We can see far away. We can be detectives! It is time to do some investigating.
1Create a checklist of five different shapes. Draw each one.
2Observe your neighborhood from the inside and outside of buildings. Tally how many you can find of each shape. Do you see objects with many shapes? Be sure to mark all of them! Write down your list of objects under each shape name.
3Look closely at small objects, even tiny rocks on the sidewalk. Look to the tippy top of buildings with binoculars to spot special structures. You may see a bell house or a weathervane!
TRY THIS! Double up your list! Be on the hunt for both 2-D and 3-D shapes.
THE NEIGHBORHOOD GROCERY STORE
Talk about shapes! They are in every aisle of the grocery store. Oranges and honeydew melons—spheres! Boxes of pasta are rectangular prisms. Even the shelves are long, long rectangles. The buttons on the cashiers’ registers are little cubes. What other shapes can you find? What tools would you use to measure these shapes?
SUPPLIES
* pencil
* graph paper
* ruler
* optional markers and crayons
Take a dip into your own pool, designed and planned by you! Planning this type of project is common. Many city planners, homeowners, building designers, property developers, and construction workers plan such projects.
1Imagine you want to put a rectangular pool in your community or behind your home. Start a diagram using one or two squares per foot.
2How long and wide will your pool be? How deep? Depth and height can be the same thing, but one measures down while the other measures up.
3Calculate length x width x height (L x W x H). That is the volume of how much water will be needed to fill the pool.
4Now, measure the perimeter of the pool. Add the four sides together to find it.
5Decorate your diagram with color if you choose!
TRY THIS! Add a hot tub or jacuzzi on the side of the pool. What is the volume? What is the perimeter? Add these smaller pools of water to your diagram. What other bodies of water can you add to your diagram?
SUPPLIES
* math journal
* pencil
* 12-inch ruler
* calculator
Volume is not just found in pools of water. Measurements of length, width, and height or depth can be found all over the neighborhood!
1Find 3-D objects in your neighborhood that you can measure, such as a mailbox. Make a chart in your math journal with columns for object, length, width, height/depth, and volume.
2Measure the lengths, the widths, and the heights or depths of the objects you find.
3Find the volumes of the objects by multiplying length x width x height/depth. If the object is a triangular prism, which is a 3-D shape with a triangle base, you will multiply half of the bottom side times the height.
4What objects have the largest volume? What objects have the smallest volume? What do you notice about the size of an object and its volume?
TRY THIS! Use a tape measure or yardstick instead of a 12-inch ruler. This will give you many more inches to work with! You can measure larger objects in your neighborhood, such as a chalkboard sign in front of a restaurant. You can calculate the volumes of these objects and discover some larger numbers!
