After a long day at school, you arrive home and toss your backpack by your desk. Your brain needs a break! Whether you head outside or stay in for some quiet time, it’s always a great idea to recharge at the end of a school day.
Even as your brain is focused on playing games or eating snacks, you can still spot geometry all around you! Lines, shapes, and angles are everywhere in your house. They are inside and outside your home.
INVESTIGATE!
What might your house look like if the builder hadn’t measured anything? Why is it important to measure the sizes of things?
standard measurement: the units of measurement used in the United States, such as inches and feet, ounces and pounds.
metric: the units of measurement based on the number 10. The metric system includes centimeters and meters, grams and kilograms.
You can find geometry on the roof, in the elevator, and in the staircases! Geometry is all over the backyard, the patio, and the porch. It is in flowers, tree rings, and leaves. Take a stroll outside and look around—what do you see?
HOW BIG IS BIG?
Look around your living room or bedroom. What is the biggest book in the room? What is the tallest piece of furniture? What is the heaviest object? To measure how big or long or tall or heavy something is, we use tools of measurement.
One tool of measurement is the ruler. The units of measure on a ruler can be standard measurement or metric. Standard measurement is used only in the United States, Burma, and Liberia. Metric measurement is used everywhere else!
TREEHOUSE LIVING
Today, some people live in treehouses that have running water, kitchens, and even toilets! Fifty years ago in the South Pacific, a tribe was discovered in New Guinea that had lived in the canopy of the forest trees for decades. This tribe is called Korowai. What kinds of shapes do you think they see from up there?
dimension: any line of a shape that can be measured.
Metric measurement is based on the number 10. Standard measurement is based on objects people were familiar with in past cultures.
When you are measuring something small, a ruler is a useful tool. Many rulers measure in inches (standard measurement) and centimeters (metric measurement). These units of measurement give the length of an object.
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DID YOU KNOW? Length, width, and height or depth are different dimensions of a shape. Length and width measure two different dimensions on a flat surface. Height or depth measure how high something is or how deep it is, giving an object three dimensions. |
Everything you see can be measured! Imagine walking through a door. What shape is the door? What is the height of the door? How wide is the door? The study of geometry includes learning how to measure different shapes!
The doorway is a space you must walk through to get outside. Even that rectangular space has dimensions. Dimensions are another word for measurements. A dimension is how tall something is, or its height. Dimensions also include the length and width, or how long and wide something is.
layout: the way the parts of something are arranged.
How tall is the door or the doorway? If you don’t have a measuring tape and you know how tall you are or how long your arms are, you can use your body to measure. Reach your arms out perpendicular to the floor or stretch your arm up high. Arms can serve as good tools to make estimates for dimensions.
Estimates are good guesses. When you estimate the length of something, you compare the length of something you know with what you want to measure. This way, you can get a good idea of what the measurement is without using any other tool.
You can check to see if your estimate is correct by using a tool. Carpenters and builders use tape measures. This tool is like a long ruler that rolls up and fits into a small holder. It can be placed on a belt or in a toolbox. Have you ever used a tape measure?
INSIDER DESIGN
Interior designers are people who design rooms to make them look a certain way and feel inviting. They decide what colors to paint the walls, what fabrics will be used in the curtains, and where the furniture will go. To make the spaces feel comfortable, they work to understand the layout of the house. It is important for interior designers to have the measurements of all the rooms and what will go in them so everything can fit! Designers also use geometry to figure out what patterns are best for wallpaper, blankets, and pillows. Designers consider shapes, colors, and different textures to make a room look and feel a certain way.
weight: the measure of the force of gravity on an object.
gravity: a force that pulls objects toward each other, and all objects to the earth.
Once you’ve done your estimating and measuring of the door, you can walk through and find more things to measure out on your porch and in the yard. Is there a set of chairs? Is there a table? What are the shapes you see?
HEAVY LIFTING!
Another thing to measure is the weight of an object. Look around outside for something that has weight. Find a tiny rock. Can you feel its weight in your hand? Find a larger item, such as a baseball bat or a small shovel. Is this heavier?
We can measure weight with a measurement tool called a scale. In standard measurement, we measure in pounds. If you place a book on a scale, it can be weighed in pounds. In the metric system, the book is measured in kilograms. These two units of measurement come in handy when we weigh objects.
Gravity is different on other planets, so your weight would be different, too. Check out what your weight would be around the solar system at this website!
KEYWORD PROMPTS
Exploratorium weight 
For decades, the scale has been a tool used for measurement. What was used before the modern scale? How did people weigh objects? One of the earliest known scales used a rod and two pans. A rod had some kind of string attached on each end. A pan was attached to each string. The object to be weighed was placed in one pan. Rocks with known weights were placed in the other pan until the two sides balanced. This is how people used to weigh things!
Measuring the dimensions of space and shapes is an important skill to have. Knowing an object’s measurements means you can compare that object to others to find out more information. Let’s take a look how!
MORE TYPES OF MEASURING
Say you are eating a slice of pizza at the picnic table in your backyard. Then, a friend comes to visit. You offer them a slice of pizza. You can eat together!
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DID YOU KNOW? Weight is caused by gravity. Gravity is what pulls us and all objects toward the earth. This pull is what gives us a weight. How much do you weigh? |
The two of you compare your pizza slices. What are the chances that the slices have the exact same measurements?
congruent: when two shapes are the same as each other.
Not likely! Pizza slices might look similar, but when you measure them, you find they are slightly different. If they were exactly the same, with the same lengths of the sides and the same triangular shape, then the two slices of pizza would be called congruent.
You might have congruent slices if the pizza came from the same restaurant. You might have congruent slices if the slices were cut in the same way. Most of the time, though, even when the pizza comes in the same box and is part of the same pie, each slice is a little different.
What about the picnic table? Are there any parts of the table that are congruent? The tabletop has two lengths, the length along the top and the length along the bottom. These two lengths are congruent. The two widths are also congruent. Can you find other objects in your yard that are congruent?
equivalent: when the measurements of different shapes are the same.
When building something, such as a pool or a building, it is important to have equivalent, or equal, measurements. This means the height on one side of the deep end of the pool must be equivalent to the height on the other side of the deep end of the pool. That way, the pool won’t be lopsided!
Equivalent parts are especially important when building a home. The floors must have equivalent-sized wooden boards. The beams that hold the home up must be equivalent. The walls must be equivalent, too, or else you’ll have to duck in certain corners! The roof must have equivalent sides as well. What would happen to a building that was not constructed with equivalent pieces of wood and steel?
RECYCLING STEEL
Almost 69 percent of all steel in North America is recycled every year. Steel has magnetic properties that make it the easiest material to separate from other waste. Every year, recycling steel saves enough energy to power almost 18 million households. Steel is found in everyday products we use. For example, steel latches on car doors help keep the doors latched during an accident. And the safety buckles for seat belts are made with steel!
“Congruent” and “equivalent” are geometry terms that often get confused. Think of it like this: We use the word congruent when we talk about the shape of an object. If two shapes can be placed exactly over one another without any extra sticking out, they are congruent. You can flip them or rotate them to see. If the measurements of two shapes are exactly the same, those shapes are equivalent.
Can you find congruent shapes in your backyard? Can you find equivalent shapes?
Learning to measure is an important part of learning geometry! Take your measuring skills beyond your backyard and discover the dimensions of more things in your neighborhood.
CONSIDER AND DISCUSS
It’s time to consider and discuss: What might your house look like if the builder hadn’t measured anything? Why is it important to measure the sizes of things?
DREAM TREEHOUSE
SUPPLIES
* pencil
* graph paper with boxes ½ inch by ½ inch or smaller—you can find graph paper online to print
KEYWORD PROMPTS
print graph paper
Do you ever dream? Many kids have dreams in the night or they look out of the window and have a “daydream.” You can use your imagination to get creative and dream up a dreamy treehouse!
1On your graph paper, draw a big tree with a large amount of space in the leafy branch area.
2Within the branches, draw one or two rooms that are as big or as small as you want. Use the squares on your graph paper to guide you. For example, one room in your tree house may be seven squares long and five squares wide. Label the length and width of the sides.
3Color and design your house! What is in that room? Is it filled with cozy pillows and fluffy blankets? That would be a comfy treehouse room!
TRY THIS! Perhaps your treehouse needs a bit of wallpaper. Wallpaper often has a repeated pattern. Use a new piece of graph paper to create a pattern. Maybe you could color half of every square or alternate colors with each square. Repeat the pattern throughout the entire piece of graph paper to see what it might look like on a wall.
SUPPLIES
* popsicle sticks
* glue
* string
* ruler
* scissors
* bird seed
Making dream treehouses is fun, but what lives in the trees? Birds! Hang this feeder from a branch or near a tree. Watch birds flock to their dream feeder!
1Lay out the popsicle sticks side by side to make the bottom of the feeder. It should take about 11 sticks. Make sure it is a square by using one stick as a measuring tool to check the length. Each stick must be parallel and congruent.
2Add glue to two more sticks. Place them across the base at each end. This will secure the bottom of the feeder! Add two more sticks across the middle to make the base more stable. These four sticks are perpendicular to the base sticks.
3When the glue dries, flip the base over. Add two sticks along the top and bottom of the base. The two sticks should be perpendicular to the base sticks.
4Add glue to the corners of these two sticks. Add sticks to overlap these sticks, like you are building a small log cabin. Repeat this about 20 times. Let your bird feeder dry.
5Cut two pieces of string. Each string should be 1 foot long. Use your ruler! One foot is 12 inches.
6Weave one of the strings down through the slats on the left side and then back up. Do the same for the right side. Tie the four ends together in one large knot.
7Fill your feeder with birdseed and find a nice place to hang the feeder for the birds.
TRY THIS! What kinds of birds visit your bird feeder? Write down the characteristics of the birds you see. You can find out about different birds by looking at this website.
KEYWORD PROMPTS
all about birds
SUPPLIES
* ½ cup dish detergent
* 4 tablespoons glycerin
* 4½ cups water
* bowl and spoon
* clay
* scissors
* drinking straws
* toothpicks
Bubbles do more than fizz in seltzer or pop when you step on bubble wrap. Bubbles might be filled with air, but they take shape, too. Bubbles can be made with soap. Get ready to get squeaky clean!
1Make some bubble solution by mixing the dish detergent, glycerin, and water in a bowl.
2Build a prism! Shape eight small balls of clay. Cut the straws into 12 pieces that are all the same length as a toothpick. Make sure they are all as congruent as possible!
3Place a toothpick inside one straw piece. Put a small ball of clay on one end. Repeat this process until you have four toothpick straws that you can connect to make a square. Make another square the same way.
4Connect these two squares with four more of your toothpick straws. You will have a cube!
5Plop the prism gently into the bowl of bubble solution. Pick it up slowly. What happens? Try dipping it again. Do you get a different bubble shape?
TRY THIS! Make different polyhedrons out of toothpicks, straws, and clay and try them in the bubble solution. What happens to the shape of the bubble when the shape of the frame changes?
SUPPLIES
* small plot of land or rectangular pot
* small shovel
* tape measure
* soil
* flower seeds, such as morning glories
* pencil and paper
The plots of land where farmers and gardeners grow crops is often a familiar 2-D shape, such as a square or a rectangle. What other shapes can you find in a garden?
1Measure a small sunny plot of land, 2 feet by 3 feet. If you want, you can use a rectangular pot to put on your porch or in your kitchen.
2If you are in the yard, dig up the grass, remove rocks, and make sure the soil is good and loose for seeds! Surround the edges of the plot of land with rocks. If you have a rectangular pot, add soil to the pot and smooth it with your shovel.
3Measure how far apart the seeds need to be planted. If the package says they need to be 4 inches apart and your plot is 3 feet long, or 36 inches, how many seeds will you plant? How far apart must each seed be?
4Sketch a diagram of your garden plot in your math journal with your measurements. Using your diagram, plant your seeds. Don’t forget to water them!
TRY THIS! What other shapes can you make your garden? There are circle-shaped gardens, U-shaped gardens, triangle-shaped gardens, and even heart-shaped gardens. Plan an “oddly” shaped garden. Put seeds in alternating patterns, by flower type or by color.
WORDS TO KNOW
crop: a plant grown for food and other uses.
SUPPLIES
* math journal
* measuring tape
* pencil
* graph paper
How big is your deck or your yard? It might be many feet long, but it can be shrunk down to a tiny little drawing. Let’s see how!
1Measure the length and width of your yard or deck. Write these measurements in your math journal.
2Measure objects in your yard or on your deck. Write down the length and width of each object.
3Now, make a scale factor. For example, one foot can be equal to one square on your graph paper. So if your deck is 14 feet long, then the length of the drawing of your deck is 14 squares long!
4Construct your mini deck or mini yard on your graph paper.
5Add all the objects, such as chairs and picnic tables, into your drawing. Color your mini model of your deck or yard!
TRY THIS! Take the measuring tape inside! Measure different rooms and draw scale models of each. Guess what? You are making a blueprint, just like an architect!
WORDS TO KNOW
blueprint: a model or detailed plan to follow.
architect: a person who designs structures.
