Helping Your Child Learn Geography

Remember thumbing through an atlas or encyclopedia as a child, imagining yourself as a world traveler on a safari in Africa, or boating up the Mississippi River, climbing the peaks of the Himalayas, visiting ancient cathedrals and castles of Europe, the Great Wall of China? We do. The world seemed full of faraway, exotic, and wonderful places that we wanted to know more about.
Today, we would like to believe that youngsters are growing up similarly inquisitive about the world. Perhaps they are, but recent studies and reports indicate that, if such imaginings are stirring in our youngsters, they’re not being translated into knowledge. Not that there ever was a 'golden age' when all our young and all our citizens were conversant about the peoples and places of the globe. Still, there is considerable evidence that such knowledge among young Americans has dipped to an alarming low.
Last year, a nine-nation survey found that one in five young Americans (18- to 24-year-olds) could not locate the United States on an outline map of the world. Young Americans knew measurably less geography than Americans 25 years of age and over. Only in the United States did 18- to 24-year-olds know less than people 55 years old and over; in all eight other nations, young adults knew more than the older ones.
No less disturbing was the fact that our young adults, when compared with young adults in other countries, came in last place in a 1980 Gallup Poll. Our 18- to 24-year-olds knew less about geography than their age-mates in every other participating nation. But it shouldn’t surprise us. Youngsters in other countries study more geography. In England, Canada, and the Soviet Union, geography is considered one of the basic academic subjects and is required of most secondary students; in the United States, only one in seven students takes a high school geography course.
You’d think that our students learn at least some geography, though, in their world history classes. Those who take world history probably do. But that’s only 44 percent of our high school graduates. More than half of our high school students are graduating without studying world history.
If youngsters are to acquire an appreciation of geography and ultimately learn to think geographically, parents and communities must insist that local schools restore it to prominence in the curriculum. They should insist that geography be studied and learned, in one form or another, through several years of the primary and secondary curriculum.
Learning should not be restricted to the classroom. Parents are a child’s first teachers and can do much to advance a youngster’s geographic knowledge. This booklet suggests some ways to do so.
It is based on a fundamental assumption: that children generally learn what adults around them value. The significance attached to geography at home or at school can be estimated in a glance at the walls and bookshelves.
Simply put, youngsters who grow up around maps and atlases are more likely to get the 'map habit' than youngsters who do not. Where there are maps, atlases, and globes, discussions of world events (at whatever intellectual level) are more likely to include at least a passing glance at their physical location. Turning to maps and atlases frequently leads youngsters to fashion, over time, their own 'mental maps' of the world--maps that serve not only to organize in their minds the peoples, places, and things they see and hear about in the news, but also to suggest why certain events unfold in particular places.
Helping every child develop his or her ability to use maps and to develop mental maps of the world ought to become a priority in our homes and schools. For, as we all know, our lives are becoming an ever tighter weave of interactions with people around the world. If our businesses are to fare well in tomorrow’s world markets, if our national policies are to achieve our aims in the future, and if our relationships with other peoples are to grow resilient and mutually enriching, our children must grow to know what in the world is where.
This booklet is designed to help parents stir children’s curiosity and steer that curiosity toward geographic questions and knowledge. It is organized around the five themes recently set forth by geographers and geography educators across the Nation--the physical location of a place, the character of a place, relationships between places, movement of people and things, and phenomena that cause us to group places into particular regions.
We encourage parents to get to the fun part--that is, the activities. The games, maps, and suggested activities that follow, while informal and easy to do, can help lay a solid foundation in experience for children’s later, more academic forays into geography.
Bruno V. Manno Deputy Assistant Secretary for Policy and Planning
Kirk Winters Research Associate
Office of Educational Research and Improvement U.S. Department of Education
Introduction
Children are playing in the sand. They make roads for cars. One builds a castle where a doll can live. Another scoops out a hole, uses the dirt to make a hill, and pours some water in the hole to make a lake. Sticks become bridges and trees. The children name the streets, and may even use a watering can to make rain.
Although they don’t know it, these children are learning the principles of geography. They are locating things, seeing how people interact with he Earth, manipulating the environment, learning how weather changes the character of a place, and looking at how places relate to each other through the movement of things from one place to another.
With this book, we hope you, as parents, will get ideas for activities that will use your children’s play to informally help them learn more geography--the study of the Earth.
Most of the suggestions in this book are geared to children under 10 years of age. The activities and games are organized around five specific themes that help focus our thinking. These themes were developed by the Joint Committee on Geographic Education of the National Council for Geographic Education and the American Association of Geographers and are now being used in many schools. They are:
1. Where are things located?
2. What makes a place special?
3. What are the relationships among people and places?
4. What are the patterns of movement of people, products, and information?
5. How can the Earth be divided into regions for study?
These themes have been adopted by many schools in the last few years and may be new to many parents. To help focus your awareness of the issues, we will begin each chapter with a brief description of the theme. This description includes examples of questions geographers use as they strive to understand and define the Earth, for geography provides us with a system for asking questions about the Earth.
Location: Position on the Earth’s Surface
Look at a map. Where are places located? To determine location, geographers use a set of imaginary lines that crisscross the surface of the globe. Lines designating 'latitude' tell us how far north or south of the equator a place is. Lines designating 'longitude' measure distance east and west of the prime meridian--an imaginary line running between the North Pole and the South Pole through Greenwich, England. You can use latitude and longitude as you would a simple grid system on a state highway map. The point where the lines intersect is the 'location'--or global address. For example, St. Louis, Missouri, is roughly at 39? (degrees) north latitude and 90? west longitude.
Why are things located in particular places and how do those places influence our lives? Location further describes how one place relates to another. St. Louis is where the Mississippi and the Missouri rivers meet about midway between Minneapolis-St. Paul and New Orleans. It developed as a trading center between east and west, north and south.
Directions
To help young children learn location, make sure they know the color and style of the building in which they live, the name of their town, and their street address. Then, when you talk about other places, they have something of their own with which to compare.
* Children need to understand positional words. Teach children words like 'above' and 'below' in a natural way when you talk with them or give them directions. When picking up toys to put away, say, 'Please put your toy into the basket on the right' or, 'Put the green washcloth into the drawer.' Right and left are as much directional terms as north, south, east, and west. Other words that describe such features as color, size, and shape are also important.
* Show your children north, south, east, and west by using your home as a reference point. Perhaps you can see the sun rising in the morning through a bedroom window that faces east and setting at night through the westerly kitchen window:
* Reinforce their knowledge by playing games. Once children have their directional bearings, you can hide an object, for example, then give them directions to its location: 'two steps to the north, three steps west ....'
* Use pictures from books and magazines to help your children associate words with visual images. A picture of a desert can stimulate conversation about the features of a desert--arid and barren. Work with your children to develop more complex descriptions of different natural and cultural features.
Maps
Put your child’s natural curiosity to work. Even small children can learn to read simple maps of their school, neighborhood, and community. Here are some simple map activities you can do with your children.
* Go on a walk and collect natural materials such as acorns and leaves to use for an art project. Map the location where you found those items.
* Create a treasure map for children to find hidden treats in the back yard or inside your home. Treasure maps work especially well for birthday parties.
* Look for your city or town on a map. If you live in a large city or town, you may even be able to find your street. Point out where your relatives or your children’s best friends live.
* Find the nearest park, lake, mountain, or other cultural or physical feature on a map. Then, talk about how these features affect your child’s life. Living near the ocean may make your climate moderate, prairies may provide an open path for high winds, and mountains may block some weather fronts.
* By looking at a map, your children may learn why they go to a particular school. Perhaps the next nearest school is on the other side of a park, a busy street, or a large hill. Maps teach us about our surroundings by portraying them in relation to other places.
* Before taking a trip, show your children a map of where you are going and how you plan to get there. Look for other ways you could go, and talk about why you decided to use a particular route. Maybe they can suggest other routes.
* Encourage your children to make their own maps using legends with symbols. Older children can draw a layout of their street, or they can illustrate places or journeys they have read about. Some books, like Winnie-the-Pooh and The Wizard of Oz, contain fanciful maps. These can be models for children to create and plot their own stories.
* Keep a globe and a map of the United States near the television and use them to locate places talked about on television programs, or to follow the travels of your favorite sports team.
Additional Activities
Children use all of their senses to learn about the world. Objects that they can touch, see, smell, taste, and hear help them understand the link between a model and the real thing.
* Put together puzzles of the United States or the world. Through the placement of the puzzle pieces, children gain a tactile and visual sense of where one place is located in relation to others.
* Make a three-dimensional map of your home or neighborhood using milk cartons for buildings. Draw a map of the block on a piece of cardboard, then cut up the cartons (or any other three-dimensional item) and use them to represent buildings. Use bottle tops or smaller boxes to add interest to the map, but try to keep the scale relationships correct.
* Use popular board games like 'Game of the States' or 'Trip Around the World' to teach your children about location, commerce, transportation, and the relationships, among different countries and areas of the world. Some of these games are available at public libraries.
* Make paper-mache using strips of old newspaper and a paste made from flour and water. If children form balls by wrapping the strips of paper-mache around a balloon, they will develop a realistic understanding of the difficulties in making accurate globes. They can also use paper-mache to make models of hills and valleys.
Place: Physical and Human Characteristics
Every place has a personality. What makes a place special? What are the physical and cultural characteristics of your hometown? Is the soil sandy or rocky? Is the temperature warm or is it cold? If it has many characteristics, which are the most distinct?
How do these characteristics affect the people living there? People change the character of a place. They speak a particular language, have styles of government and architecture, and form patterns of business. How have people shaped the landscapes?
Investigate Your Neighborhood
* Walk around your neighborhood and look at what makes it unique. Point out differences from and similarities to other places. Can your children distinguish various types of homes and shops? Look at the buildings and talk about their uses. Are there features built to conform with the weather or topography? Do the shapes of some buildings indicate how they were used in the past or how they’re used now? These observations help children understand the character of a place.
* Show your children the historical, recreational, or natural points of interest in your town. What animals and plants live in your neighborhood? If you live near a harbor, pay it a visit, and tour a docked boat. You can even look up the shipping schedule in your local newspaper. If you live near a national park, a lake, a river, or a stream, take your children there and spend time talking about its uses.
* Use songs to teach geography. 'Home on the Range,' 'Red River Valley,' and 'This Land Is Your Land' conjure up images of place. Children enjoy folk songs of different countries like 'Sur La Pont D’Avignon, .... Guantanamara,' and 'London Bridge.' When your children sing these songs, talk with them about the places they celebrate, locate them on the map, and discuss how the places are described.
Study the Weather
Weather has important geographic implications that affect the character of a place. The amount of sun or rain, heat or cold, the direction and strength of the wind, all determine such things as how people dress, how well crops grow, and the extent to which people will want to live in a particular spot.
* Watch the weather forecast on television or read the weather map in the newspaper. Save the maps for a month or more. You can see changes over time, and compare conditions over several weeks and seasons. Reading the weather map helps children observe changes in the local climate.
* Use a weather map to look up the temperatures of cities around the world and discover how hot each gets in the summer and how cold each gets in the winter. Ask your children if they can think of reasons why different locations have different temperatures. Compare these figures with your town. Some children enjoy finding the place that is the hottest or the coldest.
* Make simple weather-related devices such as barometers, pinwheels, weather vanes, and wind chimes. Watch cloud formations and make weather forecasts. Talk about how these describe the weather in your town.
Learn About Other Cultures
People shape the personality of their areas. The beliefs, languages, and customs distinguish one place from another.
* Make different ethnic foods, take your children to an ethnic restaurant, or treat them to ethnic snacks at a folk festival. Such an experience is an opportunity to talk about why people eat different foods. What ingredients in ethnic dishes are unique to a particular area? For example, why do the Japanese eat so much seafood? (If your children look for Japan on a map they will realize it is a country of many islands.)
* Read stories from or about other countries, and books that describe journeys. Many children’s books provide colorful images of different places and a sense of what it would be like to live in them. Drawings or photographs of distant places or situations can arouse interest in other lands. The Little House in the Big Woods, Holiday Tales of Sholem Aleichem, and The Polar Express are examples of books with descriptions of place that have transported the imaginations of many young readers. There is a bibliography at the end of this booklet, and your librarian will have more suggestions.
Weather Vane
Materials: wire hanger, small plastic container, aluminum foil, sand or dirt, tape or glue, scissors, crayon.
Directions:
1. Straighten out the hanger’s hook and cover half of the triangle part of the hanger with foil. Fold the edges, and tape or glue in place.
2. Fill the container with sand or loose dirt, put on the lid, and mark it N, S, E, and W. Poke the hanger through the center of the lid. The hanger should touch the bottom of the container and turn freely in the hole.
3. Put the container outside with the N facing north. When the wind blows, take a look at your weather vane. The open half of the vane shows the direction from which the wind is coming.
Reprinted from Sesame Street Magazine Parent’s Guide, June 1986. Copyright Children’s Television Workshop.
Relationships within Places: Humans and Environments
How do people adjust to their environment? What are the relationships among people and places? How do they change it to better suit their needs? Geographers examine where people live, why they settled there, and how they use natural resources. For example, Hudson Bay, the site of the first European settlement in Canada, is an area rich in wildlife and has sustained a trading and fur trapping industry for hundreds of years. Yet the climate there was described by early settlers as 'nine months of ice followed by three months of mosquitoes.' People can and do adapt to their natural surroundings.
Notice How You Control Your Surroundings
Everyone controls his or her surroundings. Look at the way you arrange furniture in your home. You place the tables and chairs in places that suit the shape of the room and the position of the windows and doors. You also arrange the room according to how people will use it.
* Try different furniture arrangements with your children. If moving real furniture is too strenuous, try working with doll house furniture or paper cutouts. By cutting out paper to represent different pieces of furniture, children can begin to learn the mapmaker’s skill in representing the three-dimensional real world.
* Ask your children to consider what the yard might look like if you did not try to change it by mowing grass, raking leaves or planting shrubs or trees. You might add a window box if you don’t have a yard. What would happen if you didn’t water the plants?
* Walk your children around your neighborhood or a park area and have them clean up litter. How to dispose of waste is a problem with a geographic dimension.
* Take your children to see some examples of how people have shaped their environment: bonsai gardens, reservoirs, terracing, or houses built into hills. Be sure to talk with them about how and why these phenomena came to be.
* If you don’t live on a farm, try to visit one. Many cities and States maintain farm parks for just this purpose. Call the division of parks in your area to find out where there is one near you. Farmers use soil, water, and sun to grow crops. They use ponds or streams for water, and build fences to keep animals from running away.
Notice How You Adapt to Your Surroundings
People don’t always change their environment. Sometimes they are shaped by it. Often people must build roads around mountains. They must build bridges over rivers. They construct storm walls to keep the ocean from sweeping over beaches. In some countries, people near coasts build their houses on stilts to protect them from storm tides or periodic floods.
* Go camping. It is easy to understand why we wear long pants and shoes when there are rocks and brambles on the ground, and to realize the importance to early settlers of being near water when you no longer have the convenience of a faucet.
* If you go to a park, try to attend the nature shows that many parks provide. You and your children may learn about the local plants and wildlife and how the natural features have changed over time.
Movement: People Interacting on the Earth
People are scattered unevenly over the Earth. How do they get from one place to another? What are the patterns of movement of people, products, and information ? Regardless of where we live, we rely upon each other for goods, services, and information. In fact, most people interact with other places almost every day. We depend on other places for the food, clothes, and even items like the pencil and paper our children use in school. We also share information with each other using telephones, newspapers, radio, and television to bridge the distances.
Travel in Different Ways
* Give your children opportunities to travel by car, bus, bicycle, or on foot. Where you can, take other forms of transportation such as airplanes, trains, subways, ferries, barges, and horses and carriages.
* Use a map to look at various routes you can take when you try different methods of transportation.
* Watch travel programs on television.
Follow the Movement of People and Things
* Play the license plate game. How many different States’ plates can you identify, and what, if anything, does the license plate tell you about each State? You don’t have to be in a car to play. You can look at the license plates of parked cars, or those traveling by when you are walking. Children can keep a record of the States whose plates they have seen. They can color in those States on a map and illustrate them with characteristics described on the license plates. Some States have county names on their plates. If you live in one of these States, keeping track of the counties could be another interesting variation.
* Go around your house and look at where everything comes from. Examine the labels of the clothes you wear and think of where your food comes from. Why do bananas come from Central America? Why does the milk come from the local dairy? Perhaps your climate is too cold for bananas, and the milk is too perishable to travel far. How did the food get to your house?
* Tell your children where your ancestors came from. Find your family’s countries of origin, and chart the birthplaces of relatives on a map. You can plot the routes they followed before they arrived at their present location. Why did they leave their previous home? Where do all your relatives live now?
* Have your children ask older relatives what their world was like when they were young. They can ask questions about transportation, heating and refrigeration, the foods they ate, the clothes they wore, and the schools they attended. Look at old pictures. How have things changed since Grandma was a child? Grandparents and great aunts and uncles are usually delighted to share their memories with the younger generation, and they can pass on a wealth of information.
Follow the Movement of Ideas and Information
Ideas come from beyond our immediate surroundings. How do they get to us? Consider communication by telephone and mail, television, radio, telegrams, telefax, and even graffiti, posters, bumper stickers, and promotional buttons. They all convey information from one person or place to another.
* By watching television and listening to the radio, your children will receive ideas from the outside world. Where dothe television shows they watch originate? What aboutradio shows?
* Ask your children how they would communicate with other people. Would they use the phone or write a letter? Encourage them to write letters to relatives and friends. They may be able to get pen pals through school or a pen pal association. (Please see the listing in the back of this booklet.)
Regions: How They Form and Change
How can places be described or compared? How can the Earth be divided into regions for study? Geographers categorize regions in two basic ways--physical and cultural. Physical regions are defined by landform (continents and mountain ranges), climate, soil, and natural vegetation. Cultural regions are distinguished by political, economic, religious, linguistic, agricultural, and industrial characteristics.
Examine Physical Regions
* Help your children understand physical regions by examining areas in your home. Is there an upstairs and a downstairs? Is there an eating area and a sleeping area? Are there other 'regions' in your home that can be described?
* Look at the physical regions in your community. Some neighborhoods grew up around hills, others developed on waterfronts or around parks. What physical regions exist in your hometown?
Examine Cultural Regions
* Take your children to visit the different political, residential, recreational, ethnic, and commercial regions of your city.
* Go to plays, movies, and puppet shows about people from different countries. These are often presented at libraries and museums.
* Give children geography lessons by tying in with ethnic holiday themes. Provide children with regional or ethnic clothes to wear. Some museums and libraries provide clothes children can borrow. Holidays provide an opportunity to learn about the customs of people around the world. You can use the library to discover how other people celebrate special days.
* Compare coins and stamps from other lands. They often contain information about the country. You may be able to find stamps from other countries where you work, or your children may get them from pen pals. Stamps tell many different kinds of things about a country, from its political leadership to native bird life.
* Learn simple words in different languages. Teach your children to count to 10 in other languages. They can also learn simple words like 'hello, .... goodbye,' and 'thank you.' Look at the different alphabets or script from various regions. All these activities expose children to the abundance of the Earth’s cultural treasures. Many libraries have language tapes and books, some especially for children.
* If you have friends who are from different countries or have either travelled or lived abroad, invite them over to talk with your children. If they have pictures, so much the better. What languages do they speak? How are their customs or dress similar to or different from yours?
Conclusion
Geography is a way of thinking, of asking questions, of observing and appreciating the world around us. You can help your children learn by providing interesting activities for them, and by prompting them to ask questions about their surroundings.
Set a good example, and help your children build precise mental images, by always using correct terms. Say, 'We are going north to New York to visit Grandma, or west to Dallas to see Uncle John,' rather than 'up to New York' or 'down to Dallas.' Use words such as highway, desert, river, climate, and glacier; and explain concepts like city, State, and continent.
Many of the words used in geography are everyday words. But, like any other field of learning, geography has a language of its own. (A glossary of basic geography terms appears in the back of this booklet.)
Expose children to lots of maps and let them see you using them. Get a good atlas as well as a dictionary. Atlases help us ask, and answer, questions about places and their relationships with other areas. Many States have atlases that are generally available through an agency of the state government.
The activities suggested in this booklet are only a few examples of the many ways that children learn geography. These activities are designed to help parents find ways to include geographic thinking in their children’s early experiences. We hope they will stimulate your thinking and that you will develop many more activities on your own.
References
Backler, Alan; and Stoltman, Joseph. 'The Nature of Geographic Literacy.' ERIC Digest (no. 35). Bloomington, IN. 1986.
Blaga, Jeffrey J.; and others. Geographic Review of Our World: A Daily Five-Minute Geography Program for Grades 3-11. GROW Publications. Racine, WI. 1987.
Duea, Joan; and others. Maps and Globes: An Instructional Unit for Elementary Grades. University of Northern Iowa. Cedar Falls, IA. 1985.
Geographic Education National Implementation Project. Walter G. Kernball (chair). K-6 Geography: Themes, Key Ideas, and Learning Opportunities. National Council for Geographic Education.
Western Illinois University. Macomb, IL. 1984.
Department of Education and Science. Geography from 5 to 16. HMSO Books. London. 1986.
Hoehn, Ann. 'Helping Children Get Their Hands on Geography' (unpublished activity guide). Milaca Public Schools. Milaca, MN. 1988.
Joint Committee on Geographic Education. Guidelines for Geographic Education, Elementary and Secondary Schools. Association of American Geographers and National Council for Geographic Education. Washington, DC. 1984.
National Council for the Social Studies. Strengthening Geography in the Social Studies, Bulletin 81. Salvatore J. Natoli (editor). Washington, DC. 1988.
National Geographic Society. Geography: An International Gallup Survey. The Gallup Organization, Inc. Princeton, NJ. 1988.
National Geographic Society. 'Geography: Making Sense of Where We Are.' Geographic Education Program. Washington, DC. 1988.
National Geographic Society. Geography Education Program. 'Teaching Geography: A Model for Action.' Washington, DC. 1988.
Wilson-Jones, Ruth Anne. 'Geography and Young Children: Help Give them the World' (unpublished paper). LaGrange, GA. 1988.
Glossary
altitude
Distance above sea level.
atlas
A bound collection of maps.
archipelago
A group of islands or a sea studded with islands.
bay
A wide area of water extending into land from a sea or lake.
boundaries
Lines indicating the limits of countries, States, or other political jurisdictions.
canal
A man-made watercourse designed to carry goods or water.
canyon
A large but narrow gorge with steep sides.
cape (or point)
A piece of land extending into water.
cartographer
A person who draws or makes maps or charts.
continent
One of the large, continuous areas of the Earth into which the land surface is divided.
degree
A unit of angular measure. A circle is divided into 360 degrees, represented by the symbol *. Degrees, when applied to the roughly spherical shape of the Earth for geographic and cartographic purposes, are each divided into 60 minutes, represented by the symbol ’.
delta
The fan-shaped area at the mouth, or lower end, of a river, formed by eroded material that has been carried downstream and dropped in quantities larger than can be carried off by tides or currents.
desert
A land area so dry that little or no plant life can survive.
elevation
The altitude of an object, such as a celestial body, above the horizon; or the raising of a portion of the Earth’s crust relative to its surroundings, as in a mountain range.
equator
An imaginary circle around the Earth halfway between the North Pole and the South Pole; the largest circumference of the Earth.
glacier
A large body of ice that moves slowly down a mountainside from highlands toward sea level.
gulf
A large arm of an ocean or sea extending into a land mass.
hemisphere
Half of the Earth, usually conceived as resulting from the division of the globe into two equal parts, north and south or east and west.
ice shelf
A thick mass of ice extending from a polar shore. The seaward edge is afloat and sometimes extends hundreds of miles out to sea.
international date line
An imaginary line of longitude generally 180? east or west of the prime meridian. The date becomes one day earlier to the east of the line.
island
An area of land, smaller than a continent, completely surrounded by water.
isthmus
A narrow strip of land located between two bodies of water, connecting two larger land areas.
lagoon
A shallow area of water separated from the ocean by a sandbank or by a strip of low land.
lake
A body of fresh or salt water entirely surrounded by land.
latitude
The angular distance north or south of the equator, measured in degrees.
legend
A listing which contains symbols and other information about a map.
longitude
The angular distance east or west of the prime meridian, measured in degrees.
mountain
A high point of land rising steeply above its surroundings.
oasis
A spot in a desert made fertile by water.
ocean
The salt water surrounding the great land masses, and divided by the land masses into several distinct portions, each of which is called an ocean.
peak
The highest point of a mountain.
peninsula
A piece of land extending into the sea almost surrounded by water.
plain
A large area of land, either level or gently rolling, usually at low elevation.
plateau (or tableland)
An elevated area of mostly level land, sometimes containing deep canyons.
physical feature
A land shape formed by nature.
population
The number of people inhabiting a place.
prime meridian
An imaginary line running from north to south through Greenwich, England, used as the reference point for longitude. range (or mountain range) A group or chain of high elevations.
reef
A chain of rocks, often coral, lying near the water surface.
reservoir
A man-made lake where water is kept for future use.
river
A stream, larger than a creek, generally flowing to another stream, a lake, or to the ocean.
scale
The relationship of the length between two points as shown on a map and the distance between the same two points on the Earth.
sea level
The ocean surface; the mean level between high and low tides.
strait
A narrow body of water connecting two larger bodies of water.
swamp
A tract of permanently saturated low land, usually overgrown with vegetation. (A marsh is temporarily or periodically saturated.)
topography
The physical features of a place; or the study and depiction of physical features, including terrain relief.
valley
A relatively long, narrow land area lying between two areas of higher elevation, often containing a stream.
volcano
A vent in the Earth’s crust caused by molten rock coming to the surface and being ejected, sometimes violently.
waterfall
A sudden drop of a stream from a high level to a much lower level.
Glossary, in part, courtesy of Hammond, Incorporated
Free or Inexpensive Materials
Maps
The following places often provide free maps, although you will probably have to go in person or send a self-addressed stamped envelope in order to receive one:
* State tourist agencies and local chambers of commerce publish walking tour maps or guidebooks to area attractions.
* Local government offices, especially those dealing with public transportation, often provide free road maps.
* Car rental companies. The Federal Government has hundreds of maps available. For a comprehensive listing, contact the Government Printing Office (GPO) bookstore in your area or the Superintendent of Documents, Government Printing Office, Washington, DC 20402. The GPO handles the printing and sales of items produced by government agencies. Some examples of what you might find there, or directly through the developing agency, include:
* Schematic maps with historical data and park activities of the areas under the care of the U.S. National Park Service. Contact the particular site, or write to the Department of the Interior, U.S. National Park Service, P.O. Box 7427, Washington, DC 20013-7127.
* Maps from the U.S. Geological Survey, the civilian mapmaking agency of the United States Government, covering a range of areas including National Wildlife Refuges to LANDSAT pictures of the Earth. For a catalog, write to the Earth Science Information Center, U.S. Geological Survey, 507 National Center, Reston, VA 22092.
* A map of the United States showing the U.S. Wildlife Refuges. Write to the U.S. Fish and Wildlife Service, Division of Refuge, 18th and C Streets NW, Washington, DC 20204.
* Maps of water recreation areas, from the Army Corps of Engineers. Write to Department of the Army, Corps of Engineers, 2803 52nd Avenue, Hyattsville, MD 20781-1102.
* A wide selection of material is available from the National Aeronautics and Space Administration (NASA), 400 Maryland Avenue SW, Washington, DC 20546. Of particular interest are NASA Facts--Planet Earth Through the Eyes of LANDSAT 4 and Earth System Science. For a full list, ask for a copy of NASA Educational Publications.
Another source is The Map Catalog (Joel Makower, editor, and Laura Bergheim, associate editor), published in 1986 by Vintage Books of Random House. It is probably at your public library.
Magazines
Look for these magazines in your school or library:
* Discover produced by Family Media, Incorporated;
* World, published by the National Geographic Society; and
* Ranger Rick and Your Big Backyard, published by the National Wildlife Federation.
Pen Pal Organizations
League of Friendship P.O. Box 509 Mt. Vernon, OH 43050 (6 14)392-3 166
Books
Easy Reading and Picture Books:
Anderson, Lonzo. Day the Hurricane Happened. Story of what a family does when a hurricane rips through their island.
Bach, Alice. Most Delicious Camping Trip Ever. Exploits of twin bears on a camping trip.
Balet, Jan. Fence, A Mexican Tale. Illustrations help tell the story of two Mexican families.
Beskow, Elsa. Children of the Forest. A family of Tomten (small forest people) work and play through the four seasons in their Nordic home.
Brenner, Barbara. Barto Takes the Subway. Barto lives in New York City. He and his sister take a trip on the subway.
Brenner, Barbara. Wagon Wheels. Three young black brothers follow a map to their father’s homestead on the Western plains.
Brinckloe, Julie. Gordon Goes Camping. When Gordon decides to go camping, his friend Marvin tells him of all the things he will need for the trip.
Buck, Pearl S. Chinese Children Next Door. A mother who had spent her childhood in China tells her children about her neighbors there.
Burningham, John. Seasons. A series of pictures that define the four seasons.
Burton, Virginia Lee. Little House. A country house is unhappy when the city with all its houses and traffic grows up around it.
Chonz, Selina. Bell for Ursli. A boy who lives in a tiny village in the mountains of Switzerland has an adventure when the spring festival comes.
Cooney, Barbara. Miss Rumphius. One woman’s personal odyssey through life to fulfill her grandfather’s wish that she make the world more beautiful.
Devlin, Wende and Harry. Cranberry Thanksgiving; Cranberry Christmas; Cranberry Mystery. A series of mystery-adventure tales set on the cranberry bog shore of Cape Cod.
Dobrin, Arnold. Josephine’s Imagination; A Tale of Haiti. Story of a young girl and her adventures in the Haitian market.
Eiseman, Alberta. Candido. Paco, a Peruvian boy, loves his pet llama but knows that he must find a way to train the animal to work as other llamas do.
Ets, Marie Hall. Gilberto and the Wind. A very little boy from Mexico finds that the wind is his playmate.
Feelings, Muriel L. Jambo Means Hello. A Swahili alphabet book.
Frasconi, Antonio. See and Say, Guarda e Parla, Mira y Habla, Regard et Parle. A picture book that gives words from four languages and prints each in a special color. Has a page of everyday expressions as well.
Garelic, May. Down to the Beach. Boats, birds, shells, sand, waves, tides and all the fun and wonder of the beach are pictured in simple, rhythmic prose and beautiful watercolors.
Goble, Paul. The Gift of the Sacred Dog and The Girl Who Loved Wild Horses. These stories, accompanied by beautiful pictures, are based on legends of the Native Americans.
Green, Norma B. Hole in the Dike. Retells the familiar story of the young Dutch boy whose resourcefulness, courage and finger save his country from being destroyed by the sea.
Hader, Berta. Reindeer Trail. The generous Laplanders bring their herds of reindeer all the way from Lapland to Alaska to help hungry Eskimos.
Hoban, Tana. Over, Under & Through, and Other Spatial Concepts. A picture book on spatial concepts.
Holling, Holling C. Paddle-to-the-Sea. Describes the journey of a toy canoe from the Great Lakes to the Atlantic Ocean.
Kessler, Ethel. Big Red Bus. An illustrated bus ride for the very beginning reader.
Krasilovsky, Phyllis. The First Tulips in Holland. Beautiful drawings about spring in Holland.
Kraus, Robert. Gondolier of Venice. The city of Venice is sinking into the sea, but Gregory, a proud gondolier, gets a clever and unusual idea to help the old city.
Lamont, Bette. Island Time. A parent and child board the ferry that takes them to their very special island on Puget Sound.
Lisowski, Gabriel. How Tevye Became a Milkman. Short tale, with illustrations of the Ukrainian countryside, based on the character also depicted in Fiddler on the Roof.
McCloskey, Robert. Blueberries for Sal. Make Way for Ducklings. One Morning in Maine. Favorites from an award winning children’s book author. Each describes a special journey and the difficulties in getting from one place to another.
Mizumura, Kazue. If I Built a Village. An idealistic picture of what a village, town and city can be ends with a small boy building with blocks.
Morrow, Suzanne Stark. Inatuk’s Friend. Story of an Eskimo child who must move from one place to another.
Musgrove, Margaret. Ashanti to Zulu: African Traditions. Read and observe 26 African tribes from A to Z.
Peterson, Hans. Big Snowstorm. Illustrations and text picture events on a Swedish farm during a raging, January blizzard.
Rockwell, Anne. Thruway. As a small boy rides along a thruway with his mother, he tells of all the things he sees.
Shortall, Leonard. Peter in Grand Central Station. Peter takes his first trip alone, but when he gets to New York, his uncle is not there to meet him.
Skorpen, Liesel Moak. We Were Tired of Living in a House. Four small children pack their bags and leave home to find a new and better house.
Spier, Peter. People. Explores the enormous diversity of the world’s population. Looks at various cultures, homes, foods, games, clothing, faces, and religions.
Van Woerkom, Dorothy. Abu Ali: Three Tales of the Middle East. Abu Ali is fooled by his friends, tricks them in turn and even fools himself in three humorous stories of trickery based on folklore of the Middle East.
Books to Read Aloud or for Better Readers:
Brink, Carol Ryrie. Caddie Woodlawn. These stories convey the flavor of pioneer life through the eyes of a little girl who lived in Wisconsin a century ago.
Bulla, Clyde Robert. A Lion to Guard Us. This is a story of the founding fathers of the Jamestown colony and the families they left behind in England.
DeJong, Meindert. Wheel on the School. Children of Shora, a Netherlands village, are determined to bring storks back to their town.
Dodge, Mary Mapes. Hans Brinker, or The Silver Skates. Poor Dutch children long to compete in a skating contest.
DuBois, William Pene. The Twenty-one Balloons. In the fall of 1883, Professor William Waterbury Sherman sets forth from San Francisco on a balloon expedition around the world.
Hansen, Judith. Seashells in My Pocket: A Child’s Guide to Exploring the Atlantic Coast from Maine to North Carolina. A look at seashells on Atlantic Coast beaches.
Henry, Marguerite. Misty of Chincoteague. A story of the wild ponies that live on an island off the eastern shore of Virginia, and of one freedom-loving pony.
Kelly, Eric. The Trumpeter of Krakow. Mystery story centering around an attack on the ancient city of Krakow in medieval Poland.
Milne. A.A. The House at Pooh Corner; Winnie-the-Pooh. Christopher Robin and his friends have adventures and tell stories.
Mowat, Farley. Owls in the family. This is a story of the author’s boyhood on the Saskatchewan prairie, raising dogs, gophers, rats, snakes, pigeons, and owls.
McNulty, Faith. Hurricane. This is a nature story that takes place when a family struggles against a hurricane.
Spyri, Johanna. Heidi. Story of a young girl who goes to live with her grandfather in the Swiss Alps. She is then taken by her aunt to live in the city and struggles to return to her grandfather.
Steig, William. Abel’s Island. A mouse lives for a year in the wilderness until his wit and courage take him back home.
Wilder, Laura Ingalls. The Little House series. Documents the life of the author and her husband a century ago.
Wyss, Johann. Swiss Family Robinson. The adventures of a Swiss family shipwrecked on a desert island.
Atlases and other reference guides for young people:
Big Blue Marble Atlas. Paula Brown and Robert Garrison. Ideals Publishing group. Milwaukee. 1988.
Discovering Maps: A Young Person’s Atlas. Hammond Incorporated. Maplewood, N.J. 1989.
Doubleday Children’s Atlas. Jane Oliver, editor. Doubleday. New York. 1987.
Facts on File Children’s Atlas. David and Jill Wright. Facts on File Publications. New York. 1987.
Life Through the Ages. Giovanni Caselli. Grossett and Dunlop. New York. 1987.
Picture Atlas of Our World. National Geographic Society. Washington, D.C. 1979.
Picture Encyclopedia of the World for Children. Bryon Williams and Lynn Williamson. Simon and Schuster. New York. 1984.
Rand McNally Children’s Atlas of the World. Bruce Ogilvie. Rand McNally and Co., Inc. Chicago. 1985.
Rand McNally Student’s World Atlas. Rand McNally and Co. Chicago. 1988.
Usborne Book of World Geography. Jenny Tyler, Lisa Watts, Carol Bowyer, Roma Trundle and Annabel Warrender. Usborne Publishing, Ltd. London. 1984.
Acknowledgments
This project could not have been completed if it were not for the help of many dedicated people. Thanks to those who shared their ideas and materials on geography and early childhood--Mark Bockenhauer of the National Geographic Society, teachers Ann Hoehn, Judy Ludovise, and Ruth Anne Wilson-Jones, and Salvatore Natoli of the National Council for the Social Studies. Thanks to the same group for reviewing the final document and to Pat Bonner of the Consumer Information Center, Robert Burch and technical staff of Hammond, Incorporated, and George Zech of the Duncan Oklahoma Schools.
Thanks to the National Mapping Division of the United States Geological Survey for becoming involved in the development of this document and for making it available to a broader audience. In addition, thanks to Ann Chaparos for the cover design and help on the layout.
Last, but not least, thanks to the staff of the Office of Educational Research and Improvement for helping make the draft into a booklet--Cynthia Dorfman, Kate Dorrell, Lance Ferderer, Mark Travaglini, Tim Burr, and Phil Carr.
City maps, time zone map, and mileage chart courtesy of Hammond Incorporated, Maplewood, NJ.

Home Education Schools Learning The GED Tests

If you left high school without graduating, the GED Tests provide a way for you to earn your GED high school diploma. Getting your GED Diploma can make a big difference in your life. Read this Information Bulletin and learn:
* What is covered on the GED Tests
* How to prepare for the GED Tests
* Where to get help
READ ON!
WHAT IS THE GED TESTING PROGRAM?
The GED testing program offers you an opportunity to earn a GED high school diploma. Many people who did not finish high school have knowledge and skills comparable to people who did graduate. This idea is the basis of the GED testing program. The GED Tests ask questions about subjects covered in high school. The GED Tests are given in all 50 states, the District of Columbia, the U.S. territories, most Canadian provinces, and the Canadian territories. Each year, about one-half million people earn their GED Diplomas.
The GED Tests are available in English, Spanish, and French. Special large-print, audiocassette, and braille editions of the GED Tests are also available, and adaptations to testing conditions are permitted for adults with disabilities.
WHAT ARE THE BENEFITS OF A GED DIPLOMA?
Education
The GED program provides an opportunity for adults to continue their education. Ninety-three percent of colleges and universities accept GED graduates who meet their other qualifications for admission.
Employment
A GED Diploma documents that you have high school-level skills. Approximately 96 percent of employers accept the GED Diploma as equivalent to a traditional high school diploma.
Self-Esteem
Many GED graduates say they have feelings of increased self-esteem and self-confidence.
Once you earn your GED Diploma, it’s up to you to pursue the individual goals you set for yourself.
WHO IS ELIGIBLE TO TAKE THE GED TESTS?
If you left high school without graduating and your high school class has graduated, you are probably eligible to take the GED Tests. Contact your nearest GED Testing Center or the department of education in your state, territory, or province for specific eligibility requirements. Information on where to call is given on pages 15 and 16 of this Bulletin.
HOW CAN I DECIDE IF I AM READY TO TAKE THE GED TESTS?
It’s a good idea to take the Official GED Practice Tests before taking the actual GED Tests. Comparing your Practice Test scores with the minimum scores required in your area will help you decide whether you are ready to take the full-length GED Tests. If your scores are high, you have a good chance of passing the GED Tests. If your Practice Test scores are low, you will probably need further study in one or more subject areas. The Official GED Practice Tests are available through your local adult education program. You can also purchase the Practice Tests yourself by ordering Form CC of the Official GED Practice Tests. See order information on the back page of this Bulletin.
HOW CAN I PREPARE FOR THE GED TESTS?
By Attending Classes...
If you need help deciding whether you’re ready to take the GED Tests or if you want help preparing for the tests, contact an adult education program in your community. Many programs that are sponsored by local school districts, colleges, and community organizations provide GED classes. The teachers at these adult education programs can help you decide whether you need to study for all of the tests, or whether you should spend time brushing up in just a few areas.
To get information regarding a program in your area, contact your local high school, adult education program, or community college. Look in the yellow pages of your local telephone directory under the heading 'Schools.' Check the listings for the high schools and community colleges in your area.
Programs offered by schools and colleges may be listed under the heading 'Adult Education,' 'Continuing Education,' or 'GED.' You can also call the general number listed for high schools, colleges, or your board of education and ask for information about GED classes.
If you cannot locate an adult education program in your area, call the number listed for your state, province, or territory on pages 15 and 16 of this Bulletin.
By Yourself...
After reading this Bulletin and possibly taking the Official GED Practice Tests, you may decide that you want to study on your own before you take the actual GED Tests. If you can’t answer some questions in this Bulletin or on the Official GED Practice Tests correctly because you have not studied these subjects in a long time, you may be able to improve your skills by studying on your own. In fact, about 20% of all GED test-takers prepare for the GED Tests in this way. Many study materials that are available through libraries, adult education centers, schools, colleges, and book stores may help you improve your skills. There is also a television series called 'GED on TV' on The Learning Channel and many public television stations throughout the country. To find out what channel in your area carries the 'GED on TV' series, call 1-800-354-9067. You may also call The Learning Line at 1-800-232-2775 to find out about self-study materials that you may purchase.
WHERE CAN I TAKE THE GED TESTS?
You can take the GED Tests at one of more than 3,000 Official GED Testing Centers in the United States and Canada. There is probably an Official GED Testing Center not far from your home. Call your nearest adult education program and ask for the location and schedule of the testing center near you. Or contact your state, territorial, or provincial department of education and ask for the location and schedule of the closest Official GED Testing Center (see pages 15 and 16 of this Bulletin).
WHAT ARE THE GED TESTS LIKE?
The GED Tests measure important knowledge and skills expected of high school graduates. The five GED Tests are:
* Writing Skills
* Social Studies
* Science
* Interpreting Literature and the Arts
* Mathematics
These tests contain multiple-choice questions that test your ability to understand and use information or ideas. In many cases, you are asked to use the information provided to solve a problem, find causes and effects, or make a judgment. Very few questions ask about narrow definitions or specific facts. Instead, the focus of questions is on the major and lasting skills and knowledge expected of high school graduates.
In addition to the multiple-choice questions, the Writing Skills Test includes an essay section. In this section, you are given 45 minutes to write an essay on the topic given. The topics are designed to be very general, so everyone can think of something to write. More information about the essay is given later in this Bulletin.
The multiple-choice questions on the five GED Tests are presented in one of three ways:
* Accompanied by a reading selection that may be as brief as one or two sentences or as long as 400 words
* Accompanied by a table, graph, chart, or illustration
* Stated as a problem to be solved (this type is most often used in the Mathematics Test)
Because most material presented in the GED Tests requires the ability to understand written text, the skill of reading comprehension is very important.
WHAT SUBJECTS ARE ON THE GED TESTS?
The next section of this Bulletin shows sample questions from each of the GED Tests, along with explanations of the correct answers. Read the sample questions to become familiar with the type of material you will find on the GED Tests.
Do not be discouraged if you feel that the questions are too hard. Most people who have been out of high school for some time need to prepare for the GED Tests before taking them. Adult education programs in your community are specially designed to help you improve your skills so that you can succeed on the GED Tests.
TEST ONE: WRITING SKILLS
The GED Writing Skills Test has two parts. Part One contains multiple-choice questions that require you to correct or revise sentences that appear in a writing selection. Part Two asks you to write an essay about a subject or an issue that is familiar.
Test One, Part One: Multiple-Choice Questions
This section of the Writing Skills Test contains paragraphs with numbered sentences followed by questions based on those sentences. Each writing selection contains about 10 to 14 numbered sentences in one or more paragraphs.
Questions in this section cover sentence structure, usage, and mechanics. You will be asked to identify and correct errors that occur in sentences throughout the selection.
Directions and Sample Questions for Writing Skills, Part One
Directions: Choose the one best answer to each item.
Items 1 to 3 refer to the following paragraph.
(1) One of the lifelong memories many of us share are the moment we obtained a driver’s license. (2) If we were teenagers at the time, these licenses signified our passage to adulthood. (3) We clearly remember practicing to handle a car well in heavy traffic and learning to parallel park. (4) We also prepared for the test by studying the driver’s booklet, memorizing rules, and learning road signs. (5) Because we dreaded possible disaster, the road test seemed worse than the written test. (6) While conducting these difficult tests, the state driving inspectors often seemed stern and unyielding. (7) Therefore, when all the tests were finally over, we felt a real sense of achievement. (8)Whether or not we have chosen to use our licenses since then, they remain of enormous value to us. (9) They symbolize our passport both to independence and to the open road.
1. Sentence 1: One of the lifelong memories many of us share are the moment we obtained a driver’s license.
What correction should be made to this sentence?
(1) change the spelling of memories to memorys
(2) insert a comma after memories
(3) change are to is
(4) change driver’s to drivers
(5) no correction is necessary
Correct Answer: 3 Difficulty Level: Moderately difficult
About half of the questions in this section of the test ask you to find and correct any errors in the sentence. Because the subject of this sentence is One (not memorieS), the main verb in the sentence, (are) must agree in number. Thus, the correct answer is (3) 'change are to is.' Options 1, 2, and 4 introduce errors into the sentence, so none of these is the best answer. Notice that this item type has an alternative (5) 'no correction is necessary.' Choose this alternative when there is no error.
2. Sentence 3: We clearly-remember practicing to handle a car well in heavy traffic and learning to parallel park.
Which of the following is the best way to write the underlined portion of this sentence? If you think the original is the best way, choose option (1).
(1) traffic and learning
(2) traffic, but learning
(3) traffic, for learning
(4) traffic, so learning
(5) traffic because learning
Correct Answer: 1 Difficulty Level: Moderately difficult
This question asks you to select the best word to join the two parts of the sentence. The best answer can be found by determining which word makes the most sense. Only the word and produces a sentence in which the meaning is clear: the two things we remember are practicing to handle a car well and learning to parallel park. Since the relationship between the two parts of the sentence is one of addition, and is the best choice. Note that in this question, the original wording is the best of the choices given.
3. Sentence 7: Therefore, when all the tests were finally over, we felt a real sense of achievement.
If you rewrote sentence 7 beginning with
Therefore, we felt a real sense of achievement the next word should be
(1) or
(2) all
(3) when
(4) while
(5) but
Correct Answer: 3 Difficulty Level: Easy
Questions like this one require you to restate the original sentence in a particular way, often using a different type of sentence structure. The important point to remember here is that the new version must retain the meaning of the original sentence. In the case of question 3, the position of the two parts in the sentence is switched. Only the word 'when' keeps the same meaning. Every other choice creates either a nonsense sentence or one in which the meaning is different from the original. In these types of questions, it is always useful to try out each of the alternatives in the new structure. By reading through the entire revised sentence, you will be better able to see the effect of each of the options on the meaning of the sentence.
Test One, Part Two: The Essay
This part of the Writing Skills Test measures your ability to write an essay about an issue or situation of general interest. No special or technical knowledge is required to write on any of the topics. All of the topics used for this part of the test require you to write an essay that presents your opinion or explains your views about the topic assigned.
How the Essay Section Is Scored
All essays written for the GED Writing Skills Test are scored by at least two trained readers who score the essays on their overall effectiveness. They will judge how clearly you make the main point of your composition, how thoroughly you support your ideas, and how clearly and correctly you write. That is, all of the elements that make up a piece of writing are taken into consideration. The readers do not count every spelling and grammar mistake, but a paper with many errors may not receive a good score.
Essays must be written 'on topic' to receive a score. Pay attention to the topic and to the questions you are asked to answer about the topic. Plan your essay carefully, and allow yourself time to read it and make corrections.
After the readers have scored your paper, their combined score is the total essay score that, together with the score for the multiple-choice section, is the Writing Skills Test composite score.
Sample Topic for the Writing Skills Test, Part Two
It always strikes me as a terrible shame to see young people spending so much of their time staring at television. If we unplugged all the television sets, our children would grow up to be healthier, better educated, and more independent human beings.
Do you agree or disagree with this statement? Write a composition of about 200 words presenting your opinion and supporting it with examples from your own experience or your observations of others.
Description and Sample of Essay
The following paper would receive a rating of 3 (highest score is 6) based on the scoring guide. This typical paper has a single purpose or point to make. The supporting ideas are presented in clear sentences so that the reader understands what the writer wants to say. The paper would have been stronger if the writer had given the names of specific television programs that are informational or entertaining. The occasional mistakes in the conventions of standard written English do not interfere with the reader’s being able to understand what is written. These mistakes would have been corrected by a stronger writer.
Sample Essay
The question of whether or not television is a positive or negative factor in grow of our children, can have its points both ways. But I feel that the argument, that all the televisions sets should be unplugged, so that our children will grow up to be healthier, better educated, and more independent human beings, is ridiculous there are many informative, and educational and fun things to watch on television.
Television offers educational stations, which have very informative shows and programs, people can learn many things from some of the programs on television. The television is also used to translate news and other information to people, without the news you would not know about the world around you, politics, big events, weather etc. Even the movies and comedies provide entertainment and relaxation, and what better place than in your own home. I agree that some of the television today is none of the above, but the responsibility of what you watch is all up to you. Our children can grow up with television, but adults should help them learn how to choose shows that are going to be good. Television can be a very instrumental thing, it can provide fun and entertainment and also educational shows, that promote learning.
While the person scoring your essay does not count mistakes, these mistakes do influence the reader’s overall impression of the writing. For this reason, some of the errors in the sample essay are identified below for you.
The first sentence of the essay is not clear because of the use of grow for growth. The first sentence of any essay is the most important one because it states what the rest of the paper will say. This sentence should be very clear. In the second sentence, there is no reason or rule for the commas after 'unplugged' and 'beings.' If you don’t know a rule for the comma, leave it out. Also in the second sentence, the use of 'fun things' is too casual or colloquial compared to the rest of the words in the essay. Colloquial expressions may be misunderstood by a reader, so don’t use them. The next sentence which starts with 'Television offers' is actually two sentences or complete ideas joined together by the comma after 'programs.' This mistake shows that the writer is not sure about what a sentence really is. Then are other mistakes like these in the rest of the essay.
Everyone makes mistakes when they write quickly. Good writers take the time to go over what is written and correct mistakes. Your writing will show your best skills if you take the time to plan what you say and review it to make any needed corrections.
If you take the Official GED Practice Tests on your own, we recommend that you ask an adult education teacher to help you score your essay. The self-scoring answer sheet for Form CC of the Official GED Practice Tests has an essay scoring guide. See order information on the back page of this Bulletin.
TEST TWO: SOCIAL STUDIES
The GED Social Studies Test contains multiple-choice questions drawn from the following content areas.
* History
* Economics
* Political Science
* Geography
* Behavioral Sciences anthropology psychology sociology
(Note that there are different U.S. and Canadian versions of the GED Social Studies Test.)
Most of the questions in the Social Studies Test refer to information provided. The information may be a paragraph, or it may be a chart, table, graph, map, cartoon, or figure. In every case, to answer the questions in the Social Studies Test, you must understand, use, analyze, or evaluate the information provided.
Directions and Sample Questions for Social Studies
Directions: Choose the one best answer to each item.
Items 1 and 2 refer to the following information.
Five amendments to the U.S. Constitution directly affect voting qualifications.
The Fifteenth Amendment, ratified in 1870, prohibited states from using race or color as standards for determining the right to vote.
The Nineteenth Amendment, ratified in 1920, prohibited the states from using gender as a voting qualification.
The Twenty-Third Amendment, ratified in 1961, granted the residents of Washington, D.C., a voice in the selection of the President and Vice President.
The Twenty-Fourth Amendment, ratified in 1964, outlawed the state poll tax as a requirement for voting in national elections.
The Twenty-Sixth Amendment, ratified in 1971, prohibited states from denying the vote to anyone 18 years old or over.
1. The overall effect of the five amendments was to extend the vote to
(1) a larger portion of U.S. citizens
(2) a limited number of citizens
(3) tax-paying citizens
(4) citizens qualified by race and gender
(5) those citizens who must pay for the privilege
Correct Answer: 1 Difficulty Level: Easy
To answer question 1 correctly, you must read and understand all of the information provided regarding the five amendments to the U.S. Constitution. Then you must decide which of the options provided best states the overall effect of the amendments.
A careful reading of the amendments should indicate to you that, in each case, the effect of the amendment was to extend voting rights to more citizens. Option (2) is a correct statement (citizens under 18 are not able to vote), but Option (2) is not the best answer to the question. The best answer is Option (1) which describes the overall effect of the five amendments. The overall effect of these amendments was to provide voting rights to more citizens.
2. Which statement about the five amendments appears to be the best summary?
(1) They affirm the right of women to vote.
(2) They limit the right of U.S. citizens to vote according to where they live.
(3) They prohibit the use of certain requirements as voting qualifications.
(4) They prohibit some citizens from voting.
(5) They permit certain qualifications to be used in voting.
Correct Answer: 3 Difficulty Level: Difficult
The key word in question 2 is summary. This is important to recognize, because several of the options present correct and accurate statements, but only one presents the best summary.
Remember that an effective summary statement must provide the main points made by the information. In this case, the summary statement must address all five of the amendments. Only option (3) does this by referring to the prohibition of 'certain requirements as voting qualifications.'
Item 3 refers to the following information.
3. Which statement is supported by information in the graph?
(1) Most parents are employed.
(2) Most parents are satisfied with their child-care arrangements.
(3) A group center is the most common arrangement used by employed parents.
(4) Most employed parents arrange for child care either in their own home or in someone else’s home.
(5) About a quarter of all employed parents use child-care facilities at their place of work.
Correct Answer: 4 Difficulty Level: Moderately difficult
About one out of every three or four questions in the Social Studies Test will refer to a map, figure, chart, or graph.
This question requires you to evaluate each of the statements to determine which one can be supported by information in the graph. To do this, you must first understand what information is being provided in the graph.
Finding the correct answer is then a matter of testing each of the statements against the graph to see if it can be supported. In questions like this one, it is most important that you select your answer only on the basis of the information provided, not on the basis of opinions or prior knowledge.
In this case, the statement in option (4) is supported by the fact that the sections of the graph that relate to the child’s own home or another home add up to 70.8%, which accounts for most parents.
TEST THREE: SCIENCE
The GED Science Test contains multiple-choice questions drawn from the following content areas:
* Biology
* Earth Science
* Physics
* Chemistry
All questions in the Science Test require you to use information provided in the test question or learned through life experience. The information may be a paragraph, or it may be a chart, table, graph, map, or figure. In every case, to answer the questions in the Science Test, you must understand the information provided or use the information to solve a problem or make a judgment.
Directions and Sample Questions for Science
Choose the one best answer to each item.
Item 1 is based on the following figure.
1. A large fiberglass tank was placed in a pit as shown in the diagram above. Before pipes could be attached and the tank filled with gasoline, the workers were asked to move the tank to another location.
Which of the following suggestions would be the best way to raise the tank off the bottom of the pit so cables could be placed under the tank?
(1) Fill the tank with gasoline.
(2) Fill the tank with water.
(3) Fill the pit with water.
(4) Fill the pit with water and the tank with gasoline.
(5) Fill both the pit and the tank with water.
Correct Answer: 3 Difficulty Level: Easy
Typical of most questions in the Science Test, this physics question presents a practical problem that must be solved. To answer the question correctly, you must be able to understand the key features of the figure and understand the physical reaction that will result from each of the proposed solutions.
Option (3) is the best answer because the method it proposes is most likely to cause the tank to float off the bottom of the pit. By filling the pit with water and leaving the tank filled only with air, the tank becomes buoyant and is likely to rise off the bottom of the pit so that cables can be placed under the tank.
2. An electric current releases heat to the wire in which it is traveling.
Which of the following electric appliances would best illustrate an application of the above statement?
(1) mixer
(2) clock
(3) vacuum
(4) toaster
(5) fan
Correct Answer: 4 Difficulty Level: Easy
Many of the questions in the Science Test, like this one, provide a scientific principle, followed by a question or problem regarding its application. Only one of the appliances named in the options--the toaster--uses heat produced by the electric current in the wire. In this sense, the toaster best illustrates an application of the principle. All of the appliances named in the other options contain wires which undoubtedly release heat, but the heat is a by-product and not central to the intended purpose of the appliance.
Item 3 refers to the following graph.
3. According to the graph above, which of the following colors of light is absorbed the least by a plant?
(1) red
(2) yellow
(3) green
(4) blue
(5) violet
Correct Answer: 3 Difficulty Level: Difficult
To answer this biology question correctly, you must first read and correctly interpret the graph that is provided. First, note that the question calls for you to identify the color absorbed the least. Next, notice the labels that identify the vertical and horizontal axes of the graph. You must recognize that the label on the vertical axis, 'Percentage of Light Absorbed,' is a measure of the quantity of light absorbed. Following the line graph to its lowest point, you can see that that point is closest to the label 'green' on the horizontal axis.
TEST FOUR: INTERPRETING LITERATURE AND THE ARTS
The GED Interpreting Literature and the Arts Test contains multiple-choice questions drawn from three content areas:
* Popular Literature
* Classical Literature
* Commentary
The questions measure your ability to understand and analyze what you read.
While most literature selections are drawn from American authors, English and Canadian authors are also represented, as are translations of important works from throughout the world. Popular and classical literature selections include fiction, prose nonfiction, poetry, and drama. Materials in the Commentary section include prose excerpts about literature and the arts.
Directions and Sample Questions for Interpreting Literature and the Arts
Direction: Choose the one best answer to each item.
Items 1 to 3 refer to the following excerpt from an essay.
WHAT WAS THE AMERICAN SMALL TOWN LIKE?
I’m glad I was born soon enough to have seen the American small town, if not at its height, at least in the early days of decline into its present forlorn status as a conduit for cars and people, all headed for some Big City over the horizon. The small town was not always a stultifying trap for bright young people to escape from; in the years before wartime travel ('How’re you gonna keep’em down on the farm/After they’ve seen Paree?') and the scorn of the Menckens and Sinclair Lewises made the cities a magnet for farm boys and girls, the town of five to twenty thousand was a selfsufficient little city-state of its own.
The main street of those Midwestern towns I remember from the thirties varied little from one place to another: there were always a number of brick Victorian buildings, labeled 'Richard’s Block' or 'Denman Block,' which housed, downstairs, the chief emporia of the town--the stores which made it a shire town for the surrounding farmlands. Each of these stores was run according to a very exact idea of the rules of its particular game. A hardware store, for instance, had to be densely hung inside with edged tools--scythes, sickles, saws--of all descriptions. It had to smell of oil, like metal, and often like the sacks of fertilizer stacked in the back room. It had to have unstained wood floors, sometimes sprinkled with sawdust, and high cabinets of small drawers containing bolts, screws, nails, and small plumbing accessories. It had to be owned and run by a middle-aged man in a blue apron, assisted by one up-and-coming young man and one part-time boy in his middle teens. It had to sell for cash on the barrelhead, and it did.
The drugstore was a horse of a different color (and order), but it was circumscribed by equally strict rules. Here you would ask the white-coated and (often rimless-spectacles) druggist for aspirin or Four-Way Cold Tablets or Bromo-Seltzer, or perhaps for paramedical advice, which he was glad to give....
These towns are by and large gone in 1974, their old stores shut up with dusty windows, or combined, two or three at a time, to make a superette, a W.T. Grant store, or a sub-and-pizza parlor. The business has moved to the big shopping center on the Interstate or on to the city over the horizon, and the depopulated old towns drift along toward oblivion, centers of nothing in the middle of nowhere.
From 'Int’l Jet Set Hits Watkins Glen' by L.E. Sissman in Selections From 119 Years of the Atlantic. Copyright * 1974. Used by permission.
1. According to the essay, what is the major reason for the decline of the American small town?
(1) Cars made people more mobile.
(2) Lack of variation from one town to another drove people away.
(3) Big cities drew people away from the towns.
(4) Their main streets were all the same.
(5) Writers criticized small town life.
Correct Answer: 3 Difficulty Level: Easy
Many of the questions on the Interpreting Literature and the Arts Test are like this one: they require you show that you understand an important idea contained in the selection. The idea may or may not be directly stated in the selection.
The information needed to answer this question is contained mainly in the first paragraph of the selection, where the author comments briefly on what drew people away from the small towns. It is here in the first paragraph that the author refers to the way the cities lured people away from the small towns.
As stated in option (3), big cities drew people away from the towns for many reasons; the way small towns were referred to in writings of the time was only one of the reasons. Option (3) is the best answer because only this answer offers the major reason.
2. How does the author feel about the American small town?
(1) angry
(2) nostalgic
(3) spiteful
(4) embarrassed
(5) relieved
Correct Answer: 2 Difficulty Level: Moderately difficult
The writer’s attitude toward the subject, or the way he or she feels about it, is another area about which questions are asked in the Interpreting Literature and the Arts Test. Rarely does an author directly state his or her feelings about this subject. Instead, you must detect or infer those feelings from the way the author writes about the subject. Answering questions like this one requires an understanding of the total selection.
The writer’s attitude comes through clearly throughout the selection. In stating that he was happy to have seen the small town 'at its height,' the author is making clear his positive attitude toward the subject. In addition, the use of the term 'forlorn' in the first sentence suggests a sadness regarding something wonderful that has passed by. Only option (2), nostalgic, expresses this attitude towards the subject.
3. Given the descriptions of the small town stores, the author would most likely view modern shopping malls as places
(1) catering to small town people
(2) taking over the role of small farm stores
(3) lacking the friendliness of small town stores
(4) providing variety and sophistication to small town clients
(5) carrying on the tradition of small town stores
Correct Answer: 3 Difficulty Level: Difficult
Several questions in the Interpreting Literature and the Arts Test ask you to use your understanding of the reading selection to predict how the author or a character will act in a different situation. The detailed descriptions of small town stores provided in the second and third paragraphs of the selection emphasize their neighborliness and emphasis on personal service. Since the author views the decline of the small town as a source of regret, it is most likely that he would view modern shopping malls as places that lack the features that characterize small town stores. Option (3) expresses this idea best.
TEST FIVE: MATHEMATICS
The GED Mathematics Test measures the ability to solve--or find the best method to solve--mathematics problems typical of those studied in high school mathematics courses. Subject matter for the GED Mathematics Test questions is drawn from three areas:
* Arithmetic
measurement numeration data analysis
* Algebra
* Geometry
Directions and Sample Questions for Mathematics
Choose the one best answer to each item.
1. If 10% of a town’s population of 10,000 people moved away, how many people remained in the town?
(1) 100
(2) 900
(3) 1000
(4) 9000
(5) 9900
Correct Answer:. 4 Difficulty Level: Moderately Difficult
This is an example of a question involving computations with percentages. Like most of the questions in the Mathematics Test, solving the problem involves more than one step.
Here is one method you could use to solve this problem. First, you must compute 10% of 10,000. You can probably do this mentally; if not, you could divide 10,000 by 10 or multiply 10,000 by. 10.
Now you know that 1000 people moved, but notice that the question asks for the number that remained in the town. So, you must subtract 1000 from the total population of 10,000 to find the correct answer of 9000 (option 4).
Item 2 is based on the following graph.
2. The figure above shows how the tax dollar was spent in a given year. According to the figure, what percent of the tax dollar was left after direct payment to individuals and national defense expenses?
(1) 3%
(2) 11%
(3) 33%
(4) 67%
(5) 114%
Correct Answer: 3 Difficulty Level: Easy
About one-third of the questions in the Mathematics Test will refer to charts, tables, or graphic materials like this one. This question requires, first, that you understand the information presented in the pie graph and recognize that the five categories of spending described in the graph equal 100%. Next, the phrase 'was left' in the question should indicate to you that the problem requires subtraction. The sum of the 42% indicated as 'Direct Benefit Payments to Individuals' and the 25% indicated as 'National Defense,' is 67%. Subtracting 67% from 100% yields a result of 33%. Thus, option (3) is the correct answer.
3. A part-time job pays $6.75 per hour. Which of the following expressions best represents an employee’s total earnings if the employee works 2 hours on Monday, 3 hours on Tuesday, 4 hours on Wednesday, 5 hours on Thursday, and 6 hours on Friday?
(1) 2+3+4+5+6
(2) 10 + 6.75
(3) 10(6.75)
(4) 20 + 6.75
(5) 20(6.75)
Correct Answer: 5 Difficulty Level: Easy
Some questions in the Mathematics Test, like this one, do not ask for a numerical solution to the problem. Instead, they ask you to select the best method for setting up the problem to arrive at a correct solution.
The first step here is to identify exactly what answer is required. In this case, it is the underlined phrase total earnings. Next, you must understand that total earnings will be the product (multiplication) of the hourly rate of $6.75 times the number of hours worked.
Understanding how total earnings is computed Will make clear to you that the solution to the problem must include the number 6.75 multiplied by some other number. The other number is the sum of 2 + 3 + 4 + 5 + 6 (the number of hours worked), or 20. So, option (5) is the correct answer.
Options (1), (2), and (4) do not indicate multiplication as a function, while option (3) uses an incorrect number of hours as a multiplier of the hourly rate.
HOW ARE GED SCORES REPORTED?
Separate scores are reported for each of the five GED Tests. GED Test results are reported on a standard score scale ranging from 20 (lowest possible score) to 80 (highest possible score). Your score on the GED Tests is not the number of correct answers or the percent correct. The Writing Skills Test score is a statistical combination of the number of questions answered correctly on the multiple-choice section with the score on the essay section (see 'How the Essay Section Is Scored' on page 6). The score for all other tests in the GED battery is based only on the number of multiple-choice questions answered correctly.
WHAT SCORE DO I NEED TO PASS?
Passing scores for the GED Tests are established by the states, provinces, and territories that administer the GED Testing Program. In general, if you answer 60 percent of the questions correctly on each test, you will earn a passing score. Your local GED Testing Center or adult education program can tell you what the minimum required standard scores are for your area. Most current requirements are set so that GED examinees must earn scores higher than those of about 30 percent of today’s high school graduates to earn a GED Diploma.
Though the score requirements vary from one jurisdiction to another, most requirements are stated in terms of a minimum score for each test and/or a minimum average score for all five tests. For example, a common passing standard score required in any state, province, or territory is 35 on any one test and an average of 45 on all five tests. If this were the score requirement in your area, you would need to achieve a standard score of at least 35 on each of the five tests and a total of at least 225 for all five tests to achieve an average of 45.
HOW SHOULD I INTERPRET MY SCORES?
Your GED Test score is an estimate of your knowledge and skills in the areas tested as compared to the knowledge and skills of recent high school graduates. As with any test, the scores are not intended to be a complete and perfect measure of all you know and can do. Rather, the GED Tests provide an estimate of your educational achievements, as compared to those of high school graduates. In fact, if you take a different form of the test covering the same content areas with slightly different questions, it is likely that your score will be slightly different.
If you take the GED Tests and do not achieve the minimum passing score required by your state, province, or territory, contact your local adult education center for assistance in interpreting your scores so that you can improve your performance in the future.
If you are taking the GED Tests for college or university admission, check with the institution you plan to attend to find out the minimum scores required for admission.
WHAT CAN I DO BEFORE TAKING THE TESTS?
Familiarize yourself with the content of the tests. You can do this in two ways. First, review the content descriptions and sample test questions in this Bulletin. The questions included here are typical of the type and difficulty of questions you will find in the actual GED Tests. Second, take the Official GED Practice Tests, either through your local adult education program or by yourself. When you take the Practice Tests, be sure to follow the time limits given in the directions. In this way, you will be able to get an accurate sense of what taking the actual GED Tests will be like, what the questions will look like, and how much time you’ll have to work on the questions. While working on the Official GED Practice Tests, try out some of the strategies suggested in this Bulletin.
* Spend time reading newspapers and news magazines. Many of the articles in these publications are similar to those used in the GED Tests.
* Don’t worry too much. A little test anxiety is normal and may be a good thing, because it makes you more alert and motivates you to do your best. To keep anxiety from getting out of hand:
-- Become familiar with the content of the tests.
-- Prepare for the tests as fully as you can. When you have done all you can, relax; if you have prepared well, you will do well.
-- Remember that there are no 'trick' questions on the tests so you don’t have to worry about being 'fooled' by the questions.
-- Remember that you don’t have to answer every question correctly to pass.
* Come to the testing session physically and mentally alert. The GED Tests are designed to measure skills acquired over a long period of time. 'Cramming' the night before will probably not help.
WHAT CAN I DO WHILE TAKING THE TESTS?
Try using some of the following strategies to help you do your best while you are taking the GED Tests.
Test-Taking Strategies
* Answer every question. Scores are based only on the number of questions answered correctly; there is no penalty for guessing.
* Read the test directions carefully for each section of the test.
* Be sure you know what the question asks for before selecting an answer. Pay particular attention to any portions of the question that may be underlined or printed in capital letters.
* Briefly scan the text or figure that accompanies the question; then read the questions and options to see what information you will need. Next, return to the text or figure for a more careful reading.
* Draw figures or charts--or list key facts--on scratch paper.
* Use your time wisely. Budget your time so that you are able to finish the test within the time permitted. Skip difficult questions and return to them near the end of the testing period.
* Remember that you are looking for the one best answer.
* For the Essay Section of the Writing Skills Test:
-- Organize your essay as a direct answer to the topic assigned. Your essay should state your answer and then explain why you answered the way you did.
-- Be sure your explanation supports your answer. For example, if you were writing on the topic on page 6 in this Bulletin and your essay included the statement that too much television is bad for children, you should provide reasons and examples that show how television harms children.
-- Use details and examples that show the reader what, why, and how. The more convincing your essay is, the more effective it is. Whatever the specific subject of the essay question may be, think of your essay as an attempt to convince the reader of the correctness of your answer.
* For the Mathematics Test:
-- Look over the answer choices before beginning to figure out the answer. See how exact you need to be. For example, instead of an answer carried to three decimal places, the options may simply present whole numbers. This will save you time in arriving at a solution.
-- Check your answer to see if it 'makes sense' in the context of the problem. For example, if your computation indicates that a one-pound bag of carrots will cost $25, you should recognize that you’ve made an error because the figure of $25 for a bag of carrots does not make sense.
-- Use the formulas page provided in the front of the Mathematics Test. You will need to determine which, if any, of the formulas to use to solve a problem, but you do not have to memorize the formulas.
-- Use your personal experience to help solve the problems. The settings used for the problems in the Mathematics Test are usually realistic. For example, in a problem that requires you to compute weekly earnings, ask yourself, 'how would I figure my weekly earnings?'

Helping Your Child Learn Math

Helping your Child Learn Math
with activities for children aged 5 through 13
By Patsy F. Kanter
Foreword
'Why?'
This is the question we parents are always trying to answer. It’s good that children ask questions: that’s the best way to learn. All children have two wonderful resources for learning--imagination and curiosity. As a parent, you can awaken your children to the joy of learning by encouraging their imagination and curiosity.
Helping Your Child Learn Math is one in a series of books on different education topics intended to help you make the most of your child’s natural curiosity. Teaching and learning are not mysteries that can only happen in school. They also happen when parents and children do simple things together.
For instance, you and your child can: sort socks on laundry day--sorting is a major function in math and science; cook a meal together--cooking involves not only math and science but good health as well; tell and read each other stories--storytelling is the basis for reading and writing (and a story about the past is also history); or play a game of hopscotch together--playing physical games will help your child learn to count and start on a road to lifelong fitness.
By doing things together, you will show that learning is fun and important. You will be encouraging your child to study, learn, and stay in school.
All of the books in this series tie in with the National Education Goals set by the President and the Governors. The goals state that, by the year 2000: every child will start school ready to learn; at least 90 percent of all students will graduate from high school; each American student will leave the 4th, 8th, and 12th grades demonstrating competence in core subjects; U.S. students will be first in the world in math and science achievement; every American adult will be literate, will have the skills necessary to compete in a global economy, and will be able to exercise the rights and responsibilities of citizenship; and American schools will be liberated from drugs and violence so they can focus on learning.
This book is a way for you to help meet these goals. It will give you a short rundown on facts, but the biggest part of the book is made up of simple, fun activities for you and your child to do together. Your child may even beg you to do them. At the end of the book is a list of resources, so you can continue the fun.
As U.S. Education Secretary Lamar Alexander has said:
The first teachers are the parents, both by example and conversation. But don’t think of it as teaching. Think of it as fun.
So, let’s get started. I invite you to find an activity in this book and try it.
Diane Ravitch Assistant Secretary and Counselor to the Secretary
Contents
Foreword
Introduction
The Basics
Important Things To Know
Math in the Home
Picture Puzzle More or Less Problem Solvers Card Smarts Fill It Up Haft Full, Haft Empty Name that Coin Money Match Money’s Worth In the News Look It Up Newspaper Search Treasure Hunt Family Portrait
Mathland: The Grocery Store
Get Ready Scan It Weighing In Get into Shapes Check Out It’s in the Bag Put It Away
Math on the Go
Number Search License Plates Total It How Long? How Far? Guess If You Can
Appendices
Parents and the Schools What Should I Expect from a Math Program? Resources
Acknowledgments
Introduction
Most parents will agree that it is a wonderful experience to cuddle up with their child and a good book. Few people will say that about flash cards or pages of math problems. For that reason, we have prepared this booklet to offer some math activities that are meaningful as well as fun. You might want to try doing some of them to help your child explore relationships, solve problems, and see math in a positive light. These activities use materials that are easy to find. They have been planned so you and your child might see that math is not just work we do at school but, rather, a part of life.
It is important for-home and school to join hands. By fostering a positive attitude about math at home, we can help our children learn math at school.
It’s Everywhere! It’s Everywhere!
Math is everywhere and yet, we may not recognize it because it doesn’t look like the math we did in school. Math in the world around us sometimes seems invisible. But math is present in our world all the time--in the workplace, in our homes, and in life in general.
You may be asking yourself, 'How is math everywhere in my life? I’m not an engineer or an accountant or a computer expert!' Math is in your life from the time you wake until the time you go to sleep. You are using math each time you set your alarm, buy groceries, mix a baby’s formula, keep score or time at an athletic event, wallpaper a room, decide what type of tennis shoe to buy, or wrap a present. Have you ever asked yourself, 'Did I get the correct change?' or 'Do I have enough gasoline to drive 20 miles?' or 'Do I have enough juice to fill all my children’s thermoses for lunch?' or 'Do I have enough bread for the week?' Math is all this and much, much more.
How Do You Feel About Math?
How do you feel about math? Your feelings will have an impact on how your children think about math and themselves as mathematicians. Take a few minutes to answer these questions:
* Did you like math in school?
* Do you think anyone can learn math?
* Do you think of math as useful in everyday life?
* Do you believe that most jobs today require math skills?
If you answer 'yes' to most of these questions, then you are probably encouraging your child to think mathematically. This book contains some ideas that will help reinforce these positive attitudes about math.
You Can Do It!
If you feel uncomfortable about math, here are some ideas to think about.
Math is a very important skill, one which we will all need for the future in our technological world. It is important for you to encourage your children to think of themselves as mathematicians who can reason and solve problems.
Math is a subject for all people. Math is not a subject that men can do better than women. Males and females have equally strong potential in math.
People in the fine arts also need math. They need math not only to survive in the world, but each of their areas of specialty requires an in-depth understanding of some math, from something as obvious as the size of a canvas, to the beats in music, to the number of seats in an audience, to computer-generated artwork.
Calculators and computers require us to be equally strong in math. Theft presence does not mean there is less need for knowing math. Calculators demand that people have strong mental math skills--that they can do math in their heads. A calculator is only as accurate as the person putting in the numbers. It can compute; it cannot think! Therefore, we must be the thinkers. We must know what answers are reasonable and what answers are outrageously large or small.
Positive attitudes about math are important for our country. The United States is the only advanced industrial nation where people are quick to admit that 'I am not good in math.' We need to change this attitude, because mathematicians are a key to our future.
The workplace is rapidly changing. No longer do people need only the computational skills they once needed in the 1940s. Now workers need to be able to estimate, to communicate mathematically, and to reason within a mathematical context. Because our world is so technologically oriented, employees need to have quick reasoning and problem-solving skills and the capability to solve problems together. The work force will need to be confident in math.
Build Your Self-Confidence!
To be mathematically confident means to realize the importance of mathematics and feel capable of learning to
* Use mathematics with ease;
* Solve problems and work with others to do so;
* Demonstrate strong reasoning ability;,
* See more than one way to approach a problem;
* Apply mathematical ideas to other situations; and
* Use technology.
The Basics
You may have noticed that we are talking about 'mathematics'--the subject that incorporates numbers, shapes, patterns, estimation, and measurement, and the concepts that relate to them. You probably remember studying 'arithmetic'--adding, subtracting, multiplying, and dividing--when you were in elementary school. Now, children are starting right away to learn about the broad ideas associated with math, including problem solving, communicating mathematically, and reasoning.
Kindergartners are building bar graphs of birthday cakes to show which month has the most birthdays for the most children in the class. Second graders are using pizzas to learn fractions, and measurements are being taken using items other than rulers (for example, the illustrator of this book used his thumb to determine how large the pictures of the pizzas should be in proportion to the size of the words on the activities pages).
What Does It Mean To
* Be a Problem Solver,
* Communicate Mathematically, and
* Demonstrate Reasoning Ability?
A problem solver is someone who questions, investigates, and explores solutions to problems; demonstrates the ability to stick with a problem for days, if necessary, to find a workable solution; uses different strategies to arrive at an answer; considers many different answers as possibilities; and applies math to everyday situations and uses it successfully.
To communicate mathematically means to use words or mathematical symbols to explain real life; to talk about how you arrived at an answer; to listen to others’ ways of thinking and perhaps alter their thinking; to use pictures to explain something; to write about math, not just give an answer.
To demonstrate reasoning ability is to justify and explain one’s thinking about math; to think logically and be able to explain similarities and differences about things and make choices based on those differences; and to think about relationships between things and talk about them.
How Do I Use this Book?
This book is divided into introductory material that explains the basic principles behind the current approach to math, sections on activities you can do with your children, and lists of resources. The activities take place in three locations: the home, the grocery store, and in transit.
The activities are arranged at increasingly harder levels of difficulty. Look for the circles, squares, and triangles that indicate the level of difficulty. The means that a child in kindergarten through 1st grade could probably play the game, the is for those in grades 2 and 3, and the signals an activity for a child in grades 4 through 8.
The activities you choose and the level of difficulty really depend on your child’s ability if your child seems ready, you might want to go straight to the most difficult ones.
The shaded box on an activity page contains the answer or a simple explanation of the mathematical concept behind the activity so that you can explain when your child asks, 'Why are we doing this?'
With these few signs to follow along the way, your math journey begins.
Important Things To Know
It is highly likely that when you studied math, you were expected to complete lots of problems accurately and quickly. There was only one way to arrive at your answers, and it was believed that the best way to improve math ability was to do more problems and to do them fast. Today, the focus is less on the quantity of memorized problems, and more on understanding the concepts and applying thinking skills to arrive at an answer.
Wrong Answers Can Help!
While accuracy is always important, a wrong answer may help you and your child discover what your child may not understand. You might find some of these thoughts helpful when thinking about wrong answers.
Above all be patient. All children want to succeed. They don’t want red marks or incorrect answers. They want to be proud and to make you and the teacher proud. So, the wrong answer tells you to look further, to ask questions, and to see what the wrong answer is saying about the child’s understanding.
Sometimes, the wrong answer to a problem might be because the child thinks the problem is asking another question. For example, when children see the problem 4 + ___ = 9, they often respond with an answer of 13. That is because they think the problem is asking What is 4+9?', instead of '4 plus what missing amount equals 9?'
Ask your child to explain how the problem was solved. The response might help you discover if your child needs help with the procedures, the number facts, or the concepts involved.
You may have learned something the teacher might find helpful. A short note or call will alert the teacher to possible ways of helping your child.
Help your children be risk takers: help them see the value of examining a wrong answer; assure them that the right answers will come with proper understanding.
Problems Can Be Solved Different Ways
Through the years, we have learned that while problems in math may have only one solution, there may be many ways to get the right answer. When working on math problems with your child, ask, 'Could you tell me how you got that answer?' Your child’s way might be different than yours. If the answer is correct and the strategy or way of solving it has worked, it is a great alternative. By encouraging children to talk about what they are thinking, we help them to become stronger mathematicians and independent thinkers.
Doing Math in Your Head Is Important
Have you ever noticed that today very few people take their pencil and paper out to solve problems in the grocery, fast food, or department store or in the office? Instead, most people estimate in their heads.
Calculators and computers demand that people put in the correct information and that they know if the answers are reasonable. Usually people look at the answer to determine if it makes sense, applying the math in their heads to the problem. This, then, is the reason why doing math in their heads is so important to our children as they enter the 21st century.
You can help your child become a stronger mathematician by trying some of these ideas to foster mental math skills:
1. Help children do mental math with lots of small numbers in their heads until they develop quick and accurate responses. Questions such as, 'If I have 4 cups, and I need 7, how many more do I need?' or 'If I need 12 drinks for the class, how many packages of 3 drinks will I need to buy?'
2. Encourage your child to estimate the answer. When estimating, try to use numbers to make it easy to solve problems quickly in your head to determine a reasonable answer. For example, when figuring 18 plus 29, an easy way to get a 'close' answer is to think about 20 + 30, or 50.
3. As explained earlier, allow your. children to use strategies that make sense to them.
4. Ask often, 'Is your answer reasonable?' Is it reasonable that I added 17 and 35 and got 367? Why? Why not?
What Jobs Require Math?
All jobs need math in one way or another. From the simplest thought of how long it will take to get to work to determining how much weight a bridge can hold, all jobs require math.
If you took a survey, you would find that everyone uses math: the school teacher, the fast food worker, the doctor, the gas station attendant, the lawyer, the housewife, the painter.
Math in the Home
This section provides the opportunity to use games and activities at home to explore math with your child. The activities are intended to be fun and inviting, using household items. Please note that the activities for K-1st grade are marked with a , the activities for grades 2 and 3 with a , and activities for grades 4 through 8 with a .
Remember,
* This is an opportunity for you and your child to 'talk math,' that is to communicate about math while investigating relationships.
* If something is too difficult, choose an easier activity or skip it until your child is older.
* Have fun!
Picture Puzzle
Using symbols to stand for numbers can help make math fun and easier for young children to understand.
What you’ll need
Paper Pencil Crayons
What to do
1. Choose some symbols that your child can easily draw to stand for 1s and 10s (if your child is older, include 100s and 1,000s).
A face could 10s, and a bow could be 1s.
2. List some numbers and have your child depict them.
For example:
More or Less
Playing cards is a fun way for children to use numbers.
What you’ll need
Coin 2 decks of cards Scratch paper to keep score
What to do
1. Flip a coin to tell if the winner of this game will be the person with 'more' (a greater value card) or 'less' (a smaller value card).
2. Remove all face cards (jacks, queens, and kings) and divide the remaining cards in the stack between the two players.
3. Place the cards face down. Each player turns over one card and compares: Is mine more or less? How many more? How many less?
This game for young children encourages number sense and helps them learn about the relationships of numbers (more or less) and about adding and subtracting. By counting the shapes on the cards and looking at the printed numbers on the card, they can learn to relate the number of objects to the numeral.
Problem Solvers
These games involve problem solving, computation, understanding number values, and chance.
What you’ll need
Deck of cards Paper Pencil
What to do
1. Super sums. Each player should write the numbers 1-12 on a piece of paper. The object of the game is to be the first one to cross off all the numbers on this list.
Use only the cards 1-6 in every suit (hearts, clubs, spades, diamonds). Each player picks two cards and adds up the numbers on them. The players can choose to mark off the numbers on the list by using the total value or crossing off two or three numbers that make that value. For example, if the player picks a 5 and a 6, the player can choose to cross out 11, or 5 and 6, or 7 and 4, or 8 and 3, or 9 and 2, or 10 and 1, or 1, 2, and 8.
2. Make 100. Take out all the cards from the deck except ace through 6. Each player draws 8 cards from the deck. Each player decides whether to use a card in the tens place or the ones place so that the numbers total as close to 100 as possible without going over. For example, if a player draws two 1s (aces), a 2, a 5, two 3s, a 4, and a 6, he can choose to use the numerals in the following way:
30, 40, 10, 5, 6, 1, 3, 2. This adds up to 97.
These games help children develop different ways to see and work with numbers by using them in different combinations to achieve a goal.
Card Support
Have your children sharpen their math skills even more.
What you’ll need
Deck of cards Paper Pencil
What to do
1. How many numbers can we make? Give each player a piece of paper and a pencil. Using the cards from 1 (ace)-9, deal 4 cards out with the numbers showing. Using all four cards and a choice of any combination of addition, subtraction, multiplication, and division, have each player see how many different answers a person can get in 5 minutes. Players get one point for each answer. For example, suppose the cards drawn are 4, 8, 9, and 2. What numbers can be made?
4+9+8+2=23 4+9-(8+2)=3 (8-4)x(9-2)=28 (9-8)x(4-2)=2
2. Make the most of it. This game is played with cards from 1 (ace) to 9. Each player alternates drawing one card at a time, trying to create the largest 5-digit number possible. As the cards are drawn, each player puts the cards down in their 'place' (ten thousands, thousands, hundreds, tens, ones) with the numbers showing. One round goes until each player has 6 cards. At that point, each player chooses one card to throw out to make the largest 5-digit number possible.
3. Fraction fun. This game is played with cards 1 (ace)-10, and 2 players. Each player receives one-half of the cards. Players turn over 2 cards each at the same time. Each player tries to make the largest fraction by putting the 2 cards together. The players compare their fractions to see whose is larger. For example, if you are given a 3 and a 5, the fraction 3/5 would be made; if the other person is given a 2 and an 8, the fraction is 2/8. Which is larger? The larger fraction takes all cards and play continues until one player has all the cards.
Players can develop strategies for using their cards, and this is where the math skills come in.
Fill It Up
Children enjoy exploring measurement and estimation. Empty containers can provide opportunities to explore comparisons, measurement, estimation, and geometry.
What you’ll need
Empty containers in different shapes (yogurt cups, margarine tubs, juice boxes with tops cut off, pie tins) Rice, popcorn kernels, or water Marker Masking tape Paper
What to do
1. Have your child choose an empty container each day and label it for the day by writing the day on a piece of masking tape and sticking it on the container.
2. Discover which containers hold more than, less than, or the same as the container chosen for that day by
filling the day’s container with water, uncooked rice, or popcorn kernels; and
pouring the substance from that container into another one. Is the container full, not full, or overflowing? Ask your child, 'Does this mean the second container holds more than the first, less, or the same?'
3. Ask your child questions to encourage comparison, estimation, and thinking about measurement.
4. Put all the containers that hold more in one spot, those that hold less in another, and those that hold the same in yet another. Label the areas 'more,' 'less,' and 'the same?
5. After the containers have been sorted, ask, 'Do we have more containers that hold more, hold less, or hold the same? How many containers are in each category?'
The process of predicting, filling the containers, and comparing how much each will hold, gives your child the opportunity to experiment with measurement without worrying about exact answers.
Half Full, Half Empty
It is helpful to explore whole numbers and fractions through measurement and estimation. Children can see relationships and the usefulness of studying fractions.
What you’ll need
Clear container with straight sides, that holds at least 4 cups Masking tape Marker Measuring cup with 1, 1/2, 1/4, 1/8 cup measures on it Uncooked rice, popcorn kernels, or water Other containers with which to compare
What to do
1. Have your child run a piece of masking tape up the side of the container so that it is straight from the bottom to the top.
2. For younger children, use a 1-cup measure. For older children, use a 1/2, 1/4, and 1/8 cup measure. Pour the chosen amount of a substance listed above into the container.
3. Mark the level of the jar on the masking tape by drawing a line with a marker and writing 1 for one cup or 1/2, 1/4, or 1/8 on the line.
4. Follow this procedure until the container is full, and the tape is marked in increments to the top of the container. Now, the jar is marked evenly to measure the capacity of other containers.
5. While filling different containers, ask your child 'thinking' questions.
How many whole cups do you think this container will hold?
How many 1/2, 1/4, or 1/8 cups do you think the container will hold?
How many 1/2 cups equal a cup?
How many 1/4 cups equal a 1/2 cup? A cup? How many 1/8 cups equal a 1/4 cup? A 1/2 cup? A 1/8 cup?
This activity provides a 'hands-on' opportunity for children to experience fractions while making connections to the real world.
Name that Coin
Children love to look at coins but sometimes cannot identify the coins or determine their value.
What you’ll need
Penny Nickel Dime Quarter
What to do
1. Look at the coins and talk about what color they are, the pictures on them, and what they are worth.
2. Put a penny, nickel, and dime on the floor or table.
3. Tell your child that you are thinking of a coin.
4. Give your child hints to figure out which coin you are thinking of. For example, 'My coin has a man on one side, a building on the other.'
5. Let your child think about what you have said by looking at the coins.
6. Ask, 'Can you make a guess?'
7. Add another clue: 'My coin is silver.'
8. Keep giving clues until your child guesses the coin.
9. Add the quarter to the coins on the table and continue the game.
10. Have your child give you clues for you to guess the coin.
This guessing game helps young children learn to recognize coins and develop problem-solving and higher level thinking skills.
Money Match
This game helps children count change. Lots of repetition will make it even more effective.
What you’ll need
A die to roll 10 of each coin (penny, nickel, dime) 6 quarters
What to do
1. For young players (5- and 6-year-olds), use only 2 different coins (pennies and nickels or nickels and dimes). Older children can use all coins.
2. Explain that the object of the game is to be the first player to earn a set amount (10 or 20 cents is a good amount).
3. The first player rolls the die and gets the number of pennies shown on the die.
4. Players take turns rolling the die to collect additional coins.
5. As each player accumulates 5 pennies or more, the 5 pennies are traded for a nickel.
6. The first player to reach the set amount wins.
7. Add the quarter to the game when the children are ready.
Counting money, which involves counting by 1s, 5s, 10s, and 25s, is a challenging skill and usually does not come easily to children until about the third grade.
Money’s Worth
When children use coins to play games, it may help them use coins in real life situations.
What you’ll need
Coins Coupons
What to do
1. Coin clues. Ask your child to gather some change in his or her hand without showing what it is. Start with amounts of 25 cents or less. Ask your child to tell you how much money and how many coins there are. Guess which coins are being held. For example, 'I have 17 cents and 5 coins. What coins do I have?' (3 nickels and 2 pennies.)
2. Clip and save. Cut out coupons and tell how much money is saved with coins. For example, if you save 20 cents on detergent, say 2 dimes. Ask your child what could be purchased using the savings from the coupon. A pack of gum? A pencil? How much money could be saved with 3, 4, or 5 coupons? How could that money be counted out in coins and bills? What could be purchased with that savings? A pack of school paper? A magazine? How much money could be saved with coupons for a week’s worth of groceries? How would that money be counted out? What could be purchased with that savings? A book? A movie ticket?
Counting money involves thinking in patterns or groups of amounts: 1s, 5s, 10s, 25s. Start these activities by having your child first separate the coins or coupons by types: all the pennies together, all the nickels, all the dimes, all the quarters; the coupons for cereal, the coupons for cake and brownie mixes, the coupons for soap.
In the News
Young children love to look at the newspaper. It is fun for them to realize that there are things for them to see and do with the paper.
What you’ll need
Newspaper Glue Paper Scissors Pencil or crayon
What to do
1. Newspaper numbers. Help your child look for the numbers 1-100 in the paper. Cut the numbers out and glue them in order onto a large piece of paper. For children who cannot count to 100 or recognize numerals that large, only collect up to the number they do know. Have your child say the numbers to you and practice counting. Collect only numbers within a certain range, like the numbers between 20 and 30. Arrange the numbers on a chart, grouping all the numbers with 2s in them, all the numbers with 5s, and so on.
2. Counting book. Cut out pictures from the newspaper and use them to make a counting book. Page one will have one thing on it, page 2 will have 2 things that are alike, page 3 will have 3 things that are alike, and so on. All the things on the pages have to be the same. At the bottom of each page, write the number of items on the page and the word for the item. Have your child dictate a story to you about what is on the page.
Being able to read and understand the newspaper involves more than just the ability to read the words and understand what they say. It also involves the ability to read and understand numbers.
Look It Up
These activities help children understand how items can be organized and grouped in logical ways.
What you’ll need
Newspaper Paper Scissors Glue
What to do
1. Section selection. Show your child that the paper is divided into different sections and explain that each section serves a purpose. Show him that each section is lettered and how the pages are numbered.
2. Ad adventure. Provide your child with grocery store ads from the newspaper. Help him see how many items are listed and the prices. Compare the prices at different stores. Ask which store has the best bargain and why. Talk about the difference in prices between items bought at regular price, items on sale, and items bought with coupons. What happens when an item is bought on sale and bought with a coupon?
3. Solid search. Look at the store ads or coupons for pictures of all the cylinders, boxes, or cubes you can find. What are their different uses? Paste the pictures on paper and make a 'book of geometric solids.' Have one page for each solid.
Understanding that there is a logical order to the way things are arranged in the newspaper, and in the book of solids, helps show that math skills can be used in organizing written material. Comparing information, such as the sale prices at stores, also helps children see logical relationships that can be applied to writing.
Newspaper Search
Search through the newspaper for mathematical data.
What you’ll need
Newspaper
What to do
1. Numbers in the news. Find the following things in the paper:
a graph a number less than 10 something that comes in 2s, 3s, 4s a number more than 50 the days of the week a number more than 100 a number that is more than 100 but less than 999 a symbol or word for inches, feet, or yards a schedule of some kind a triangle a weather symbol a percent sign sports statistics
2. List it. Provide your child with the grocery section of the newspaper in order to make up a list of food that will feed the family for a week and meet a budget of a certain amount of money. Have your child make a chart and use a calculator to figure the cost of more than one item. If the total for the groceries is too great, talk about which items can be eliminated. Could the list be cut down by a few items or by buying less of another item? What will best serve the needs of the family?.
3. For a fraction of the cost. Give your child a few coupons and grocery ads from the paper. Help your child match the coupons to some of the grocery items in the ad. What fraction of the cost is the coupon? For example, if an item costs 79 cents and the coupon is for 10 cents off, what fraction of the cost can be saved? (About 1/8.) What percent are you saving on the item? (About 12 1/2 percent.)
One of the main ways people use numbers is for planning. Knowing how to plan how much things will cost before going to the store and how to read schedules and weather information from the paper will help your child understand the world.
Treasure Hunt
Everyone’s house has hidden treasures. There is a lot of math you and your child can do with them.
What you’ll need
Buttons Screws Washers Bottle caps Old keys Sea shells Rocks or anything else you can count
What to do
1. Find a container to hold the treasures.
2. Sort and classify the treasures. For example, do you have all the same sized screws or keys? How are they alike? How are they different?
3. Use these treasures to tell addition, subtraction, multiplication, and division stories. For example, if we share 17 buttons among three friends, how many will we each get? Will there be some left over? Or, if we have 3 shirts that need 6 buttons each, do we have enough buttons?
4. Organize the treasures by one characteristic and lay them end-to-end. Compare and contrast the different amounts of that type of treasure. For example, there are 3 short screws, 7 long screws, and 11 medium screws. There are 4 more medium screws than long ones. This may also provide an opportunity to talk about fractions: 7/21 or 1/3 of the screws are long.
Finding a container to hold the treasures gives your child practice in spatial problem solving. The treasures may help you to explain the concepts of addition, subtraction, multiplication, and division because they can be moved around and grouped together so your child can count the items.
Family Portrait
Have your child get to know members of your family by collecting information and picturing it on a graph.
What you’ll need
Paper Pencil Crayons
What to do
1. Choose an inherited family characteristic: hair colors, for example.
2. Count how many people in the family have the different hair colors.
3. Make a graph. For example, if 5 people have brown hair, draw 5 heads side by side to show these five people. Do the same for the other hair colors.
Graphs help everyone, including adults, understand information at a glance. By looking at the lengths of the lines of heads, your child can quickly see which hair color, for example, is most common.
Mathland: The Grocery Store
The grocery store is one of the best examples of a place where math is real. Since trips to the grocery usually affect everyone in the family, the following activities include various levels of difficulty within the activity. Look for the symbols to determine which parts of the activities are for which ages:
for grades K-1
for grades 2 and 3
for grades 4 through 8.
All of these activities can take place over many visits to the store.
Get Ready
Getting ready to go shopping can help parents and children share their thinking strategies about math with one another.
What you’ll need
Paper Pencil Coupons (if you use them)
What to do
1. Involve the family in making a list. List each item and mark with checks or tallies to indicate the number needed.
2. Look at the price of an item you bought last week and intend to buy this week. How much did it cost last week? How much does it cost this week? Do you want to
Pay this week’s price?
Wait until the price comes down?
Or, stock up if it is on sale?
3. Involve the group in deciding how much milk or juice will be needed for a week. You might decide to estimate by cups, explaining that 4 cups are equal to a quart and 4 quarts are a gallon.
4. If you collect coupons, organize them. Choose the coupons that match the items on the grocery list. Discuss how much money will be saved on various items by using coupons.
Practicing measurement and estimation will help improve your children’s ability to predict amounts with accuracy.
Scan It
Shopping is a part of life which really necessitates our being mathematically informed to be good consumers.
What you’ll need
Prices
What to do
1. Notice whether the grocery store has prices on the items or whether the pricing is dependent on scanners.
2. If there are no prices on the items, notice the prices listed on the shelves.
3. Assign each child the job of remembering the price of a few items, particularly those listed on sale.
4. Being aware of the prices of items will help you verify that the scanners are working properly and that the total is accurate when you go to check out.
The ever increasing use of technology in the grocery store puts the burden on you to beware. Your protection lies in having strong mental math skills.
Weighing In
One fun place to try out estimation and measurement skills in the grocery store is the produce section where everyone can have the opportunity to participate.
What you’ll need
The grocery scale
What to do
1. Help your child examine the scale. Explain that pounds are divided into smaller parts called ounces and 16 ounces equal a pound.
2. Gather the produce you are purchasing, and estimate the weight of each item before weighing it.
3. Use sample questions to foster thinking about measurement and estimation. You might Want to ask your child,
How much do you think 6 apples will weigh? More than a pound, less than a pound, equal to a pound? How much do the apples really weigh? Do they weigh more or less than you predicted? How about the potatoes? Will 6 potatoes weigh more or less than the apples? How much do potatoes cost per pound? If they cost ___ cents per pound, what is the total cost?
Some grocery stores have scales that tell all the answers to these questions, so in that case, estimate using the same procedure to make sure the machines are accurate.
Activities like this help children develop number sense for weight and foster the ability to compare items when measuring.
Get into Shapes
The grocery store is filled with geometric shapes.
What you’ll need
Items at the store
What to do
1. Show your child the pictures of the shapes on this page before going to the store. This will help to identify them when you get to the store.
2. At the store, ask your child questions to generate interest in the shapes.
Which items are solid? Which are fiat?
Which shapes have fiat sides?
Which have circles for faces? Rectangles?
Do any have points at the top?
3. Point out shapes and talk about their qualities and their use in daily life.
Look to see what shapes stack easily. Why?.
Try to find some cones. How many can you find?
Look for pyramids.
Determine which solids take up a lot of space and which ones stack well.
Discuss why space is important to the grocer and why the grocer cares about what stacks well.
Boxes, cans, rolls of toilet paper or paper towels, ice cream cones and cones that hold flowers, plus produce such as oranges, grapes, and tomatoes are all geometric shapes. Recognizing these shapes helps children connect math to the real world.
Check Out
The check out counter is where we commonly think about math in the grocery store. It’s where the total is added up, the money is exchanged, and the change is returned.
What you’ll need
All the items you intend to buy
What to do
1. Have your child estimate the total.
2. Ask, if I have 10 one-dollar bills, how many will I have to give the clerk? What if I have 20 one-dollar bills? 5? How much change should I receive? What coins will I get?
3. Count the change with your child to make sure the change is correct.
One way to make estimating totals easy is to assign an average price to each item. If the average price for each item is $2 and if you have 10 items, the estimate would be about $20.
It’s in the Bag
Here’s some fun estimation to do with bags full of groceries.
What you’ll need
Bags of groceries
What to do
1. Have your child guess how many objects there are in a bag. Ask: Is it full? Could it hold more? Could it tear if you put more in it? Are there more things in another bag of the same size? Why do some bags hold more or less than others?
2. Estimate the weight of the bag of groceries. Does it weigh 5 pounds, 10 pounds, or more? How can you check your estimate? Now, compare one bag to another. Which is lighter or heavier? Why?
This activity exposes children to the experiences of counting items and comparing qualities, as well as to judging spatial relationships and capacity. It shows how to estimate weight by feeling how much the bag weighs, comparing it to a known weight (such as a 5-pound bag of sugar), or weighing it on a scale.
Put It Away
Now, the sorting begins as you put away the groceries.
What you’ll need
Your bags of groceries Counter top or table to group items on
What to do
1. Find one characteristic that is the same for some of the products. For example, some are boxes and some are cans.
2. Put all the items together that have the same characteristic.
3. Find another way to group these items.
4. Continue sorting, finding as many different ways to group the items as you can.
5. Play 'Guess My Rule.' In this game, you sort the items and invite your child to guess your rule for sorting them. Then, your child can sort the items, and you can guess the rule.
Sorting helps children develop classifying and reasoning skills and the ability to examine data and information.
Math on the Go
In this busy world, we spend a lot of time in transit. These are some projects to try while you are going from place to place.
While you’re moving, have your children keep theft eyes open for:
* street and building numbers;
* phone numbers on the sides of taxis and trucks;
* dates on buildings and monuments; and
* business names that have numbers in them.
Number Search
The object is to look for numbers around you: on cars, buses, subways, and on foot.
What you’ll need
Some type of transportation or A place from which to observe Paper Pencil Ruler
What to do
1. Create a chart that lists the numbers from 1-50.
2. Write down each number as family members locate that number on a car, a sign, a building.
3. Write down words that have numbers in them such as 'one-stop shopping,' 'two-day service,' or 'Highway 20.'
This is a great challenge for family members of all age, because even young children can learn to recognize numbers.
License Plates
License plates have numbers and are fun to use to play games while on the go.
What you’ll need
License plates Paper Pencil
What to do
1. Copy down a license plate. Read it as a number (excluding the letters). For example, if the license is 663M218, the number would be six hundred sixty-three thousand, two hundred eighteen.
2. Find other license plates and read their numbers. Is the number less than, greater than, or equal to yours?
3. Estimate the difference between your number and another license plate. Is it 10, 100, 1,000, or 10,000?
4. Record the names of the states of as many different license plates as you see. From which state do you see the most? Which has the fewest? Prepare a chart or graph to show your findings.
These activities encourage reading, recognizing numbers, noticing symbols, writing, counting, and graphing.
Total It
This is a good game for practicing quick mental computation.
What you’ll need
License plates
What to do
1. Call out the numbers on the license plate.
2. See who can add the numbers up correctly. What strategies were used? (Were the numbers added by 10’s like 2+8; were doubles like 6+6 used?)
3. Try different problems using the numbers in a license plate.
For example, if you use the plate number 663M218, ask, 'Using the numbers on the plate, can you:
make a 1 using two numbers? Yes, 3-2=1. make a 1 using three numbers? Yes, 6-(3+2)=1 make a 1 using four numbers? Yes, (6+6)-8-3-1 make a 1 using five numbers? Yes, 3-[(6+6)-8-2]=1 make a 1 using six numbers? Yes, 8x2-(6+6)-3=1 make a 2 using 1 number? Yes, the 2.
The problem solving and computation going on in your child’s head is very important. It helps your child be creative with numbers.
How Long? How Far?
Many times when you are on the go, you are headed somewhere that requires you be there by a certain time.
What you’ll need
Information about how far you’re traveling and how long it will take
What to do
1. Ask your children how far they think you are traveling. Yards? Blocks? Miles?
2. Talk about how long it takes to get there. If it is 3:15 now, and it takes 45 minutes to get there, will we make it for a 4:15 appointment? How much extra time will we have? Will we be late?
These types of questions help children see the usefulness of understanding distance and time.
Guess If You Can
When children practice asking questions about numbers, they can develop an understanding of the characteristics and meanings of numbers.
What you’ll need
Questions about numbers
What to do
1. Let your child think of a number between a stated range of numbers while you try to guess the number by asking questions. Here is a sample conversation.
Child: I am thinking of a number between 1 and 100.
Parent: Is it more than 50?
Child: No.
Parent: Is it an even number?
Child: No.
Parent: Is it more than 20 but less than 40?
Child: Yes.
Parent: Can you divide this number up into 3 equal parts?
And so on ...
2. After you have guessed your child’s number, let your child guess a number from you by asking similar questions.
The questions asked demonstrate many different levels of math. They can serve as learning tools for explaining concepts. For example, you can take the opportunity to explain what an even number is if your child does not know.
Parents and the Schools
Here are a few ideas that might help you support a positive math environment in your child’s school:
1. Visit the school and see if the children:
* Are actively engaged in math;
* Are talking about mathematics;
* Are working together to solve math problems;
* Have their math work on display;
* Use manipulatives (objects that children can touch and move) in the classroom.
2. Explore the math program with your child’s teacher, curriculum coordinator, or principal. Here are some questions you might ask:
* Are there manipulatives in the classroom?
* Are you familiar with the National Council of Teachers of Mathematics standards (see next page)?
* How are the standards being used in this school?
* What can I do to help foster a strong math program where children can explore math concepts before giving the right answer?
3. If you would like to help out, here are some suggestions for parent groups:
* Make games for teachers;
* Help seek out sponsors who believe in a strong math program for the school and who might provide materials and resources;
* Support math classes for families at your school.
4. Keep a positive attitude even if you don’t like what you see. Work to improve the math curriculum by doing some of the things mentioned throughout this book.
5. Share this book with your child’s teacher.
What Should I Expect from a Math Program?
The National Council of Teachers of Mathematics (NCTM) has recently endorsed standards by which math should be taught in the elementary and middle grade years. The powerful nature of these standards is that they not only have the endorsement of the academic community, but they are also heavily endorsed by corporations. These endorsements, together with the technological advances of our society and the lack of math confidence in our work force, have combined to produce tremendous support for the standards.
These standards make some assumptions about the way math should be taught and what parents might see when visiting the classroom. Here are some examples:
1. Children will be engaged in discovering mathematics, not just doing many problems in a book.
2. Children will have the opportunity to explore, investigate, estimate, question, predict, and test their ideas about math.
3. Children will explore and develop understanding for math concepts using materials they can touch and feel, either natural or manufactured.
4. The teacher will guide the students’ learning, not dictate how it must be done.
5. Children will have many opportunities to look at math in terms of daily life and to see the connections among math topics such as between geometry and numbers.
6. Children will be actively involved in using technology (calculators and computers) to solve math problems.
The complete list of standards is available from NCTM, 1906 Association Drive, Reston, Virginia 22091-1593 (1-800-235-7566).
Resources
1. Math for parents:
Burns, Marilyn. Math for Smarty Pants. Little, Brown and Company.
Burns, Marilyn. The I Hate Mathematics Book. Little, Brown and Company.
Curriculum and Evaluation Standards for School Mathematics. National Council of Teachers of Mathematics. Reston, Virginia
Help Your Child Learn Number Skills. Usborne Parents’ Guides, EDC Publishing, 10302 East 55th Place, Tulsa, Oklahoma 74146.
The Learning With Series. Cuisenaire Company, P.O. Box 5026, White Plains, New York 106025026, 1-800-237-3142.
Parker, Tom, (1984). In One Day. Houghton Mifflin Company.
Reys, Barbara. Elementary School Mathematics: What Parents Should Know about Estimation. National Council of Teachers of Mathematics. Reston, Virginia. 10 for $7.50.
Reys, Barbara. Elementary School Mathematics: What Parents Should Know About Problem Solving. National Council of Teachers of Mathematics. Reston, Virginia. 10 for $7.50.
Room, Adrian. The Guiness Book of Numbers. Sterling Publishing Company, Inc., 387 Park Avenue South, New York, New York 10016-8810.
Stenmark, Virginia Thompson and Ruth Cossey. Family Math. Lawrence Hall of Science, University of California at Berkeley, Berkeley California 94720.
Thomas, David A., (1988). The Math-Computer Connection. Franklin Watts.
Thomas, David A., (1988). Math Projects for Young Scientists. Franklin Watts.
Math Matters. National PTA and Exxon Foundation. Video tape and pamphlet useful for parent meetings.
The following pamphlets are available from the National Council of Teachers of Mathematics, 1906 Association Drive, Reston, Virginia 22091-1593 (1-800-235-7566). All are priced 20 for $5, 100 for $15.
'Family Math Awareness Activities'
'Help Your Child Learn Math'
'Using Calculators to Improve Your Child’s Math Skills'
2. Books for children:
Almost every book you read with your child will offer the opportunity to talk about math, because math is everywhere. Some books lend themselves more to in-depth and specific math discussion. Only a fraction of these books could be listed here.
Anno, Mitsumasa. Anno’s Counting Book. Thomas Y. Crowell.
Anno, Mitsumasa. Anno’s Counting House. Philomel Books.
Anno, Mitsumasa. Anno’s Hat Trick. Philomel Books.
Anno, Mitsumasa. Anno’s Math Games. Philomel Books.
Anno, Mitsumasa. Anno’s Mysterious Multiplying Jar. Philomel Books.
Carle, Eric. The Grouchy Ladybug. Philomel Books.
Carle, Eric. 1,2,3 to the Zoo. Philomel Books.
Carle, Eric. The Very Hungry Caterpillar. Philomel Books.
Carter, David. How Many Bugs in a Box? Simon and Schuster.
Cobb, Vicki and Kathy Darling. Bet You Can. Avon.
Cobb, Vicki and Kathy Darling. Bet You Can’t. Avon.
Conran, Sebastian. My First 123 Book. Aladdin Books.
Daly, Eileen. 1 Is Red. Western.
Dee, Ruby. Two Ways to Count to Ten. Holt.
Demi. Demi’s Count the Animals 123. Grosset and Dunlap.
Feelings, Muriel. Moja Means One: Swahili Counting Book. Dial.
Grayson, Marion. Let’s Count. Robert B. Luce, Inc.
Grayson, Marion. Count Out. Robert B. Luce, Inc.
Hoban, Tana. Circles, Triangles, and Squares. MacMillan Publishing Company, Inc.
Hoban, Tana. Count and See. Macmillan Publishing Company, Inc.
Hoban, Tana. Is It Rough, Is It Smooth, Is It Bumpy? Macmillan Publishing Company, Inc.
Hudson, Cheryl. Afro-Bets 123 Book. Just Us Productions.
Hutchins, Pat. The Doorbell Rang. Greenwillow Books.
Hutchins, Pat. One Hunter. Greenwillow Books.
Jones, Carol. This Old Man. Houghton Mifflin Company.
Keats, Ezra Jack. Over in the Meadow. Scholastic. Kitchen, Bert. Animal Numbers. Dial.
Kredenser, Gaff. One Dancing Drum. Phillips.
Lionni, Leo. Numbers To Talk About. Pantheon Books.
Marley, Deborah. Animals One to Ten. Raintree.
McMillan, Bruce. Counting Wildflowers. Lothrop, Lee & Shepard Books, Inc.
McMillan, Bruce. One, Two, One Pair. Scholastic. Nolan, Dennis. Monster Bubbles. Prentice Hall.
Pluckrose, Henry. Know about Counting. Franklin Watts.
Pomerantz, Charlotte. The Half-Birthday Party. Clarion Books.
Ross, H.L. Not Counting Monsters. Platt and Munk.
Schwartz, David M. How Much Is a Million? Lothrop, Lee & Shepard Books, Inc.
Schwartz, David M. If You Made a Million. Lothrop, Lee & Shepard Books, Inc.
Tafuri, Nancy. Who’s Counting? William Morrow & Co.
Testa, Fulvio. If You Take a Pencil. Dial.
Viorst, Judith. Alexander Who Used To Be Rich Last Sunday. Atheneum.
Vogel, Ilse-Margret. 1 Is No Fun, But 20 Is Plenty.t Atheneum.
Ziefert, Harriet. A Dozen Dizzy Dogs. Random House.
3. Magazines and periodicals:
Dynamath. Scholastic. Available from the school division. Filled with many different activities that involve all strands of math. Children in grade 5 particularly like this. Nine publications are sent each school year. $5.00 for the subscription.
Games Magazine, P.O. Box 10147, Des Moines, Iowa 50347. The adult version of Games Junior (see below). Older children may prefer this to Games Junior.
Games Junior, P.O. Box 10147, Des Moines, Iowa 50347. A challenging but fun magazine of all different kinds of games that give children hours of 'brain workouts.' Appropriate for ages 7 and up.
Math Power. Scholastic. Available from the school division. Exciting and inviting, this magazine is filled with many activities that involve all types of math. Good for grades 3 and 4. Nine publications are sent each school year for $5.00.
Puzzlemania. Highlights, P.O. Box 18201, Columbus, Ohio 43218-0201. Includes puzzles involving words, logical thinking, hidden pictures, spatial reasoning, etc. The cost is about $7.50 per month.
Zillions. Consumer Reports, P.O. Box 54861, Boulder, Colorado 80322. Children’s version of Consumer Reports. Shows math in the real world and offers children the opportunity to see how gathering data and information can lead to good decision-making. The cost is approximately $2.75 per issue.
Acknowledgments
This book was made possible with help from the following people: Phil Demartini, Headmaster, St. Francis School, Goshen, Kentucky;, Janet G. Gillespie, Teacher, Woodlawn Elementary School, Portland, Oregon; David Kanter; Sharon Nelson, Principal, Lower School, Isidore Newman School, New Orleans, Louisiana; Kathy Rabin, Teacher, Isidore Newman School; and Annette Raphel, Curriculum Coordinator, Milton Academy, Milton, Massachusetts.
Others who reviewed early drafts or provided information and guidance include: Iris Carl, Past President, National Council of Teachers of Mathematics; Mary Connolly, Marketing Manager, Elementary Mathematics, DC Heath; Julie Fisher, Visiting Mathematics Educator, National Council of Teachers of Mathematics; Vera M. White, Principal, Jefferson Junior High School, Washington, D.C.; and many people in the U.S. Department of Education.
Special thanks go to Leo and Diane Dillon for their advice on how to work with illustrators and to Alison Goldstein and Emily Dorfman, two Maryland third graders who marked the manuscript for color overlays. Appreciation is also expressed to Nathan and Julie Kanter for testing many of the activities contained in this book.
Patsy E. Kanter is Assistant Principal/Curriculum Coordinator at the Isidore Newman Lower School in New Orleans, Louisiana. She is also an instructor of family math and a consultant for the Louisiana Children’s Museum. She has been an elementary school mathematics teacher, and she founded the Newman Math Institute at Newman School. She is the author, with Janet Gillespie, of Every Day Counts and Math Every Day and has written articles on mathematics for professional magazines. She has a B.A. from Newcomb College, and, in listing her academic credentials, she credits her mother, Louise Hirsch Friedler, as being her first teacher, 'who always tried to make learning interesting for me.'
Jerry Guillot is the art teacher for Isidore Newman Lower School in New Orleans, Louisiana, where he has taught for the past 24 years. He has a B.A. from Lousiana State University and received his teaching certification from Tulane University. He has taught classes and workshops on elementary art for both college students and private organizations. He is also a graphic artist for a New Orleans company.
Brian A. Griffin (pages 10, 11, 30, 35, 45, 46) is a designer for the San Jose Mercury News, San Jose, California. He was formerly the Art Director of Kids Today, a weekly children’s newspaper published by Gannett Co., Inc. He has won awards from the Society of Newspaper Design, PRINT Regional Design Annual, and the Art Director’s Club of Metropolitan Washington.
What We Can Do To Help Our Children Learn:
Listen to them and pay attention to their problems.
Read with them.
Tell family stories.
Limit their television watching.
Have books and other reading materials in the house.
Look up words in the dictionary with them.
Encourage them to use an encyclopedia.
Share favorite poems and songs with them.
Take them to the library--get them their own library cards.
Take them to museums and historical sites, when possible.
Discuss the daily news with them.
Go exploring with them and learn about plants, animals, and local geography.
Find a quiet place for them to study.
Review their homework.
Meet with their teachers.
Do you have other ideas?