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Math Concept Reader
Math Concept Reader City of the FUTURE ca56os_lay_070108ap_ll.indd 1 1/9/07 1:47:06 AM DIGITAL FINAL PROOF Expedition: Antarctica by Aenea Mickelsen ca62xs_lay_061207ad_am.indd 4 1/9/07 9:09:15 AM DIGITAL FINAL PROOF Copyright © Gareth Stevens, Inc. All rights reserved. Developed for Harcourt, Inc., by Gareth Stevens, Inc. This edition published by Harcourt, Inc., by agreement with Gareth Stevens, Inc. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the copyright holder. Requests for permission to make copies of any part of the work should be addressed to Permissions Department, Gareth Stevens, Inc., 330 West Olive Street, Suite 100, Milwaukee, Wisconsin 53212. Fax: 414-332-3567. HARCOUR T and the Harcourt Logo are trademarks of Harcourt, Inc., registered in the United States of America and/or other jurisdictions. Printed in the United States of America ISBN 13: 978-0-15-360200-9 ISBN 10: 0-15-360200-7 1 2 3 4 5 6 7 8 9 10 179 16 15 14 13 12 11 10 09 08 07 by Ilse Ortabasi Math Concept Reader City of the FUTURE ca56os_lay_070108ap_ll.indd 3 1/9/07 1:47:08 AM DIGITAL FINAL PROOF Mrs. Ng’s students are looking forward to the annual City of the Future competition. A team of students represents Edison School at the competition each year. The students, with their teachers’ help, design and construct a scale model of a futuristic city . Not long ago, the Edison School team’s city model won first prize in the regional competition. The students constructed their model city using containers and everyday materials such as plastic jugs, glass jars, and aluminum cans. They traveled to the national finals in W ashington, DC, where they competed with schools from around the country . Mrs. Ng tells her students that they will study three- dimensional solid figures before the competition. “Can anyone tell me what a solid fi gure is?” she asks the class. Huang raises his hand and says that a solid figure is a three-dimensional figure, such as a cube or a sphere. It has length, width, and height. “Very good Huang,” Mrs. Ng says. 2 Chapter 1: Getting Ready ca56os_lay_070108ap_ll.indd 2 1/9/07 1:47:09 AM DIGITAL FINAL PROOF Mrs. Ng draws a cube on the board. Then she writes face on one of the flat sides of the cube. She explains that the segment where two faces meet is called an edge, while the vertex is the point where the edges meet. Mrs. Ng gives each student a sheet of construction paper . She tells everyone to draw a two-dimensional pattern on the paper , which can be cut and folded to construct a cube. This two- dimensional figure is called a net. For homework the class must find the number of faces, edges, and vertices that a cube has. Mrs. Ng announces at the end of class that students will build models from solid figures for the City of the Future competition this year . She tells the students to visualize how spheres, cylinders, prisms, pyramids, and cones could be used to construct buildings for their city. She encourages the students to use a variety of different forms. It’s a futuristic city, so their imaginations can run wild. 3 FACE EDGE VERTEX ca56os_lay_070108ap_ll.indd 3 1/9/07 1:47:09 AM DIGITAL FINAL PROOF The class continues to study solid figures and their nets in great detail. Finally, Mrs. Ng announces that the students are ready to begin the next step in their preparation for the City of the Future competition. It is time to see how solid fi gures can be used in the construction of buildings. Mrs. Ng sets up the class computer and projector on her desk. After adjusting the lights and closing the blinds, she shows the fi rst photo to the class. It is a picture of the Great Pyramid of Giza in Egypt. Mrs. Ng tells the class, “People have been using solid fi gures to construct buildings for thousands of years. This pyramid was built in ancient Egypt more than 5,000 years ago. Does anyone know what type of solid figure we are looking at here?” “The Great Pyramid of Giza is an example of a square pyramid,” Zoe answers. “It has four triangular faces and a square base.” “That’ s correct,” says Mrs. Ng. 4 The Great Pyramid of Giza is an example of a square pyramid. ca56os_lay_070108ap_ll.indd 4 1/9/07 1:47:15 AM DIGITAL FINAL PROOF Mrs. Ng asks the students to find the definition of base in the glossary of their math book. Zoe flips to the back of the book and quickly finds the answer. She reads, “A base is a solid figure’s face by which the figure is measured or named.” Next, Mrs. Ng asks the students to look up the definition of a square pyramid. Nathan finds it and reads, “A solid figure with a square base and with four triangular faces that have a common point.” He adds that a square pyramid has fi ve vertices and eight edges. Huang wonders what the net for a square pyramid would look like. He draws in his math notebook while Mrs. Ng sketches the net for a square pyramid on the board. Mrs. Ng suggests that the students build a square pyramid out of construction paper . Soon everybody is busy with rulers, pencils, paper , scissors, and glue. 5 ca56os_lay_070108ap_ll.indd 5 1/9/07 1:47:15 AM DIGITAL FINAL PROOF Students will construct a variety of solid figures to prepare for the City of the Future competition. The nets help them identify the faces, edges, surfaces, and vertices of some of the solid figures. As they take the solid fi gures apart, they will be able to see which plane figures the solids are made from. The nets will also be patterns that Mrs. Ng’ s class can use to construct the figures they will use in their futuristic model city. Later, the class visits the media center. The students are buzzing with excitement as they research existing buildings that are made from solid fi gures such as cubes, prisms, spheres, pyramids, and cylinders. The students are surprised to find so many interesting buildings in different places around the world. The media specialist, Mrs. Shulz, helps the students search the Internet, books, and magazines for photographs of interesting buildings. 6 Chapter 2: Buildings Shaped Like Solid Figures ca56os_lay_070108ap_ll.indd 6 1/9/07 1:47:15 AM DIGITAL FINAL PROOF Kendra shows her classmates a photograph of an interesting cone-shaped building in Spain. The unusual structure stands next to another building that has a unique design with attention- grabbing features. Kendra explains why she finds the cone-shaped building so fascinating. “What I like is that the two buildings are very different in shape,” she says. “The cone is a good example of the solid figures we’ve been studying in class. The other building has curved features that make it stand apart from the cone shape. The differences make them complement each other . They go together in a way that makes each building really stand out.” Kendra and Daniel decide to include a cone-shaped building in the design of the City of the Future. They are convinced that this piece will make their model city stand apart from the rest of the entries in the competition. They know that classes in other schools are coming up with all sorts of interesting ideas, so their models have to really be different to get noticed. 7 This cone-shaped building can be found in Spain. ca56os_lay_070108ap_ll.indd 7 1/9/07 1:47:18 AM DIGITAL FINAL PROOF Damon finds an aerial photo of a building that is made up of five rectangular prism-shaped buildings. The five buildings meet at skewed, or slanted, angles at an entrance hall in the middle. “Looking at the buildings from overhead makes it easier to see the solid figures,” Damon explains. This is the Nasher Museum at Duke University in North Carolina. The museum has a collection of modern and ancient art. The building was built in 2005, designed by an architect named Rafael Viñoly. Damon and Natalie cut and fold the net for 5 rectangular prisms, just like those in the Nasher Museum. Each of the rectangular prism-shaped buildings has 6 rectangular faces, 12 edges, and 8 vertices. While they work on the nets, they decide whether they want to have more than one rectangular prism- shaped building in the model city . “I think we should include five solid figures, so that it looks like the Nasher Museum,” Natalie suggests. Damon agrees that a building like the museum would be a great addition to the futuristic model city . 8 The Nasher Museum at Duke University houses a collection of modern and ancient art. ca56os_lay_070108ap_ll.indd 8 1/9/07 1:47:31 AM DIGITAL FINAL PROOF [...]... helps the students plan the residential part of the city Before long, the classroom is full of colorful construction paper models of solid figures Mrs Ng tells the students that their next task is to start constructing the City of the Future using all of the forms they have created The students talk and laugh as they exchange their ideas on how the city should be set up Mrs Ng reminds them that if they... planning The students write a description of the city in their project plan The description explains how everything will work when the futuristic city is built Finally, the class starts the construction of the model city As they cut, paste, and glue a wide variety of forms, the students laugh and talk There are many problems to solve and decisions to make as they build the city The students agree that math. .. important in solving all the problems of city planning Three students from the class will take the model city to the regional competition At the competition, they will show the model to the judges and will explain the key design features of their futuristic city They hope the judges appreciate all of their hard work and imagination They would love to win the competition and earn a trip to the national finals... attached to the sides of the structure The style and color of the cubes against the building gives the appearance that the solid figures are floating off the structure Looking at the building, Bob wonders what it would be like to stand in one of the cubeshaped boxes He constructs five cubes from their nets and carefully glues them together The result looks just like the cube-shaped parts of the apartment... they run out of shapes, they can always make more The class will construct the model city on a large piece of plywood Mrs Ng divides the class into three groups One group will build the residential part of the city This is where the people of the city will live Another group will build the commercial and industrial areas, with factories, stores, and more The third group will construct the city s transportation... The people of the future will want lots of space to enjoy their free time As they get busy working, the students talk about the images they have researched They’ve seen so many interesting buildings that they have plenty of ideas to create an amazing model city 14 ca56os_lay_070108ap_ll.indd 14 1/9/07 1:47:50 AM DIGITAL FINAL PROOF City of the Future competition encourages students to think about city. .. Emily thinks about the kinds of materials she could use to build a cylinder for the City of the Future She decides to use a paper towel roll to form the main body of the cylinder For the ends, or bases, she cuts two circular sheets of construction paper and attaches them to the open ends of the paper towel roll 10 ca56os_lay_070108ap_ll.indd 10 1/9/07 1:47:41 AM DIGITAL FINAL PROOF This geodesic dome... that the class would like to construct a triangular pyramid for the competition Mrs Shulz is glad to help him, and together they search for drawings of a triangular pyramid and its net Daniel discovers that the net of an equilateral triangular pyramid is a triangle, too It is four times the area of one of the faces of the pyramid 13 ca56os_lay_070108ap_ll.indd 13 1/9/07 1:47:47 AM DIGITAL FINAL PROOF... FINAL PROOF This is a cubed-shaped apartment building in the Netherlands Bob sits at a computer and searches the Internet for a cubeshaped building He finds a photograph of an apartment building in Rotterdam Rotterdam is in the Netherlands, a country in Europe Bob shows the picture of the building to other students His classmates like the structure because it combines so many geometric shapes The building... imagination They would love to win the competition and earn a trip to the national finals in Washington, D.C When the day of the competition arrives, everyone wishes the students good luck The students carefully load their City of the Future model on the bus and then climb aboard to head for the regional competition 15 ca56os_lay_070108ap_ll.indd 15 1/9/07 1:47:54 AM . the design of the City of the Future. They are convinced that this piece will make their model city stand apart from the rest of the entries in the competition. They know that classes in other. variety of solid figures to prepare for the City of the Future competition. The nets help them identify the faces, edges, surfaces, and vertices of some of the solid figures. As they take the solid. models of solid figures. Mrs. Ng tells the students that their next task is to start constructing the City of the Future using all of the forms they have created. The students talk and laugh as they