Math Clues. Book 4: Geometry and Measurement. Written by Charlene Zastrow and Rebecca Stark Illustrated by Karen Birchak

Transcription

1 Math Clues ook 4: Geometry and Measurement Written by Charlene Zastrow and Rebecca Stark Illustrated by Karen irchak

2 The purchase of this book entitles the individual teacher to reproduce copies of the student pages for use in his or her classroom exclusively. The reproduction of any part of the work for an entire school or school system or for commercial use is prohibited. ISN Educational Impressions, Inc., Hawthorne, NJ EDUCATIONAL IMPRESSIONS, INC. Hawthorne, NJ Printed in the United States of America.

3 Contents To the Teacher...5 Learning Objectives...6 INTRODUCTION AND REVIEW Points, Lines and Planes...8 Types of Lines...9 Practice with Points, Lines, and Planes...10 Angles Using a Protractor...14 Practice Identifying and Drawing Angles...15 Congruency...16 Polygons...17 Quadrilaterals...18 Triangles Circles Circumference and π...25 Perimeter of a Polygon...26 Perimeter of a Rectangle or Square...27 Practice Finding the Perimeter of a Polygon...28 Area...29 Finding the Area of a Parallelogram...30 Finding the Area of a Triangle or a Trapezoid...31 Practice Finding the Area of a Polygon...32 Finding the Area of a Circle Volume...35 Measurement Tables...36 Linear Measurement: U.S. Customary Units Capacity: U.S. Customary Units...40 Weight: U.S. Customary Units...41 Linear Measurement: Metric System Capacity: Metric System...44 Mass: Metric System...45 Measuring Time Measuring Temperature...48 SKILL-UILDER WORD PROLEMS Mystery Math Club (Points, Lines and Planes) A Scavenger Hunt: Jake s List (Types of Angles)...52 A Scavenger Hunt: Megan s List (Complementary and Supplementary Angles)...53 Educational Impressions, Inc. Geometry and Measurement 3

4 A Scavenger Hunt: Megan s List (Complementary and Supplementary Angles)...54 A Secret Message (Quadrilaterals and Other Polygons)...55 Trish s Triangles (Types of Triangles)...56 A Day at the Zoo ( Circles) Round Is eautiful! (Circumference and π)...59 A alancing Act! (Perimeter of Polygons)...60 Miffy s Mansion ( Area of Parallelograms) Fifi s Fortress (Area of Triangles and Trapezoids) Party in the Round (Area of a Circle)...65 Guess the Number (Volume of Cubes and Rectangular Shapes)...66 That s Amazing! (Linear Measurement: U.S. Customary Units)...67 Math Awareness Month (Capacity: U.S. Customary Units)...68 Let s Eat (Weight: U.S. Customary Units)...69 Can You elieve It? (Linear Measurement: Metric System)...70 The Tenth Day of the Tenth Month (Capacity: Metric System)...71 Snacks for All (Mass: Metric System)...72 A Part-time Job (Adding and Subtracting Time)...73 Hot Clues! (Temperature)...74 CHALLENGE WORD PROLEMS Lost at Sea...76 Island of Amazing Shapes Wild Goose Chase...79 Where Did You Go?...80 A Fact a Day Penpals...83 The Great Pizza-Eating Contest...84 New in Town Penny Fussbudget: At Home...87 Penny Fussbudget: At the Mall...88 Super Granny...89 Super Granny s Great Adventure...90 ANSWER SECTION Geometry and Measurement Educational Impressions, Inc.

5 To the Teacher The usage of mathematics brings our everyday experiences to life; not a day passes when we fail to encounter a skill in mathematics. The Math Clues Series is an extensive resource that provides a clear understanding of basic mathematical concepts. Developing the understanding of the relationship of one concept to another is demonstrated throughout the series. The language of mathematics is precise and the skill of each concept is fully developed with lessons, practice, and motivating story problems. In ook 4 of the series, Geometry and Measurement, students will explore the basic concepts of geometry, including points, lines, perimeter, area, and volume. They will also learn about measurement, both standard and metric. Through the mastery of these skills, other mathematical skills of problem-solving and creative thinking are discovered. Geometry and Measurement is divided into three sections: Introduction and Review of Concepts The lessons in this section present important mathematical concepts and teach students important computation skills. Step-by-step directions and easy-to-understand definitions clearly explain each concept and procedure. This section will serve as a useful reference guide for the lessons in the last two sections. Skill-uilding Word Problems Creative story problems use mystery and humor to hold students interest. Each lesson in this section deals with a particular skill and students are aware of the skill being practiced in each. Challenge Word Problems These pages add an additional challenge for students who understand all of the concepts and have mastered the computational skills covered in this resource. The same type of problems that were presented in the second section are presented in this section with one important exception students are not told which skills are involved. Note: You may want to allow students to use a calculator for some of these exercises. Use your discretion. Educational Impressions, Inc. Geometry and Measurement 5

6 Learning Objectives Geometry and Measurement was designed to help teachers implement the standards developed by the National Council of Teachers of Mathematics. Geared for students in grades 3 through 5, the lessons will help students meet the following objectives: GEOMETRY understand the terminology associated with geometry; understand and work with points, lines, line segments, and rays; understand the meaning of angles; name, draw, measure, and compare different angles; identify the characteristics and the measurement of the angles of triangles; understand and recognize types of polygons; determine the perimeter of a polygon; understand the various parts of a circle; determine the circumference of a circle; understand and use formulas to determine the area of a parallelogram; understand and use formulas to determine the area of a triangle and trapezoid; understand and use formulas to determine the area of a circle; and understand and use formulas to determine the volume of a cube or rectangular solid. MEASUREMENT understand attributes of customary linear measurement; understand attributes of customary capacity measurement; understand attributes of customary weight measurement; understand attributes of metric linear measurement; understand attributes of metric capacity measurement; understand attributes of metric mass measurement; compare, order, and make simple conversions within each type of measurement; recognize the measurement of temperature in both Celsius and Fahrenheit; and identify the need for working with customary and metric measurement. 6 Geometry and Graphing Educational Impressions, Inc.

7 Points, Lines, and Planes Geometry is all around us. In order to understand the basic concepts of geometry, you must first understand about points, lines, and planes! A point is an exact location in space. You cannot measure a point. Points are usually given letter names. K C J N The above points would be identified as Point J, Point K, Point N, and Point C. A line is a set of points along a straight path; it extends infinitely in both directions. A line has length but no width and no endpoints. You name a line by its first and last labeled points. A C D The above is called AD (read as Line AD ) because the first and last labeled points are A and D. The arrows pointing in both directions signify that it is a line. A line segment is part of a line between any two specific points on the line. A line segment includes all of the points that fall between those two endpoints. C This line segment is called C (read as Line Segment C ) because its endpoints are and C. A ray is a segment of a line that extends from one endpoint and continues indefinitely in the other direction. You name a ray by the endpoint and a point on the line. C This ray is called C (read as Ray C ) because the endpoint is and Point C is a point on the line. Points and lines lie in a plane. A plane is the set of all the points on an endless flat surface. It has no thickness and extends indefinitely in all directions. A plane is often represented as a four-sided figure like the one below and is named by three or more points which are not in a straight line. C D This above figure is called CD (read as Plane CD ). 8 Geometry and Measurement Educational Impressions, Inc.

8 Types of Lines Intersecting lines cross each other (intersect) at a point. In the above figure, ST intersects UY at Point F. Perpendicular lines intersect at right angles. The square corner at the point where the lines intersect represents a right angle (90 ). The following is the symbol for perpendicular:. In the above figure, XY is perpendicular to UV (XY F Parallel lines are in the same plane but never cross each other. They are the same distance apart at all points. The following is the symbol for parallel lines:. T U Y S U X V Y T UV). T E D F In the above figure, D is parallel to EF (D EF). Practice Draw and label an example of each of the following. 1. QRS 2. ST 3. JK 4. A GH 5. QR KL 6. CD intersects EF T Educational Impressions, Inc. Geometry and Measurement 9