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Math Analogies Beginning Teaching Suggestions Teaching Suggestions Analogies occur in life and frequently in high-stakes tests. Understanding analogies and the ability to reason analogically (reasoning used to identify, evaluate, and solve an analogy) are also important problem-solving skills. It is, therefore, beneficial for students to learn about analogies as soon as reasonably possible. The immediate benefit is to recognize and solve simple analogies. The long-term benefits are improved reasoning skills that enable students to break problems into their component parts, recognize analogies imbedded in arguments, and evaluate them. Problem-solving is an essential part of mathematical development. Analogies provide practice in breaking math problems down into their component parts, making it easier to recognize familiar formats that enable students to produce solutions. Analogical reasoning is not easy, particularly for younger students whose thinking skills are in the formative stages of development. At this age, children commonly use guesswork instead of organized analysis to solve problems. For example, ask young children for two numbers between 10 and 15 and they will often guess or start counting from 1 to find the answer. A challenge for young students learning to solve analogies is reading the format. For example, "A is to a as B is to" is not common language for a youngster. The interpretation skills mandate the realization that the phrase "is to" implies a connection between the. item to the left and right of the phrase. Then, the word "as" relays the idea that there is a similar connection between the next two items, only one of which is provided. On pages iv and v, we provide introductory lessons to help students read and understand analogies. We encourage teachers to work one-on-one with K-1 students through this lesson and then monitor student work until it is clear the student grasps the meaning of an analogy. We recommend that students draw and verbalize their answers. The drawing develops fine motor skills and the verbalization develops communication skills. Some young children may find drawing answers too challenging, but might be able to verbalize solutions. At this age, that is fine. However, these children should be encouraged to attempt to draw the solution after they verbalize it. Remember to keep learning fun. The beauty of many of the items presented here is that they are language independent. Thus, non- native English-speaking students have the opportunity to participate with all other students in the challenges presented. When all students are involved, each one has the opportunity to learn the basics and beauty of logic and mathematics while developing and strengthening language skills. The National Council of Teachers of Mathematics defined five content strands that should appear in the K-12 mathematics curriculum. These five strands are: Number and Operations Algebra Geometry Measurement Data Analysis and Probability The entries in this book are built around grade-appropriate standards for each of those five strands. While some of the analogies may appear too difficult or too easy for a student, there will be other related entries that should be suitable. If the analogies in this book become too easy for the student, try the next level, which is more challenging. "Remember to keep learning fun," ii © 2009 The Critical Thinking Co. ™ • www.CriticaIThinking.com • 800-458-4849
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Math Analogies Beginning Table of Contents Table of Contents INTRODUCTION Teaching Suggestions ii Sample Lessons iv-v About the Authors vi EXERCISES 1-38 NCTM Standards (National Council of Teachers of Mathematics) 1,4, 7, 12, 15, 17, 23, 26, 30, 32, 34, 37, 39,44, 46, 50, 52, Number and 55, 56, 58, 60, 63, 65, 67, 70, 74, 76, 81, 83, 86, 92, 98, 102, Operations 106, 110, 114, 118, 122, 126, 129, 132, 135, 139, 143, 146, 149 2, 3, 5, 8, 13, 16, 18,22, 24, 27, 31, 33, 35, 38, 40, 45, 47, 51, Algebra 53, 57, 59, 61, 66, 68, 71, 75, 77, 82, 84, 87, 89, 91, 93, 95, 97,99,101,103, 105, 1(~7, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 130, 133, 136, 140, 145, 147, 150 Geometry 6, 9, 10, 14, 19, 25, 28, 36, 41, 48, 54, 62, 69, 72, 78, 85, 88, 94,104,108,112,120,128,131,141,144,148 Measurement 11, 20, 21, 29, 42, 49, 64, 73, 79, 90, 96, 116, 124, 134, 138, 142, 145, 151 Data Analysis 43, 80, 100, 137, 152 and Probability ANSWERS 39 © 2009 The Critical Thinking Co. ™ • www.CriticaIThinking.com • 800-458-4849 iii
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