Authentic Learning Activities in Middle School Mathematics: Number & Operation

 
9781895997156: Authentic Learning Activities in Middle School Mathematics: Number & Operation
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Authentic Learning Activities in Middle School Mathematics is a series of five outstanding modules designed to capture the spirit and intent of the NCTM's Principles and Standards for School Mathematics 2000. The five modules correspond to the five strands of this Standards document and each module contains the following elements: ten rich learning activities that contain student pages which can be photocopied. teacher notes containing answers to all the exercises, reduced student pages, complete lesson plans and teaching tips. rubrics for assessing student work. samples of student work classified according to the levels in the rubric. Internet-based extensions that refer students to Internet sites for guided exploration. graphing calculator explorations to reinforce and expand concepts. correlations to the expectations in the NCTM's Principles and Standards 2000. discussion of the new trends in mathematics education including NCTM policy statements pertaining to constructivism, assessment, and the use of technology.The first draft of these modules was commissioned by the Ontario Ministry of Education and Training and field tested across Ontario in 1998 and 1999. The overwhelming impact of these materials and the enthusiastic responses from teachers and students provided the impetus for the creation of these modules for American classrooms. This module addresses the expectations for grades 6 through 8 in the Number & Operation strand of the NCTM's Principles and Standards for School Mathematics 2000. There are two units with five activities per unit. The content of the activities in each unit is described below.Unit 1Activity 1 involves students in estimating the height of the CN Tower, world's tallest free-standing structure, relative to a typical student height. Using data pertaining to the dimensions, mass, capacity, and elevators of this tower, students create a bank of word problems for solution by their classmates.Activity 2 moves from traditional word problems toward Fermi problems (defined on page 16) by posing the questions, How long would it take you to count to one billion? and How many times will your heart beat in your lifetime? To address these problems, students must make some general assumptions and then compute some approximations. Students are also prompted to discover the relative sizes of one million and one billion. In Activity 3, students calculate the height of a stack of dollar coins required to pay off the U.S. national debt. They also solve a variety of single and multi-step word problems involving whole numbers, decimals, and fractions. Then in Activity 4, students tackle the Fermi problem: Can Spaceship Earth (at EPCOT Center) hold all the worlds golf balls? Answers to all the exercises and activities are provided.Unit 2Activity 1 presents two familiar contexts in which we are called upon to do mental arithmetic tipping and taxing. In some states, the sales tax is 5%. Since a standard gratuity is about 15%, the mental calculation of 5% and 15% can be linked. Students first attempt to develop their own algorithm for calculating 15% mentally. Then they analyse and compare given algorithms and apply them in various contexts. In Activity 2 students compare fractions to answer the question, Which culture had the best approximation to ? The focus on fractions is extended to fraction concepts in Activity 3, where students grapple with two famous fraction paradoxes. Fraction concepts are further expanded in Activity 4 where students investigate what fraction of the numbers in Pascals triangle are even. This provides a gentle, intuitive, and pictorial introduction to fractals.

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About the Author:

Brendan Kelly has a Ph.D. in pure mathematics with a specialization in Number Theory from the University of Toronto. He also has an Ed.D. in computer applications from OISE/UT. Dr. Kelly is currently a full professor of mathematics and mathematics education at OISE/UT, where he won the Teacher of the Year Award in 1995-96. He has written over 60 books including textbooks for students at all levels from primary through college.

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