Brendan Kelly Authentic Learning Activities In Middle School Mathematics - Number and Operation

• By Dr. Brenden Kelly
• This module addresses the expectations for grades 6-8 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.
• Activity 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.
• In Activity 4, students tackle the Fermi problem: Can Spaceship Earth (at EPCOT Center) hold all the world¹s golf balls?
• Answers to all the exercises and activities are provided.
• Unit 2:
• Activity 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 ¼? 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 Pascal¹s triangle are even. This provides a gentle, intuitive, and pictorial introduction to fractals.