Mathability gives students the experience and ability to analyze and solve real-life mathematical problems, and explain their methods for arriving at the solution. Mathability is an excellent resource for preparing students for the performance tasks of standards-based tests. The six units in this book each have 10 problems that deal with a variety of real-life situations, such as those at a construction site, on vacation, in a business, and at home. The open-ended problems let students hone their skills in geometry, probability, percentages, use of charts, algebra, number relations/operations, money, and decimals.
Open-ended performance tasks have become a mainstay of standards-based testing. It is one of the tasks that most students perform at below proficiency level. Much of this low performance is due to a student's lack of experience with writing explanations of the mathematics that made it possible to solve the problem. Mathabilty presents a systematic approach that will lead students to proficiency.
Within each unit, this book provides four different levels of problems. The Step-by-Step Level leads a student through the problem and provides a format for presenting their answers. The Prompted Level provides the format for presenting the solution and hints on how to solve the problem. The Independent Level allows students to solve and explain their answers on their own, and the Challenge Level problems present a venue for gifted and talented students to push their skills to a higher level.
Table of Contents
Construction Malfunction 1.1 The Founding of the Foundation area of a complex polygon, problem solving using formula step-by-step practice 1.2 Up Against the Walls problem solving using a diagram, perimeter prompted practice 1.3 Dry Wall My Wall rate and time independent practice 1.4 Debating on Painting cost of materials, number operations step-by-step practice 1.5 Winter Worries cost of materials, measurement, using the area formula prompted practice 1.6 The White Room ratio, area independent practice 1.7 Carpeting the Stairs measurement conversion, number operations independent practice 1.8 Roof over Their Heads rate, time, cost challenge 1.9 Live Wire measurement, number operations, estimation independent practice 1.10 Plenty of Pipes measurement, number operations, total cost challenge Making Ends Meet 2.1 Figuring Out the Furniture real number operations, comparing numbers step-by-step 2.2 Checking and Balancing real number operations, algebra, comparing numbers prompted practice 2.3 Catching the Bus rate, time, drawing a diagram, algebra challenge 2.4 Dirty Laundry fractions, proportion, number relations, algebra step-by-step 2.5 More Dirty Laundry percent, proportion, determining pertinent information prompted practice 2.6 Mall Madness discount, percent of decrease independent practice 2.7 Ticket to Ride schedules, time independent practice 2.8 Lots of Lottery Tickets probability challenge 2.9 Food for Thought number operations, percent independent practice 2.10 Wear and Tear percent of decrease challenge A Well Deserved Vacation 3.1 Fill’er Up ratio, number operations, problem solving step-by-step 3.2 Sandwich Assembly Line unit prices prompted practice 3.3 Car Trouble time, rate, drawing a diagram independent practice 3.4 Repair Scare rate, unit prices step-by-step 3.5 Middle of Nowhere rate, scale, number conversion prompted practice 3.6 Hotel at Last percent of discount independent practice 3.7 Dining Out number operations, percent independent practice 3.8 Amusements at the Park algebra challenge 3.9 Bungle in the Jungle probability independent practice 3.10 Road Side Attraction similar figures, ratio, proportion independent practice Care and Feeding 4.1 Lost and Found unit price step-by-step 4.2 It’s in the Bag unit price, comparing real numbers prompted practice 4.3 Doing the Can Can unit price, comparing real numbers independent practice 4.4 Walking the Dog measure of central tendency step-by-step 4.5 How Big Will It Get? finding a pattern, making a graph, extrapolating prompted practice 4.6 Vet Bills and Budget Chills percent, number operations independent practice 4.7 The Dog Show You Know permutations, combinations independent practice 4.8 Don’t Fence Me In perimeter, measurement, number operations independent practice 4.9 Gear Is Here surface area challenge 4.10 How Much Does It Eat time, rate, unit price, projected cost challenge Minding a Business 5.1 Time and Time Again units of time and labor cost, multi-step problem solving independent practice 5.2 Laboring Over Cost creating and applying formulas, using new information independent practice 5.3 Triangle Tangle Pythagorean formula, number operations step-by-step 5.4 Ramp Champ Pythagorean formula, operations with variables, order of operation prompted practice 5.5 Dawning of the Awning transform the Pythagorean formula, operations with variables independent practice 5.6 Moving Belts and Improving Belts Pythagorean formula, multi-step problem challenge 5.7 As the Tire Turns measurement, circumference, number operations prompted practice 5.8 Tired of Tires measurement, circumference formula, completing a chart independent practice 5.9 Thanks for the Water Tanks volume of a cylinder challenge 5.10 Bang for the Banquet using a table, applying information, multi-step problem solving independent practice Home Sweet Home 6.1 Holiday Savings algebra, interest step-by-step 6.2 Saving for a Rainy Day simple interest, algebra prompted practice 6.3 Stocking Stuffers real number operations independent practice time, units of measure conversion step-by-step 6.5 Bus Fuss rate, distance, algebra, comparing numbers prompted practice 6.6 Buses and Trains schedules, time independent practice 6.7 Furnishing a Room algebra, number operations independent practice 6.8 How Does the Garden Grow? geometric formulas, number operations independent practice 6.9 Preparing for Winter geometric formulas, percent, comparing real numbers independent practice 6.10 Birthday Celebration percent, operations with decimals independent practice Answers
A veteran teacher with more than 19 years teaching experience, Michael Cain currently teaches middle school mathematics. Having initially received a degree in art, Cain worked full-time as a maintenance and construction foreman to put himself through the University of Pittsburgh where he received his second degree. He continually utilizes his work, art, and life experience in the classroom and in his written work.
In 1996, with some of his computer students, Cain created the award-winning mathematics game, "Absurd Math." In addition, he has created more than 500 Internet learning applications. Cain also has appeared as the on-camera instructor for a video math series on basic mathematics. He has worked as an online facilitator for PBS Teacherline and Mathline. The father of four children, Cain has devoted his life to education and parenting.
This book is great if you are looking for a program to supplement your curriculum and give your students an alternative to pages of disconnected word problems.,Susan Alicea,Mathematics Teaching in the Middle School, 1/1/06
The book offers many advantages to the elementary school mathematics program. As a supplement to the mathematics program, each of the activities contains an area for students to complete their calculations and explain the solution process. To help the students focus on the solution process, only one problem appears on each page. All the Mathability activities represent an application of the Standards-based curriculum. The book also presents a structure for an assessment rubric that includes four levels: mastery, proficient level, near-proficient answers, and nonproficient answers. Mathability provides students with extended-response practice while emphasizing a Standards-based curriculum through the application of real-world problems.,Diane McElwain,Teaching Children Mathematics, 2/1/07
Expertly written by Michael Cain and quite nicely illustrated by Mary Lou Johnson, Mathability: Math in the Real World is a consumable workbook whose exercises and activities are specifically designed to teach children in grades 5 through 8 how people use math in their daily lives. By practicing the mathematics involved in each of the presented “real life" situations, the children will learn, practice, and come to an understanding of key techniques and problem-solving strategies, as well as seeing practical applications for the math they are learning in school. Mathability is especially commended as a curriculum supplement for homeschooling.,James A Cox,Midwest Book Review, 6/20/05