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Book Resource—Awesome Math Problems for Creative Thinking

Resource
Awesome Math Problems for Creative Thinking
Findell, C. R., Gavin, M. K., Greenes, C. E., Sheffield, L. J.
Chicago, IL: Creative Publications
2000
Creative Thinking
Students have a wide range of 50 questions, each with their own difficulty. Some questions ask students to find the weight of certain objects with limited information; others ask “in this given sequence, what is the 245th number?”
Description
These books (set of 6) provide advanced mathematics problems for high-level students. Each book contains 50 problems with answers. Questions range from probability to evaluation questions to deductive reasoning. The books start at level (grade) 3 and go up to level 8 (see level on the back of each book, represented in dots).
 
These books are written to create high interest and challenge for students with math talent. Students who love math enjoy working on the problems whenever they have an opportunity The problems can be used as enrichment in the classroom or as a journal assessment of mathematical thinking. They are also excellent gift ideas for parents.
Appeal and User Friendliness
Each book is easily accessible and does not require teacher assistance. Questions are concise and well worded. Hints are given on some of the more difficult problems. Answers to all the problems are in the back of the book.

 
Web Resource—Exploring Connections Between Mathematics and Art

Grade Levels
Because of the content background knowledge needed, this activity would be appropriate for students in grades 5-8.
Creative Thinking
This interactive applet stimulates creative and divergent thinking by asking students to find and explore mathematics through the art at the San Francisco Museum of Modern Art.
Description
Through virtual tours, springboard questions are posed, prompting students to evaluate what they see and how it connects to mathematics. Thus, the investigation tries to provide a context in which aspects from the process standards and two content standards; Algebraic Reasoning and Geometry are developed. Students will be asked questions such as,” Directly in front of the revolving door you will see a curve on the ground that separates black and white areas of the cement. How could you find an equation for this curve? Do you think it is a circle?”
Appeal and User Friendliness
Traveling through this I-math investigation is fairly straightforward. Each question raises new ideas and asks students to determine creatively how they would go about solving the problem. To do this, students must determine which mathematics within their knowledge base is appropriate and apply what they already know to new situations. While this activity focuses on the “how to” rather than specific computational answers, teachers may want to use this activity as an introduction and then have students create specific questions that focus on the same math concepts but relate to their own world.
Website
www.fayar.net/east/teacher.web/Math/Illuminations/imath/across/connections/index.html [website no longer active]

 
Web Resource—Mathematics of Cartography

Creative Thinking
Students are asked to solve problems but at the same time find a creative way to do it. Students must use map techniques in addition to mathematics.
Description
Mathematics of Cartography mixes the world of maps and mathematics. Background information on mapping (cartography) is available as well as mathematical problems in cartography. Four questions, dealing with distance, scale and algebra, take the concepts of mathematics and ask students to find the farthest point from their house, using an online map source.
 
While there are only 4 questions, these questions are a great start for students who are interested in mapping, or simply need a more realistic approach to mathematics. Many links on this site direct the reader to informational sites regarding mapping and mathematics.
Appeal and User Friendliness
This site provides easy navigation by any individual. Only four problems are presented. Teachers may want to use this site as a springboard into mapping or make up their own problems.

 
Web Resource—MEGA Mathematics

Creative Thinking
Each major idea presented has varied levels of projects. Students must use higher levels of thinking to compare and contrast presented materials. Creativity is highlighted.
Description
This site is recommended more for teachers to use than students. Mega Math provides many different ideas and projects for students. Each activity is written in a lesson plan format. There are many excellent creative explorations.
 
All of the activities involve hands-on exploration, and lots of opportunities for mathematical thinking, problem-solving and communication. All of the topics are live, important areas of current mathematical research.
Appeal and User Friendliness
This site is easily navigated by teachers. Many of the projects do not have projected ages or grade levels, so teachers must choose which projects best suit their needs. The ideas presented are current and interesting, even to younger students. Each main idea has several subparts, allowing a varied level of instruction.
Sample Problem
Mega Math offers many different opportunities, each stressing a new idea of mathematics. Projects like Untangling the Mathematics of Knots, investigate different forms of the same concept, in this case knots.
Website
www.c3.lanl.gov/mega-math [website no longer active]

 
Web Resource—Pumas

Creative Thinking
Students are asked to evaluate and solve problems on the local and global level. Problems range in topic from traffic light settings to the human eye construction.
Description
PUMAS (poo’ á mas)—is a collection of one-page examples of how math and science topics taught in K-12 classes can be used in interesting settings, including everyday life.
 
Students and teachers may peruse through problem titles to find appropriate questions. This site would be great for bright middle school students. All the problems are submitted by active scientists and engineers, and are available through the website for anyone. The site continues to welcome new submissions of problems.
Appeal and User Friendliness
The navigation throughout the site is easy. Teachers and students may choose their problem by title or they may choose to search the site by header field, content or multiple criteria.
Sample Problem
This site offers countless examples of problems students can use to apply mathematics to real world situations. Problems like “Could a World of Swimmers Raise Sea Level?” challenge students to think divergently about their life and apply their own actions to problems.