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Book Resource—20 Thinking Questions for Geoboards: Grades 3-6

Resource
20 Thinking Questions for Geoboards: Grades 3-6
Walker, K., Reak, C., and Stewart, K.
Chicago, IL: Creative Publications
1995
Grade Level
This resource book is written for students in grades 3-6. Some activities are appropriate for younger talented math students as well.
Creative Thinking
20 Thinking Questions for Geoboards is one of fifteen books in a series from Creative Publications designed to develop mathematical thinking skills using a specific manipulative. This particular book is designed to help students in grades 3-6 develop mathematical thinking strategies using geoboards to solve problems. Each of the 20 questions in the book serves as the basis of an activity that challenges students to explore a number of geometry, measurement, and fraction concepts.
Description
This book contains 20 questions that encourage students to explore a variety of math topics such as the properties of polygons, perimeter, area, symmetry, and fractions. Each activity begins with the teacher presenting a question. Students are then encouraged to manipulate geoboards as they follow their own logic in finding solutions to the problem. Each open-ended question encourages multiple problem-solving methods and has multiple solutions. Students are asked to record and explain their work in writing, before engaging in a group discussion. Finally, students respond to a journal prompt that encourages them to reflect on new understandings and insights that were gleaned as a result of the investigation.
Appeal and User Friendliness
This book can easily be adapted to create a “thinking strand” for students within the current curriculum. Most questions take one to two class periods to complete. The 20 questions are arranged from easiest to most difficult. However, teachers of high ability students may want to select those questions that best fit student abilities and not present them in the order given. The teacher notes offer excellent guidance to facilitate students through each activity. A section labeled “What You Might See” gives illustrated sample answers and solution methods. Also included are hints on what teachers can do to redirect students’ work when necessary and what to look for in assessing student understanding.
Sample Problem
How many different-sized squares can you find on your geoboard? Record the squares. Explain how you know each square is different and how you know you have found all possible squares.

 
Book Resource—20 Thinking Questions for Pattern Blocks: Grades 3-6

Resource
20 Thinking Questions for Pattern Blocks: Grades 3-6
Walker, K., Reak, C., and Stewart, K.
Chicago, IL: Creative Publications
1995
Grade Level
This mathematics resource book is written for students in grades 3-6 and appropriate for talented elementary students.
Creative Thinking
20 Thinking Questions for Pattern Blocks is designed to help students develop creative thinking strategies in mathematics using Pattern Blocks to solve problems. Each of the 20 open-ended questions in the book serves as the basis of an activity that challenges students to explore a number of geometry, measurement, and fraction concepts.
Description
This book contains 20 questions that encourage students to explore a variety of math topics such as perimeter, area, symmetry, angle measure, patterns, fractions and percents. Each activity begins with the teacher presenting a question. Students are then encouraged to manipulate Pattern Blocks as they follow their own logic in finding solutions to the problem. Each question encourages creative problem-solving methods and has multiple solutions. As part of the problem-solving process, students are asked to record and explain their work in writing, before engaging in a group discussion where solutions and strategies are shared. As a culminating part of the activity, students respond to a journal prompt that encourages them to reflect on new understandings and insights that were gleaned as a result of the investigation.
Appeal and User Friendliness
20 Thinking Questions can easily be adapted to work within a current curriculum to create a “thinking strand” for students. Most questions take one to two class periods to complete. Since questions are arranged from easiest to most difficult, teachers of high-ability students may want to select those questions that best fit student abilities and not present them in the order given. The teacher notes offer excellent guidance to facilitate students through each activity.
Sample Problem
Question 13, page 46
Can you make a design where 1/4 of the area is green? Use your Pattern Blocks to make a design. Then record your design and explain how you know that 1/4 of the area is green.

 
Book Resource—Awesome Math Problems for Creative Thinking

Resource
Awesome Math Problems for Creative Thinking
Findell, C. R., Gavin, M. K., Greenes, C. E., and Sheffield, L. J.
Chicago, IL: Creative Publications
2000
Grade Levels
Elementary
Creative Thinking
Students are offered an array of 50 problems covering all 5 NCTM Content Standards that require them to think divergently to find solutions.
Description
These are a set of 6 soft-covered pocket books that 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, at a learning center, or as a journal assessment of mathematical thinking. They are also excellent gift ideas for parents.
Appeal and User Friendliness
Each problem is written in a clear articulate manner. Hints are given on some of the more difficult problems. Answers to all the problems are in the back of the book.

 
Book Resource—Puddle Questions: Assessing Mathematical Thinking

Resource
Puddle Questions: Assessing Mathematical Thinking
Westely, J.
Mountain View, CA: Creative Publications
1994
Grade Levels
A series of books written for all students in grades 1-8. Appropriate for talented students in grades 1-5.
Creative Thinking
Puddle Questions is a series of math resource books that present open-ended, problem-solving challenges designed to help assess students’ thinking, use of tools, execution of ideas, and communication in mathematics. These investigations encourage divergent thinking and creative approaches to solving problems. The challenges allow for multiple entry points and enable students to come up with their own ways to solving the problems.
Description
This series of books contains rich, open-ended investigations that focus on statistics, probability, measurement, estimation, reasoning, arithmetic, geometry, math language, and visual thinking.
 
The Puddle Problem, “How would you measure a puddle?” is the first investigation of eight in each of the grade level books. This problem encourages students to record all the different ways a puddle can be measured. Since a puddle is not a regular solid object, students must come up with creative and interesting ways to measure it. As students gain experience with measurement through the grades, their responses become more detailed and elaborate. All the challenges presented in this series require students to think critically and to present their work in a careful manner. Students are asked to write a “report” to explain their reasoning, draw pictures of their plan, or organize and display data in a meaningful fashion. Holistic scoring rubrics and samples of student work are also included to assist teachers in assessing student performance. Each book in the series contains blackline masters for the investigations, and they are written in both English and Spanish.
Appeal and User Friendliness
The context for each investigation is age-appropriate and appeals to the students’ interests. The open-ended problems allow for great differentiation. The teacher notes presented with each problem offer excellent support and guidance. Also included are wonderful follow-up activities that serve as a natural outgrowth to extend and enhance the learning experience in each investigation. The samples of student work that serve as benchmarks for each level on the scoring rubric are extremely helpful in supporting teachers, especially those who have little experience evaluating performance tasks.

 
Web Resource—MEGA Mathematics

Creative Thinking
Each major idea presented has a variety of projects at different levels of challenge. 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 for classroom implementation. Even though it is not student interactive, this site has so many great ideas, it should not be overlooked.
 
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, but designed for 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, something everyone has dealt with from the day they learned to tie a shoe.
Website
www.c3.lanl.gov/mega-math (website no longer active)