MATH DETECTIVES

Introduction

This site was developed to help fifth grade teachers address the ISAT math "open ended" questions.  The Illinois standards and benchmarks demand a combination of knowledge and skills.  No longer is just the answer enough.  The student is now expected to explain in written language how he/she found the solution to the problem.  The student needs to understand the conceptual knowledge in addition to the procedural knowledge.

A detective theme will be used to achieve the goals listed above.  Students will assume the job of detective trainees needing to not only solve the "cases" they are assigned, but to also explain their procedures.   If they are successful in solving two cases, they will become a full-time detective. The cases will be both fun and challenging providing problems that the students will look forward to solving, instead of the too common comment. " Oh, no! Not more story problems!"

Content Area and Grade Level

These lessons are developed for a fifth grade level, and will involve math problem solving and language arts writing and communication skills.  Many of the problems may be adjusted to fourth and sixth grade ability levels.

Curriculum Standards

This Math Detective Quest addresses the following Math and Language Arts Illinois State Goals and Learning Standards (Grade 5).

Math State Goal 6

Demonstrate and apply a knowledge and sense of numbers, including numeration and operations, patterns, ratios, and proportions.
Learning Standard B, Benchmark 6.B.2
Learning Standard C, Benchmarks 6C.2a and 6C2b

Math State Goal 7

Estimate; make and use measurements of objects, quantities and relationships; and determine acceptable levels of accuracy.
Learning Standard A, Benchmark 7.A.2a and 7.A.2b

Language Arts State Goal 3

Write to communicate for a variety of purposes.
Learning Standard A, Benchmark 3.A.2
Learning Standard B, Benchmark 3.B.2a and 3B.2b
Learning Standard C

Lessons may be organized according to a teacher's needs and the availability of computers.

Some of these sites present problems that may be presented and solved in one class period.  Others take longer.   The "Fizz and Martina's Math Adventures" take five class periods to complete.  " Math Mysteries" requires a half hour per problem (7 problems) for the whole class CD, and two to three hours total for the students' CD.  Students work alone or in pairs on this CD program so the time involved would relate to how many computers are available.  Teachers may also have their students trade math problems on-line with other classrooms so this may be as often as a teacher would like.

Some of the programs can be used in a one computer classroom ( such as Tom Snyder's "Fizz and Martina's Math Adventures"), and others are better if each student, or each group of students, have their own computer.

Resources Needed

COMPUTER SOFTWARE
Tom Snyder

 "Prime Time Math", Grades 4-9

Engages students in real world dramatic stories.
Students working in teams watch a video and solve problems.
"Adrift" - maps and geometry for grades 4 and 5
"Lost!" - decimals and geometry for grades 5 and 6
To preview click here

"Fizz & Martina's Math Adventures ",Grades 1 - 6

This is a one computer classroom program. Students watch an episode and then solve a problem in cooperative groups.  Students must explain their strategy in writing and are then quizzed verbally.  Team success depends on individual success.
"Project Sphinx" - multiplication and division for grades 4 and 5
" Lights, Camera, Fractions" - fractions for grades 5 and 6
To preview click here

              "Math Mysteries", Grades 4 - 7

The teacher will first model the problem solving process on the computer.  Students then work. on their own or in groups, at computers to solve problems as mysteries unfold.  This series includes programs on fractions, measurement, and whole numbers.
To preview click here

INTERNET RESOURCES

Math Magic

This site posts challenges for grades 4 through 6.  Registered teams engage in problem solving dialog.

Math Mysteries Make Your Own Problem

This site provides a worksheet and lists the steps a student must go through in writing a problem.  Students may make up their own settings and characters or choose from those listed.

Math Mysteries Share a Problem

Students may post their own problems at this site.   Students may also work on other students' problems, and will be told if their answers are correct or incorrect.

Cool Math

What a great site!  Under the math topic, there is a sub topic with 48 word problems.  The site gives hints to solving each problem, and then tells the answer to each problem.   Under the math art and games topic, the students will find a variety of 34 different math games.

BOOKS

Writing Activities to Develop Mathematical Thinking by Dr. M. Ann Dirkes
This book enables you to individualize math activities for children from 1st to 6th grade.  It covers creative problem solving, and has examples and activities.

Designing Creative Mathematics Activities by Dr. Julie Ellis and Hank Boer.
This book has units to foster a child's creativity and develop creative problem solving techniques.  Grades 1 to 6.

Problemoids by Bill McCandiss and Dr. Albert Watson.
This program was created for advanced students in math in grades 4, 5, and 6.  This allows them to work at their own pace.  It focuses on learning and using problem solving strategies.  There are student workbooks, separate solution sheets with strategies for solving the problems, and a teacher manual.  A computer supplement is available.

Entry Level Skills and Knowledge

Students will need to know the four basic math operations and have basic problem solving skills. Problems will be solved using the following steps: understand the problem, devise a plan, collect information and carry out the plan, and then explain the solution.  These problem solving skills will be fine tuned as students practice them more and more.

Teacher needs to preview lessons and sites for appropriateness.

Evaluation

The students will be evaluated by their peers and then their teacher.  They are to orally present the two cases they solved to their peers.  They must demonstrate that they have followed all the steps mentioned in the above "Entry Level Skills and Knowledge."  They must also present a written explanation of their strategies and solutions to their teacher.  The peers and teacher must accept two of their cases before they can become a full-time licensed detective.  It will be up to each individual teacher to recognize this accomplishment with a certificate, badge, etc..

Possible Variations

Teachers may require a different number of solved cases for a student to become a full-time detective.  Students may work alone or in a small group.

Conclusion

The Illinois State Math Achievement Tests now demand a combination of knowledge and communication skills. The programs and internet sites listed in this web quest will provide practice and reinforcement of these particular skills.

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