The foundation for success in advanced mathematics is built on problem solving skills. Problem solving requires strong skills in reasoning, analysis, and argument construction, and the ability to apply innovative strategies to find a solution. While these skills should be taught at all levels, it's especially important to help students develop them as progress toward the more complex math concepts they will learn in high school.

To help students become skilled problem solvers in grades 4 through 8, teachers can prepare problems to use in whole-class instruction; provide explicit problem-solving instruction that teaches students to use visual representations, employ multiple strategies, and links mathematical concepts and notation to problems; and allow time to reflect and debrief on their strategies and solutions with classmates.

To learn more about the research underlying these practices, view the IES Practice Guide, Improving Mathematical Problem Solving in Grades 4 Through 8.

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Pre-Algebra Fencing Task

At Papillion Junior High School, seventh-grade students work in groups on a non-routine geometry problem. This sample material has a fencing task worksheet and photos of students’ presentations of...

Sample Material
Document
03/03/2014
866 views

Fraction Problem: Part of a Part

Grade 6 students at Patriot Elementary use several strategies to solve a real-world, part of a part problem. This sample material has the scenario and statement of the problem along with pictures...

Sample Material
Document
03/03/2014
876 views

Using Visual Representations

Teachers can use these examples for ideas to help students create visual representations for different types of problems.

Sample Material
Document
03/03/2014
1038 views

Frank's Problem

Grade 6 students at Madison Elementary School use visual representations to present their solutions to Frank’s Fresh Farm Produce problem. The first page of the sample material has a statement of...

Sample Material
Document
03/03/2014
824 views

Roll Around the Clock

Students use a clock visual for fractions and problem solve with fraction concepts while playing Roll Around the Clock. This sample material presents instructions for the game along with a clock...

Sample Material
Document
03/03/2014
881 views

Who Finishes When?

At Worthington Hooker School, pre-algebra students work on the Who Finishes When? problem. They use visual representations to interpret the information in the problem. This sample material has the...

Sample Material
Document
03/03/2014
849 views

Questions and Prompts for Developing Mathematical Thinking

This sample material is a copy of the classroom poster from Coach Talk: Preparing for Problem Solving that teachers use as guidance for the problem-solving process. It was developed by the...

Sample Material
Document
02/28/2014
908 views

Resources for Planning Problems

This sample material contains publications from the National Council of Teachers of Mathematics (NCTM) and other sources. There are links to 12 websites that have collections of problems and...

Sample Material
Document
02/28/2014
872 views

Pre-Conference Planning Form

Elementary math coaches in the Papillion-La Vista School District use a lesson pre-conference planning form with teachers. Coaches work with teachers to consider goals and students’ experience and...

Sample Material
Document
02/28/2014
1071 views
Visual Diagram: Problem Solving

Visual Diagram: Problem Solving

The visual diagram illustrates three essential practices (preparation of problems, instructional approaches, and reflection and monitoring) based on the recommendations in the Practice Guide,Visual...

Visual Diagram
Document
02/27/2014
890 views
Helping Students Debrief

Helping Students Debrief

Dr. Mark Driscoll provides practical advice on building students' habits of reasoning by structuring discussions using particular questions and written tools. See also Multiple Problem-Solving...

Expert Interview
Video
02/14/2014
535 views
Monitoring the Problem-Solving Process

Monitoring the Problem-Solving Process

Listen to Dr. Sybilla Beckmann describe strategies for helping students monitor and reflect during the problem-solving process.

Expert Interview
Audio
02/14/2014
964 views
  • Items 13 - 24 of 47