### DOE Archives

#### New Jersey Core Curriculum Content Standards

May 1996

Mathematics Standards And Progress Indicators
Standard 4.1:
All Students Will Develop The Ability To Pose And Solve Mathematical Problems In Mathematics, Other Disciplines, And Everyday Experiences

Descriptive Statement: Problem posing and problem solving involve examining situations that arise in mathematics and other disciplines and in common experiences, describing these situations mathematically, formulating appropriate mathematical questions, and using a variety of strategies to find solutions. By developing their problem-solving skills, students will come to realize the potential usefulness of mathematics in their lives.

Cumulative Progress Indicators

By the end of Grade 4, students:

 1 Use discovery-oriented, inquiry-based, and problem-centered approaches to investigate and understand mathematical content appropriate to early elementary grades. 2 Recognize, formulate, and solve problems arising from mathematical situations and everyday experiences. 3 Construct and use concrete, pictorial, symbolic, and graphical models to represent problem situations. 4 Pose, explore, and solve a variety of problems, including non-routine problems and open-ended problems with several solutions and/or solution strategies. 5 Construct, explain, justify, and apply a variety of problem-solving strategies in both cooperative and independent learning environments. 6 Verify the correctness and reasonableness of results and interpret them in the context of the problems being solved. 7 Know when to select and how to use grade-appropriate mathematical tools and methods (including manipulatives, calculators and computers, as well as mental math and paper-and-pencil techniques) as a natural and routine part of the problem- solving process. 8 Determine, collect, organize, and analyze data needed to solve problems. 9 Recognize that there may be multiple ways to solve a problem.

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued progress in Indicators 4, 5, 6, 7, and 8 above, by the end of Grade 8, students:

 10 Use discovery-oriented, inquiry-based, and problem-centered approaches to investigate and understand mathematical content appropriate to the middle grades. 11 Recognize, formulate, and solve problems arising from mathematical situations, everyday experiences, and applications to other disciplines. 12 Construct and use concrete, pictorial, symbolic, and graphical models to represent problem situations and effectively apply processes of mathematical modeling in mathematics and other areas. 13 Recognize that there may be multiple ways to solve a problem, weigh their relative merits, and select and use appropriate problem-solving strategies. 14 Persevere in developing alternative problem-solving strategies if initially selected approaches do not work.

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued progress in Indicators 4, 5, 6, 7, 8, 12, and 14 above, by the end of Grade 12, students:

 15 Use discovery-oriented, inquiry-based, and problem-centered approaches to investigate and understand the mathematical content appropriate to the high school grades. 16 Recognize, formulate, and solve problems arising from mathematical situations, everyday experiences, applications to other disciplines, and career applications. 17 Monitor their own progress toward problem solutions. 18 Explore the validity and efficiency of various problem-posing and problem-solving strategies, and develop alternative strategies and generalizations as needed.

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