# Authentic Problem Solving

In front of them was a grass-covered hill where thousands of cubic feet of thorium are buried.

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In Years 7–8, students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.

In Years 9–10, students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.

These investigations of the connectedness and complexity of real-world problems nurture collaboration among learners, provide instructional tasks appropriately challenging for the targeted students, and promote performance assessments based upon the context of each learning situation.

Problem-based learning turns instruction topsy-turvy. Students meet an “ill-structured problem” before they receive any instruction.

includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns.

Year 4includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns.Nor will they know exactly what actions are required for resolution.After they tackle the problem, the definition of the problem may change.After visiting the West Chicago site, surveying the community, and conducting experiments, they presented their solutions to state government experts, scientists, and community activists.Not that the “thorium problem” is an easy problem to solve.Activists want all the material moved somewhere else even if the solution bankrupts the company.And some members of the Illinois General Assembly want the thorium removed from the state even though there is no place in the country currently licensed to accept the material.In the place of covering the curriculum, learners probe deeply into issues searching for connections, grappling with complexity, and using knowledge to fashion solutions.As with real problems, students encountering ill-structured problems will not have most of the relevant information needed to solve the problem at the outset.In F–2, students solve problems when they use mathematics to represent unfamiliar or meaningful situations.In Years 3–6, students solve problems when they use mathematics to represent unfamiliar or meaningful situations and plan their approaches.

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