Introduction to the LMR Lessons

The LMR Curriculum

The LMR curriculum focuses on core ideas about the representation of number on the number line. As students progress through the curriculum, they develop rich understandings of integers and fractions as they solve number line problems and justify their solutions. LMR’s strategy is to engage students with explicitly defined mathematical ideas as resources for mathematical argumentation and justification. You can download all of the lessons and materials here.

5-Phase Structure of Lessons

Each of the 25 LMR lessons follows a 5-phase structure:

Opening Problems establish the focus of the day's lesson. These problems are generally non-routine tasks that elicit a diversity of student ideas. "Fill in the missing number" on a number line with unequal intervals (as displayed in the figure on the right) is an example of an opening problem
Opening Discussion provides a context for surfacing the diversity of students' ideas and reasoning about conflicts among ideas linked to opening problems
Partner Work engages students in building on the ideas in the Opening Discussion. Students work in pairs to solve variations of the Opening Problems.
Closing Discussion is the context for resolving remaining contradictions and reviewing key ideas.
Closing Problems serve as formative assessment of students' progress.

Each of the downloadable 26 lessons include files that contain opening and closing problems to support formative assessment, partner worksheets, principle/definition posters, and a complete guide.

Fig 3x.pdf

Scope and Sequence

Before progressing further on the site, you may find it useful to review the scope and sequence of the lessons by clicking on the links to positive integers, negative integers, and fractions. Then, consider reading the Lesson Guide Introduction, which provides essential background on LMR and a rationale for the scope and sequence. More specifically, the lesson guide introduction describes the motivation for the lessons, the rationale for the choice of the number line as a central representational context for the lessons, the design principles that guided the lesson development process, an overview of the studies that provided a foundation for lesson development, and an overview of the lessons’ organization including supports for teachers who may be implementing the lessons.

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