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##### Developing Algebraic Reasoning

The transition from arithmetic or algebraic reasoning has been a stumbling block for many middle grade and early high school students. Prior to learning formal methods of simplifying symbolic expressions and solving equations, students need to be comfortable with informal, intuitive strategies for problem solving.

Viewing operations as more than computation increases the recognition of the relationship between quantities and clarifies the meaning of operations.  Teachers will learn how to plan coherent and developmental lessons that increase students' understanding of algebraic concepts by analyzing student strategies.

Participants will use Algebraic Habits of Mind to examine methods to scaffold student engagement from direct modeling experiences to using concrete objects, pictures, tables, various graphs, formulas, verbal descriptions to more complexed relationships with abstract symbols.  Teachers will also learn to "algebrafy" problems for classroom use as well as increase their effectiveness in analyzing student work.

3 -12 Hours / Grades 6-9

#### Mathematics

##### Manipulative Mania

Have you wondered what to do with those manipulatives collecting dust on your classroom shelf? Designed to promote critical thinking, the activities shared in this session not only address this question but also incorporate objectives that meet the most critical standards outlined in the Common Core. Without requiring any other ancillary materials, the session utilizes the standard manipulatives found in the NC State Math Manipulatives Kit for ETA Cuisenaire.

Model Drawing: A Pictorial Approach

Problem solving consists of many strategies, such as guessing and checking; making an organized list; looking for patterns; working backwards, etc. Model drawing is a powerful problem-solving tool that offers an additional option for students to solve word problems. The model drawing strategies are adapted from the Singapore math curriculum, which focuses on moving students from concrete to pictorial to abstract thinking levels, reinforcing students' ability to visualize and understand mathematical concepts and processes. Participants will review a variety of problems, utilizing the 8-step model drawing process, with a focus on questioning techniques that will facilitate the use of fewer problems with greater instructional depth.

##### Unpacking Proportional Reasoning

Middle grades' mathematics curriculum transitions from absolute to relative cognitive processes.  This session helps teachers develop and extend student flexibility to visualize problems from different perspectives. Participants learn to identify the different types of proportional reasoning problems and learn implementable strategies for solving proportional reasoning problems in classroom instruction.  Additionally, participants will review student work to assess how students process proportional reasoning situations and how to identify and increase the 13 characteristics of effective proportional thinkers.