A unique component of Math Trailblazers is the use of a laboratory method that helps students build and analyze mathematical models of authentic situations, providing opportunities to reason quantitatively, construct viable arguments, attend to precision, and persevere as problem solvers. Students use multiple representations (e.g., objects, graphs, tables, pictures, and equations) to describe and analyze the mathematical situation, allowing them to access the mathematics, apply conceptual understanding, and develop problem solving strategies. The contexts for solving problems help the students in a Math Trailblazers classroom learn to use mathematics in meaningful ways.

In every experiment, students draw some kind of a picture or diagram that identifies the variables and explains what the experiment is about. The second part is a data table; data is collected and organized in some way. Third, the data is almost always graphed, so there’s a visual representation of the data. In these experiments there is generally a pattern in the data that can be expressed in some mathematical way. The last step is using that data to answer questions about the physical situation. The ultimate goal is for students to have a strong foundation by the time they get to the middle grades that allows them to learn proportional reasoning, to understand fractions, and to really understand what a function is.

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