+ MIRA, MIRA ON THE WALL Hands on Constructions in Geometry Kyndall Brown Executive Director California Mathematics Project

+ Overview of Presentation CaCCSS-M on Constructions Introduction to the MIRA Geometric Constructions

+ CaCCSS-M on Constructions Geometry-Congruence Make Geometric Constructions 12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. 13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

+ CaCCSS-M on Constructions Standards for Mathematical Practice Use appropriate tools strategically Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, astatistical package, or dynamic geometry software. Attend to precision Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They are careful about specifying units of measure. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

+ Beyond Good Teaching: Advancing Mathematics Education for ELLs (2012) Guiding Principles for Teaching Mathematics to ELLs 4. Mathematical tools and modeling as resources Mathematical tools and mathematical modeling provide a resource for ELLs to engage in mathematics and communicate their mathematical understanding and are essential in developing a community that enhances discourse

+ Geometric Construction The drawing of geometric items, such as lines and circles using only compasses and straightedge (ruler). Reflective Devices Paper Folding Dynamic Geometry Software

+ History of Constructions To thoroughly examine the history of geometry, it is necessary to go back to ancient Egyptian mathematics. From Egypt, Thales brought geometric ideas and introduced them to Greece. In early geometry, the tools of the trade were a compass and a straightedge. A compass was used to make circles of a given radius. A straightedge was to be used only for drawing a segment between two points. There were specific rules about what could and could not be used for mathematical drawings. These drawings, known as constructions, had to be exact. If the rules were broken, the mathematics involved in the constructions was often disregarded.

+ Mathematics of Constructions Isometry-A transformation of a geometric figure that preserves the size and shape of a figure Reflection-A type of isometry that produces a mirror image. A line of reflection defines a reflection. The line of reflection is the perpendicular bisector of any segment joining a point in the figure with the image of the point. If a point in the figure is on the line of reflection, then the point is its own image.

+ Thank You ETA Hand2Mind-Sara Moore MIRA’s Compasses Straightedges

+ Kyndall Brown Mathematics-Project/ (310)