This lesson unit is intended to help teachers assess how well students are able to: use the area of right triangles to deduce the areas of other shapes; use dissection methods for finding areas; organize an investigation systematically and collect data; deduce a generalizable method for finding lengths and areas (The Pythagorean Theorem.)

An interactive applet that allows the user to graphically explore the properties of a quadratic equation. Specifically, it is designed to foster an intuitive understanding of the effects of changing the three coefficients in the function. The applet shows a large graph of a quadratic (ax^2 + bx +c) and has three slider controls, one each for the coefficients a,b and c. As the sliders are moved, the graph is redrawn in real time illustrating the effects of these variations. The roots of the equation are shown both graphically and numerically, including the case where the roots are imaginary. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This resource was created by Tessa Avery and Chris Swalley, in collaboration with Dawn DeTurk, Hannah Blomstedt, and Julie Albrecht, as part of ESU2's Integrating the Arts project. This project is a four year initiative focused on integrating arts into the core curriculum through teacher education, practice, and coaching.

This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

An interactive applet and associated web page that show the definition and properties of a rectangle in coordinate geometry. The applet has a rectangle with draggable vertices. As the user re-sizes the rectangle the applet continuously recalculates its width, height and diagonals from the vertex coordinates. Rectangle can be rotated on the plane to show the more complex cases. The grid, coordinates and calculations can be turned on and off for class problem solving. The applet can be printed in the state it appears on the screen to make handouts. The web page has a full definition of a rectangle when the coordinates of the points defining it are known, and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page showing how to find the area and perimeter of a rectangle from the coordinates of its vertices. The rectangle can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area and perimeter, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This short video and interactive assessment activity is designed to teach fifth graders about identifying the properties of rectangles.

This short video and interactive assessment activity is designed to teach third graders an overview of squares and rectangles.

This task is a reasonably straight-forward application of rigid motion geometry, with emphasis on ruler and straightedge constructions, and would be suitable for assessment purposes.

The goal of this task is to give students an opportunity to experiment with reflections of triangles on a coordinate grid. Students are not prompted in the question to list the coordinates of the different triangle vertices but this is a natural extension of the task.

The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions. In the case of reflecting a rectangle over a diagonal, the reflected image is still a rectangle and it shares two vertices with the original rectangle.

This short video and interactive assessment activity is designed to give fifth graders an overview of reflective symmetry.

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles. In particular, the task has students link their intuitive notions of symmetries of a triangle with statements proving that the said triangle is unmoved by applying certain rigid transformations.

This task examines some of the properties of reflections of the plane which preserve an equilateral triangle: these were introduced in ''Reflections and Isosceles Triangles'' and ''Reflection and Equilateral Triangles I''. The task gives students a chance to see the impact of these reflections on an explicit object and to see that the reflections do not always commute.

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focussing on the class of isosceles triangles.

An interactive applet and associated web page that show the relationship between the perimeter and area of a triangle. It shows that a triangle with a constant perimeter does NOT have a constant area. The applet has a triangle with one vertex draggable and a constant perimeter. As you drag the vertex, it is clear that the area varies, even though the perimeter is constant. Optionally, you can see the path traced by the dragged vertex and see that it forms an ellipse. A link takes you to a page where this effect is exploited to construct an ellipse with string and pins. The applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This Remote Learning Plan was created by Chelsey Greene in collaboration with Rick Meyer as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for 4th Grade Math students. Students will identify lines, line segments, points and rays. This Remote Learning Plan addresses the following NDE Standard: MA 4.3.1.c Identify and draw points, lines, line segments, rays, angles, parallel lines, perpendicular lines, and intersecting lines, and recognize them in two-dimensional figures. 

This Remote Learning Plan was created by Becky Schueth in collaboration with Craig Hicks and Tyler Cronin as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for Grades 9-11 Geometry students. Students will solve problems involving angle sum in polygons. This Remote Learning Plan addresses the following NDE Standard: MA 11.3.1.c. It is expected that this Remote Learning Plan will take students 120 minutes to complete. Here is the direct link to the Google Doc:https://docs.google.com/presentation/d/16WqWgnppJZhU4JyQyvj7afv3kG91vwpuVZdHTGwAOyg/edit?usp=sharing

This Remote Learning Plan was created by Chelsey Greene in collaboration with Rick Meyer as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for 4th Grade Math students. Students will learn how to find the Perimeter of a Polygon. This Remote Learning Plan addresses the following NDE Standards: *MA 4.3.3.a Apply perimeter and area formulas for rectangles. *MA 4.3.3.b Identify and use the appropriate tools, operations, and units of measurement, both customary and metric, to solve real-world problems involving time, length, weight, mass, capacity, and volume.

This Remote Learning Plan was created by Becky Schueth in collaboration with Craig Hicks and Tyler Cronin as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for grades 9-11 Geometry students. Students will solve problems involving quadrilaterals. This Remote Learning Plan addresses the following NDE Standard: MA 11.3.1.c. It is expected that this Remote Learning Plan will take students 120 minutes to complete. Here is the direct link to the Google Doc: https://docs.google.com/presentation/d/1pnnojSoDEzmNx3jD4M1y1sD-nhRJIHMkA3w-S-Z7mTA/edit?usp=sharing