Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.

This challenging problem and brainteaser gives students an opportunity to compose and decompose polygons to make rectangles.

The purpose of this task is to provide students an opportunity to use mathematics addressed in different standards in the same problem.

This high level task is an example of applying geometric methods to solve design problems and satisfy physical constraints. This task is accessible to all students. In this task, a typographic grid system serves as the background for a standard paper clip.

The objective of this lesson is to illustrate how a common everyday experience (such as playing pool) can often provide a learning moment. In the example chosen, we use the game of pool to help explain some key concepts of physics. One of these concepts is the conservation of linear momentum since conservation laws play an extremely important role in many aspects of physics. The idea that a certain property of a system is maintained before and after something happens is quite central to many principles in physics and in the pool example, we concentrate on the conservation of linear momentum. The latter half of the video looks at angular momentum and friction, examining why certain objects roll, as opposed to slide. We do this by looking at how striking a ball with a cue stick at different locations produces different effects.

This task can be implemented in a variety of ways. For a class with previous exposure to properties of perpendicular bisectors, part (a) could be a quick exercise in geometric constructions, and an application of the result. Alternatively, this could be part of an introduction to perpendicular bisectors, culminating in a full proof that the three perpendicular bisectors are concurrent at the circumcenter of the triangle, an essentially complete proof of which is found in the solution below.

Students learn about and practice graphing, plotting points, drawing line segments, and finding the coordinates of points of intersection.

This task is part of a series presenting important foundational geometric results and constructions which are fundamental for more elaborate arguments. They are presented without a real world context so as to see the important hypotheses and logical steps involved as clearly as possible.

This KET animation illustrates positive and negative measurement on a straight line and on a flat plane using a point of origin.

This interactive applet reinforces students' knowledge of the properties of rectangles and gives them a game in which to form and test hypotheses. In a 5x5 grid in which a rectangle has been hidden, students try to fix the location with the fewest number of probes (Note: press 'Start' to hide a different rectangle). Ideas for implementation, extension and support are included along with printable sheets and video clips of classroom testing.

Precalculus 1 & 2 / Trigonometry provides a study of functions and their graphs, including polynomial, rational, exponential, and logarithmic functions. Additionally, right-triangle trigonometry, trigonometric functions and their applications are covered.

In this video segment from Cyberchase, the CyberSquad breaks down an action into a series of steps in order to program a robot to do what they need it to do.

This activity gives students a chance to visualize a two-dimensional net of a three-dimensional object. Students are shown three views of a decorated cube and a net of six plain squares. They must decorate the net so that it folds to a cube consistent with the views. An interactive applet is provided. Ideas for implementation, extension and support are included along with three printable sheets (pdf).

This brief article describes some of the mathematics of Pythagoras and his society. It relates what they believed to be the natural significance of numbers and the well-known Pythagorean Theorem. A link to a printable page is included.

This video lesson presents a real world problem that can be solved by using the Pythagorean theorem. The problem faces a juice seller daily. He has equilateral barrels with equal heights and he always tries to empty the juice of two barrels into a third barrel that has a volume equal to the sum of the volumes of the two barrels. This juice seller wants to find a simple way to help him select the right barrel without wasting time, and without any calculations - since he is ignorant of Mathematics. The prerequisite for this lesson includes knowledge of the following: the Pythagorean theorem; calculation of a triangles area knowing the angle between its two sides; cosine rule; calculation of a circle's area; and calculation of the areas and volumes of solids with regular bases.

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra.

The objective of this lesson plan is to help students identify and explain quadrilaterals.

This lesson focuses on quadrilaterals and attributes in order to classify each shape (parallelogram, rhombus, square, rectangle, and trapezoid). Students will review traits, identify shared traits and names of quadrilaterals, by identifying quadrilaterals in a video story. Then they will show their understanding by creating a quadrilateral story that explains traits and shared traits/names between quadrilaterals.This lesson will take approx 2 math sessions (or approx 120 min.)Thumbnail Image Citation: Bouwhuis, Laura. "Quadrilateral Stories." Canva.com, 11 July 2022, https://www.canva.com/design/DAFGK89WzOM/A_89J6XLB-lNJrcMHjihgg/edit?utm_content=DAFGK89WzOM&utm_campaign=designshare&utm_medium=link2&utm_source=sharebutton

Studies how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Models of randomized computation. Data structures: hash tables, and skip lists. Graph algorithms: minimum spanning trees, shortest paths, and 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.

This lesson is created as a review/assessment of geometric figures for 5th grade mathematics students. Students will create a presentation with pictures to match the figures they have learned and reviewed.