This task is part of a series presenting important foundational geometric results …
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.
An interactive applet and associated web page that demonstrate polygons. The applet …
An interactive applet and associated web page that demonstrate polygons. The applet shows a polygon which is initially an irregular convex pentagon. The user can drag any vertex and a message shows if it becomes concave. The user can also alter the number of sides from 3 to 99, the title changing to reflect it's name up to 12 sides. You can also make it regular, dragging a vertex then changes all vertices to maintain it as regular. The web page has many definitions and links to the various forms and orders of polygon. 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.
Students take a close look at truss structures, the geometric shapes that …
Students take a close look at truss structures, the geometric shapes that compose them, and the many variations seen in bridge designs in use every day. Through a guided worksheet, students draw assorted 2D and 3D polygon shapes and think through their forms and interior angles (mental “testing”) before and after load conditions are applied. They see how engineers add structural members to polygon shapes to support them under compression and tension, and how triangles provide the strongest elemental shape. A PowerPoint® presentation is provided. This lesson prepares students for two associated activities that continue the series on polygons and trusses.
Students learn about the role engineers play in designing and building truss …
Students learn about the role engineers play in designing and building truss structures. Simulating a real-world civil engineering challenge, student teams are tasked to create strong and unique truss structures for a local bridge. They design to address project constraints, including the requirement to incorporate three different polygon shapes, and follow the steps of the engineering design process. They use hot glue and Popsicle sticks to create their small-size bridge prototypes. After compressive load tests, they evaluate their results and redesign for improvement. They collect, graph and analyze before/after measurements of interior angles to investigate shape deformation. A PowerPoint® presentation, design worksheet and data collection sheet are provided. This activity is the final step in a series on polygons and trusses.
In this video segment from Cyberchase, the CyberSquad breaks down an action …
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 video lesson presents a real world problem that can be solved …
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 Flexbook is community contributed through ck12.org. It covers three lessons on …
This Flexbook is community contributed through ck12.org. It covers three lessons on the Pythagorean Theorem. 1) Introduction and Determining if the Triangle is a Right Triangle, 2) Finding the Hypotenuse, and 3) Finding a leg. It includes step by step instructions, application problems, and answers (at the end of each lesson). Ck12.org material is downloadable, editable, and accessible offline and online.
This is a cross curricular art project for 8th grade math students. …
This is a cross curricular art project for 8th grade math students. Students are first introduced to what the Wheel of Theodorus is, ponder where they see it in the world around them and then instructed on how to create their own. When they have finished constructing their Wheel of Theodorus they are asked to creatively and colorfully turn it "into" something. Examples are given. After they Wheel of Theodorus is complete, students are then asked to measure all the sides lengths of the triangles in the wheel. They should quickly see that they can use the Pythagorean Theorem to do this and that it follows a predictable pattern. No ruler will be required for this part of the project!
This is a cross curricular art project for 8th grade math students. …
This is a cross curricular art project for 8th grade math students. Students are first introduced to what the Wheel of Theodorus is, ponder where they see it in the world around them and then instructed on how to create their own. When they have finished constructing their Wheel of Theodorus they are asked to creatively and colorfully turn it "into" something. Examples are given. After they Wheel of Theodorus is complete, students are then asked to measure all the sides lengths of the triangles in the wheel. They should quickly see that they can use the Pythagorean Theorem to do this and that it follows a predictable pattern. No ruler will be required for this part of the project!
This resource goes throught the Pythagorean Theorem by explaining what the theorem …
This resource goes throught the Pythagorean Theorem by explaining what the theorem is, proving the theorem, and using the theorem. This resource contains an article, videos, powerpoint, and link to practice questions on Khan Academy.
This lesson teaches students about the history of the Pythagorean theorem, along …
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.
This lesson unit is intended to help teachers assess how well students …
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.)
Reviewing the Pythagorean Theorem. Did you know the Scarecrow states the Pythagorean …
Reviewing the Pythagorean Theorem. Did you know the Scarecrow states the Pythagorean Theorem incorrectly in The Wizard of Oz? At the end is a clip of Homer Simpson also stating the Pythagorean Theorem incorrectly
An interactive applet that allows the user to graphically explore the properties …
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.
An interactive applet and associated web page that show the definition and …
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.
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