An interactive applet and associated web page that demonstrate the properties of …
An interactive applet and associated web page that demonstrate the properties of a cube. A 3-D cube is shown in the applet which can be interactively manipulated using the mouse. Research has shown that some younger students have difficulty visualizing the parts of a 3D object that are hidden. To help with this, the student can rotate the cube in any axis simply by dragging it with the mouse. It can also be 'exploded' - where a slider gradually separates the faces to reveal the ones behind. The cube can also be made translucent so you see through it to the other side. Applet can be enlarged to full screen size for use with a classroom projector, and printed to make handouts. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
CurvedLand is an applet for showing what the world would look like …
CurvedLand is an applet for showing what the world would look like with different geometry. It is named CurvedLand in tribute to the science fiction novel, Flatland, by Edwin Abbott, which describes the adventures of a two-dimensional being who is visited by a stranger from the third dimension.
One of the central ideas of Einstein's theory of relativity is that space and time curve in response to the matter and energy within them. A curved space is one that doesn't obey the usual laws of Euclidean geometry: the angles of a triangle don't generally add up to 180 degrees, the circumference of a circle isn't pi times the diameter, parallel lines can either converge towards each other or move apart, and so on.
Since the geometry we observe is very close to Euclidean, however, it is hard for most of us to picture what this difference would mean physically. If you draw a circle and a diameter, how could the ratio be anything other than pi? To answer this question, imagine that as you move around in space the shapes of objects appear to distort. This is what happens in curved space. If you draw a circle around yourself and then start walking around it to pace out the circumference, it will look to you like you are walking along a constantly changing ellipse.
CurvedLand illustrates this distortion as it would appear in a two-dimensional curved space. The structure is similar to a mapping program. You can place objects of different shapes in different places in the world and then move around the space to see what they look like from different perspectives.
Teachers will take students through a presentation so they can collect data to …
Teachers will take students through a presentation so they can collect data to look for a pattern in similar 45-45-90 triangles' and 30-60-90 triangles' side lengths. Best suited for after students are able to apply the Pytahgroean Theorem, there are guided notes for students to complete, along with practice pages to apply the patterns the students themselves derive. Standards: IN G.T.10 - Explore the relationship between the sides of special right triangles (30° - 60° and 45° - 45°) and use them to solve realworld and other mathematical problems.
Students learn how to use wind energy to combat gravity and create …
Students learn how to use wind energy to combat gravity and create lift by creating their own tetrahedral kites capable of flying. They explore different tetrahedron kite designs, learning that the geometry of the tetrahedron shape lends itself well to kites and wings because of its advantageous strength-to-weight ratio. Then they design their own kites using drinking straws, string, lightweight paper/plastic and glue/tape. Student teams experience the full engineering design cycle as if they are aeronautical engineers—they determine the project constraints, research the problem, brainstorm ideas, select a promising design and build a prototype; then they test and redesign to achieve a successful flying kite. Pre/post quizzes and a worksheet are provided.
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: Select appropriate mathematical methods to use for an unstructured problem; interpret a problem situation, identifying constraints and variables, and specify assumptions; work with 2- and 3-dimensional shapes to solve a problem involving capacity and surface area; and communicate their reasoning clearly.
Students learn about the mathematical characteristics and reflective property of ellipses by …
Students learn about the mathematical characteristics and reflective property of ellipses by building their own elliptical-shaped pool tables. After a slide presentation introduction to ellipses, student “engineering teams” follow the steps of the engineering design process to develop prototypes, which they research, plan, sketch, build, test, refine, and then demonstrate, compare and share with the class. Using these tables as models to explore the geometric shape of ellipses, they experience how particles rebound off the curved ellipse sides and what happens if particles travel through the foci. They learn that if a particle travels through one focal point, then it will travel through the second focal point regardless of what direction the particle travels.
This short video and interactive assessment activity is designed to teach fifth …
This short video and interactive assessment activity is designed to teach fifth graders about determining unknown angles within rectangles and squares.
This short video and interactive assessment activity is designed to teach third …
This short video and interactive assessment activity is designed to teach third graders about determining unknown angles within rectangles and squares.
This video explains and shows definitions and example of the words: volume, …
This video explains and shows definitions and example of the words: volume, area, surface area, and base. It also talks about word problems associated with volume and area. Students need to figure out if the provided story problems are finding the correct thing, volume or area, based on the object. Explanations of the correct answer are provided.
This task gives students the opportunity to verify that a dilation takes …
This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.
Through this lesson and its two associated activities, students are introduced to …
Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. The practice of developing scale models is often used in engineering design to analyze the effectiveness of proposed design solutions. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheets—which involves side and radius dimensions, perimeters, circumferences and areas—guiding them to discover the relationships between the side length of a square and its area, and the radius of a circle and its area. They also think of real-world engineering applications of the geometry concepts.
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