An interactive applet and associated web page that demonstrate the properties of a 30-60-90 triangle. The applet shows a right triangle that can be resized by dragging any vertex. As it is dragged, the remaining vertices change so that the triangle's angles remain 30 degrees, 60 degrees and 90 degrees The text on the page points out that the sides of a 30-60-90 triangle are always in the ratio of 1 : 2 : root 3 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 demonstrate the properties of a 3:4:5 triangle - one of the Pythagorean triples. The applet shows a right triangle that can be resized by dragging any vertex. As it is dragged, the remaining vertices change so that the triangle's side remain in the ration 3:4:5. The text on the page has an example of how the triangle can be used to measure a right angle on even large objects. 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 demonstrate the properties of a 45-45-90 isosceles right triangle. The applet shows a right triangle that can be resized by dragging any vertex. As it is dragged, the remaining vertices change so that the triangle's angles remain 45 degrees, 45 degrees and 90 degrees The text on the page points out that the sides of a 45-45-90 triangle are always in the ratio of 1 : 2 : root 2 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 shows that angle-angle-angle (AAA) is not enough to prove congruence. The applet shows two triangles, one of which can be dragged to resize it, showing that although they have the same angles they are not the same size and thus not congruent. The web page describes all this and has links to other related pages. 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 the AAA similarity test works. Two similar triangles are shown that can be resized by dragging. The other triangle adjusts to remain similar and the angle-angle-angle elements are highlighted to show how they are involved in this test of similarity. (all three interior angles congruent). The web page describes all this and has links to other related pages. 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 reference book project at http://www.mathopenref.com.

An interactive applet and associated web page that shows how triangles that have two angles and a non-included side the same must be congruent. The applet shows two triangles, one of which can be reshaped by dragging any vertex. The other changes to remain congruent to it and the two angles and non-included side are outlined in bold to show they are the same measure and are the elements being used to prove congruence. The web page describes all this and has links to other related pages. 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 shows how triangles that have two angles and their included side the same must be congruent. The applet shows two triangles, one of which can be reshaped by dragging any vertex. The other changes to remain congruent to it and the two angles and the included side are outlined in bold to show they are the same measure and are the elements being used to prove congruence. The web page describes all this and has links to other related pages. 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 demonstrate the three types of triangle: acute, obtuse and right. The applet shows a triangle that is initially acute (all angles less then 90 degrees) which the user can reshape by dragging any vertex. There is a message changes in real time while the triangle is being dragged that tells if the triangle is an acute, right or obtuse triangle and gives the reason why. By experimenting with the triangle student can develop an intuitive sense of the difference between these three classes of triangle. 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 calculate the area of a triangle using the formula method in coordinate geometry. The applet has a triangle with draggable vertices. As you drag them the triangle's area is recalculated from the vertex coordinates using the formula. The grid and coordinates can be turned on and off. The area 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 using the formula method, 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.

An interactive applet and associated web page that explain the area of a triangle. The applet shows a triangle that can be reshaped by dragging any vertex. As it changes, the area is continually recalculated using the 'half base times height' method. The triangle has a fixed square grid in its interior that can be used to visually estimate the area for later correlation with the calculated value. The calculation can be hidden while estimation is in progress. The text page has links to a similar page that uses Heron's Formula to compute the area. 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 calculate the area of a triangle using the box method in coordinate geometry. The applet has a triangle with draggable vertices. As you drag them the triangle's bounding box is shown and the area recalculated by subtracting the areas of the outside triangles. The grid and coordinates can be turned on and off. The area 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 using the box method, 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.

An interactive applet and associated web page that demonstrate the concept of congruent triangles. Applets show that triangles a re congruent if the are the same, rotated, or reflected. In each case the user can drag one triangle and see how another triangle changes to remain congruent to it. The web page describes all this and has links to other related pages. 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 provide step-by-step instructions on how to construct an equilateral triangle with a given side length using only a compass and straightedge. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 provide step-by-step animated instructions on how to construct the incenter of a triangle. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 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.

Students use simple materials to design an open spectrograph so they can calculate the angle light is bent when it passes through a holographic diffraction grating. A holographic diffraction grating acts like a prism, showing the visual components of light. After finding the desired angles, students use what they have learned to design their own spectrograph enclosure.

An interactive applet and associated web page that demonstrate equilateral triangles (all sides the same length). The applet presents an equilateral triangle where the user can drag any vertex. As the vertex is dragged, the others move automatically to keep the triangle equilateral. The angles are also updated continuously to show that the all interior angles are always congruent. 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 develop and solidify their understanding of the concept of "perimeter" as they engage in a portion of the civil engineering task of land surveying. Specifically, they measure and calculate the perimeter of a fenced in area of "farmland," and see that this length is equivalent to the minimum required length of a fence to enclose it. Doing this for variously shaped areas confirms that the perimeter is the minimal length of fence required to enclose those shapes. Then students use the technology of a LEGO MINDSTORMS(TM) NXT robot to automate this task. After measuring the perimeter (and thus required fence length) of the "farmland," students see the NXT robot travel around this length, just as a surveyor might travel around an area during the course of surveying land or measuring for fence materials. While practicing their problem solving and measurement skills, students learn and reinforce their scientific and geometric vocabulary.

Origami is the Japanese art of paper folding, originally from China and now practiced all over the world. In this activity, create an origami star. Introduce children to both geometry and analytical skills in a creative way.

Overall Goal: During this lesson we will cover basic shapes and learn how they can be used in everyday objects. Our goal is for students to know the basic shapes, find them in objects such as playgrounds, be able to create their own playground using shapes, and finally be able to tell the class about the playground they made and the shapes used.  Standard: K.G.3: Model shapes in the world by composing shapes from objects (e.g., sticks and clay balls) and drawing shapes. Learning Objectives: The students will be able to show they know what each of the basics shape are by correctly drawing a square, triangle, rectangle, circle, and oval.Students will be able to create playground with the basic shapes by using everyday objects such as play-doh, craft sticks, etc.Students will be able to complete the project by creating their dream playground; using all of the shapes covered in the lesson.Students can explain their playgrounds and shapes they used, and why their specific playground represents their “dream playground” by presenting their project to the class. Key Terms:SquareRectangleTriangleOvalCircle Lesson Introduction:We will visit the school playground to have the students find the different shapes in the playground equipment. We want students to use the playground visit to help them decide how they would build their dream playground using the basic shapes. We will give the students a packet (found in the Resources section) that includes a few activities for them to do before the main lesson. They will take this to the playground and fill out the second page by writing down the different playground structures that fit each shape. They will be able to explore the playground on their own, so that they can have different answers than each other. Main Lesson:In class, we will have the students create, by drawing, their ‘dream playground’ using the specific basic shapes they are given to work with (squares, triangles, circles, rectangles, and ovals). They will be given 20 minutes to complete their drawing. They will be able to draw this on paper or use a computer application to create this.After this, the students will be given play-doh and popsicle sticks to recreate the shapes and structures that they had on their paper. The crafting process should take around 50 minutes. The drawings and crafts will be assessed by if the students correctly demonstrate their knowledge of the different shapes and how to create them.At the end, the kids will present their own playgrounds to the class and show what shapes they used and be able to explain and defend why it is their dream playground. This is so that the teacher can tell if the student knows the shapes and is able to defend their argument of what makes it a dream playground. The students will be able to use pencil and paper to draw or use tablets/iPads and use a drawing application. Lesson Ending:When the students are done creating their projects, they will each present their playgrounds to the class and explain the individual shapes that they used. The students will also explain why they believe their playground model is the best. The students should answer the following questions when they defend why their playground is the best. How many of each shape are in your playground? Is one of the five shapes better for making playgrounds than the others and why? The way that we can assess is if the student created the shapes correctly and correctly referenced them in their presentation. Rubric:The students will be graded as Good, Average, or Poor. The following is what they are going to be graded on:Students know basic shapesStudents use shapes correctly to build a playgroundStudents complete all parts of the projectStudents present their playgrounds to the class and can explain how they built their playground with the basic shapes Differentiation:This project should not affect students of different gender, race, culture, or sexual identity. Students with behavioral challenges will be worked more one-on-one than the other students to make sure that any confusion or frustration will be handled. The higher ability learners can go beyond the four shapes specified, if they feel comfortable. The project does not require out of school time where they would absolutely need a computer or Wifi access.Examples:If high ability students feel like they can add shapes that are not on the required list, they may do so with permission from the teacher. They will not be given any extra credit for adding other shapes, but this is a good way for the teachers to see where some students are at academically.If there is a child with dyslexia they will receive extra help from the teacher to be sure that they can accurately read the instructions on the papers.If a student needs to use a computer drawing application for sketching the playground because of a disability but doesn’t understand how to use it, they may come into class early to spend some extra time navigating the site.Since the students will be doing a worksheet after the activity, there might be students who struggle with reading. If the students struggle with reading the worksheet, they may ask, and we will help them through the parts that they find confusing. If the student has translation issues with some of the words, we will also help them translate it. This will be done just through being familiar with the material and specific language. Anticipated Difficulties:There could be difficulty with children being distracted at the playground and while crafting. We will need to be sure that everyone is staying on task by keeping them engaged during all of the activities. Children can sometimes become distracted if they are just listening to someone speak and by keeping them engaged and involving them during all of the lesson they will be more likely to stay focused. When on the playground we can use students to help point out the shapes that we find and also ask questions during this time to keep students attentive. Students might be at different learning levels and could struggle with learning the shapes. If so, we could always split the children into a few groups based on learning levels to help the lesson run smoother.