This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.
The purpose of this lesson is to use what has been learned about squares and square roots to find the side lengths of a right triangle.
Included is a YouTube video to support Grade 8 Blended Learning Math - Unit 1.5: Square Roots and Pythagorean Theorem - The Pythagorean Theorem.
The purpose of this lesson is to look at various triangles and explore how to identify right triangles using Pythagorean Theorem.
Included is a YouTube video to support Grade 8 Blended Learning Math - Unit 1.6: Square Roots and Pythagorean Theorem - Exploring the Pythagorean Theorem.
The purpose of this lesson is to use the Pythagorean Theorem and its corresponding algebraic expression solve a variety of problems.
Included is a YouTube video to support Grade 8 Blended Learning Math - Unit 1.7: Square Roots and Pythagorean Theorem - Applying the Pythagorean Theorem.
The purpose of this lesson is to approximate the square roots of non-perfect squares.
Included is a YouTube video to support Grade 9 Blended Learning Math - Unit 1.2: Square Roots and Surface Areas - Square Roots of Non-Perfect Squares.
The purpose of this lesson is to determine the surface area of composite objects made from right rectangular prisms and right cylinders.
Included is a YouTube video to support Grade 9 Blended Learning Math - Unit 1.4: Square Roots and Surface Areas - Surface Areas of Objects Made from Other Composite Objects.
The purpose of this lesson is to discover the relationship between a radius and a tangent, then solve related problems.
Included is a YouTube video to support Grade 9 Blended Learning Math - Unit 8.1: Circle Geometry - Properties of Tangents to a Circle.
The purpose of this lesson is to relate a chord, its perpendicular bisector and the center of a circle. Then, solve problems using these relationships.
Included is a YouTube video to support Grade 9 Blended Learning Math - Unit 8.2: Circle Geometry - Properties of Chords in a Circle.
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.
In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.
In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles. The module begins with the definition of dilation, properties of dilations, and compositions of dilations. One overarching goal of this module is to replace the common idea of same shape, different sizes with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.
Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented to students, it is important that the lessons in Modules 2 and 3 related to the Pythagorean Theorem are taught (M2: Lessons 15 and 16, M3: Lessons 13 and 14). In Modules 2 and 3, students used the Pythagorean Theorem to determine the unknown length of a right triangle. In cases where the side length was an integer, students computed the length. When the side length was not an integer, students left the answer in the form of x2=c, where c was not a perfect square number. Those solutions are revisited and are the motivation for learning about square roots and irrational numbers in general.
Students explore the concept of similar right triangles and how they apply to trigonometric ratios. Use this lesson as a refresher of what trig ratios are and how they work. In addition to trigonometry, students explore a clinometer app on an Android® or iOS® device and how it can be used to test the mathematics underpinning trigonometry. This prepares student for the associated activity, during which groups each put a clinometer through its paces to better understand trigonometry.
Sal introduces the famous and super important Pythagorean theorem! This lesson includes an introduction video followed by examples and practice problems involving finding the hypotenuse, finding a side, finding area of an isosceles triangle, and determining if a triangle is a right triangle. It is followed by a unit on Pythagorean theorem applications.
Students explore in detail how the Romans built aqueducts using arches—and the geometry involved in doing so. Building on what they learned in the associated lesson about how innovative Roman arches enabled the creation of magnificent structures such as aqueducts, students use trigonometry to complete worksheet problem calculations to determine semicircular arch construction details using trapezoidal-shaped and cube-shaped blocks. Then student groups use hot glue and half-inch wooden cube blocks to build model aqueducts, doing all the calculations to design and build the arches necessary to support a water-carrying channel over a three-foot span. They calculate the slope of the small-sized aqueduct based on what was typical for Roman aqueducts at the time, aiming to construct the ideal slope over a specified distance in order to achieve a water flow that is not spilling over or stagnant. They test their model aqueducts with water and then reflect on their performance.
Discover Mathigon, the Mathematical Playground. Learning mathematics has never been so interactive and fun!
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Puzzles, Activities and Lesson Plans - Student Explorations/Activities for students to complete ; Fully developed lessons plans ; Ready to play puzzles and games ; Teaching ideas using Polypad to explore new ideas; Tutorials - Learn how to use Polypad
Almanac of Interesting Numbers
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The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever _AXB is a right angle.
Students learn that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts â basic geometry and trigonometry â that have been used for thousands of years.