An interactive applet and associated web page that demonstrate the concept of arc length. The applet shows a circle with part of its circumference highlighted and the central angle shown. As the user drags either end of the arc it is redrawn and the calculation for arc length changes as you drag. The text on the web page gives the formula for calculating the arc length. 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.
This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).
This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied throughout the year. It also includes the specific properties of triangles, special quadrilaterals, parallel lines and transversals, and rigid motions established and built upon throughout this mathematical story. This module's focus is on the possible geometric relationships between a pair of intersecting lines and a circle drawn on the page.
This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, it will help you identify and help students who have difficulty: decomposing complex shapes into simpler ones in order to solve a problem; bringing together several geometric concepts to solve a problem; and finding the relationship between radii of inscribed and circumscribed circles of right triangles.
This lesson unit is intended to help teachers assess how well students are able to solve problems involving area and arc length of a sector of a circle using radians. It assumes familiarity with radians and should not be treated as an introduction to the topic. This lesson is intended to help teachers identify and assist students who have difficulties in: Computing perimeters, areas, and arc lengths of sectors using formulas and finding the relationships between arc lengths, and areas of sectors after scaling.
This concept review is a study guide for the Circles from a Geometric Perspective Unit, which is Module 7 from the Secondary Mathematics II Curriculum of Mathematics Vision Project. Each concept that is covered in the review document has an accompanying video tutorial and set of guided notes that follow along with the videos. Resources Included:1) Link to the Mathematics Vision Project Curriculum Module 7- Circles from a Geometric Perspective 2) Link to a Google Document containing links to videos and Guided Notes documents for each of the key concepts. Image, “Apollonian Gasket Variation” was created by fdecomite. This work is licensed under a Creative Commons Attribution 2.0 Generic License.
This task combines two skills from domain G-C: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment (G-C.2), and computing lengths of circular arcs given the radii and central angles (G-C.5). It also requires students to create additional structure within the given problem, producing and solving a right triangle to compute the required central angles (G-SRT.8).
Modeling Our World with Mathematics Unit 2: Environmental Science Topic 2 - Sustainable Forestry
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Three circles, each having radius 2, are mutually tangent as pictured below: What is the total area of the circles together with the shaded region?...
This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: solving problems by determining the lengths of the sides in right triangles; and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.