This lesson begins with a demonstration prompting students to consider how current generates a magnetic field and the direction of the field that is generated. Through formal lecture, students learn Biot-Savart's law in order to calculate, most simply, the magnetic field produced in the center of a circular current carrying loop. For applications, students find it is necessary to integrate the field produced over all small segments in an actual current carrying wire.

This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems.

An interactive applet and associated web page that demonstrate how to find the perpendicular distance between a point and a line using trigonometry, given the coordinates of the point and the slope/intercept of the line. The applet has a line with sliders that adjust its slope and intercept, and a draggable point. As the line is altered or the point dragged, the distance is recalculated. The grid and coordinates can be turned on and off. The distance 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 concept of the concepts, 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.

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.

This task complements ``Seven Circles'' I, II, and III. This is a hands-on activity which students could work on at many different levels and the activity leads to many interesting questions for further investigation.

This task provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function. When the task is complete, new insight is shed on the ``Seven Circles I'' problem which initiated this investigation as is noted at the end of the solution.

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: In the July 2013 issue of United Airlines' Hemisphere Magazine the following article appeared: Write down an equation that describes Captain Bowers' me...

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 aspects of the task and its potential use.

Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2.  To be able to discuss similarity, students must first have a clear understanding of how dilations behave.  This is done in two parts, by studying how dilations yield scale drawings and reasoning why the properties of dilations must be true. Once dilations are clearly established, similarity transformations are defined and length and angle relationships are examined, yielding triangle similarity criteria.  An in-depth look at similarity within right triangles follows, and finally the module ends with a study of right triangle trigonometry.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

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.

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.

The purpose of this task is to engage students in an open-ended modeling task that uses similarity of right triangles, and also requires the use of technology.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

Así como se utilizan movimientos rígidos para definir la congruencia en el Módulo 1, se agregan dilataciones para definir la similitud en el Módulo 2. Para poder discutir la similitud, los estudiantes primero deben comprender claramente cómo se comportan las dilataciones. Esto se hace en dos partes, al estudiar cómo las dilataciones producen dibujos de escala y razonando por qué las propiedades de las dilataciones deben ser ciertas. Una vez que las dilataciones se establecen claramente, se definen transformaciones de similitud y se examinan las relaciones de longitud y ángulo, lo que produce criterios de similitud triangular. Sigue una mirada profunda a la similitud dentro de los triángulos rectos, y finalmente el módulo termina con un estudio de trigonometría del triángulo recto.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2.  To be able to discuss similarity, students must first have a clear understanding of how dilations behave.  This is done in two parts, by studying how dilations yield scale drawings and reasoning why the properties of dilations must be true. Once dilations are clearly established, similarity transformations are defined and length and angle relationships are examined, yielding triangle similarity criteria.  An in-depth look at similarity within right triangles follows, and finally the module ends with a study of right triangle trigonometry.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

 This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

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 task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?