Module 7 begins with work related to the Pythagorean Theorem and right ...

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.

In this problem, students are given a picture of two triangles that ...

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.

This task asks students to use similarity to solve a problem in ...

This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.

This lesson unit is intended to help teahcers assess how well students ...

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.

Students learn the importance of the Pythagorean theorem as applied in radar ...

Students learn the importance of the Pythagorean theorem as applied in radar imaging. They use a sensor unit with IRED (infrared emitting diode) to measure triangle distances and the theorem to calculate and verify distances. Student groups calibrate the sensor units to ensure accurate distance measurements. A "pretend" outdoor radar imaging model is provided to groups for sensor unit testing.

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.

In this activity, learners arrange triangles together to make patterns to create ...

In this activity, learners arrange triangles together to make patterns to create paper quilts. Learners experiment arranging the triangles in different ways to make various designs. Use this activity to illustrate how triangles can be combined to make other shapes, reflection, and the different types of triangles (isosceles, right, equilateral, scalene). This resource includes the quilt templates and shapes.

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 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.

CK-12's Texas Instruments Geometry Student Edition Flexbook is a useful collection of ...

CK-12's Texas Instruments Geometry Student Edition Flexbook is a useful collection of exercises intended to enrich a student's understanding of basic geometric principles.

This task complements ``Seven Circles'' I, II, and III. This is a ...

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. ...

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 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 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.

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