Informal Geometry (#1206300)

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The course was/will be terminated at the end of School Year 2021 - 2022

Course Standards

General Course Information and Notes

Version Description

The fundamental purpose of the course in Informal Geometry is to extend students’ geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school standards. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The critical areas, organized into five units are as follows.

Unit 1- Congruence, Proof, and Constructions: In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. Students informally prove theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.

Unit 2- Similarity, Proof, and Trigonometry: Students apply their earlier experience with dilations and proportional reasoning to build a formal understanding of similarity. They identify criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles, with particular attention to special right triangles and the Pythagorean theorem.

Unit 3- Extending to Three Dimensions: Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas.

Unit 4- Connecting Algebra and Geometry Through Coordinates: Building on their work with the Pythagorean theorem in 8th grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to work done in the first course.

Unit 5- Circles With and Without Coordinates: In this unit students study the Cartesian coordinate system and use the distance formula to write the equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations, which relates back to work done in the first course, to determine intersections between lines and circles or parabolas.

General Notes

Important Note: This Informal Geometry course content does not align with the End-of-Course Assessment required for graduation.

General Information

Course Number: 1206300

Course Path:

Section: Grades PreK to 12 Education Courses > Grade Group: Grades 9 to 12 and Adult Education Courses > Subject: Mathematics > SubSubject: Geometry >

Abbreviated Title: INF GEO

Course Length: Year (Y)

Course Type: Core Academic Course

Course Level: 2

Course Status: Terminated

Grade Level(s): 9,10,11,12

Student Resources

Vetted resources students can use to learn the concepts and skills in this course.

Original Student Tutorials

The Year-Round School Debate: Identifying Faulty Reasoning – Part Two:

This is Part Two of a two-part series. Learn to identify faulty reasoning in this interactive tutorial series. You'll learn what some experts say about year-round schools, what research has been conducted about their effectiveness, and how arguments can be made for and against year-round education. Then, you'll read a speech in favor of year-round schools and identify faulty reasoning within the argument, specifically the use of hasty generalizations.

Make sure to complete Part One before Part Two! Click HERE to launch Part One.