Students learn about common geometry tools and then learn to use protractors (and Miras, if available) to create and measure angles and reflections. The lesson begins with a recap of the history and modern-day use of protractors, compasses and mirrors. After seeing some class practice problems and completing a set of worksheet-prompted problems, students share their methods and work. Through the lesson, students gain an awareness of the pervasive use of angles, and these tools, for design purposes related to engineering and everyday uses. This lesson prepares students to conduct the associated activity in which they “solve the holes” for hole-in-one multiple-banked angle solutions, make their own one-hole mini-golf courses with their own geometry-based problems and solutions, and then compare their “on paper” solutions to real-world results.

The lesson starts with a review of basic geometric terms.Angles are defined.There are four types of angles.A right angle measures 90° and forms a square corner. If you were to sit inside a right angle, you would be sitting straight up.An acute angle measures less than 90° and is open less than a right angle. Acute angles have a smaller measurement. Think of them as small and cute. =) If you were sitting inside an acute angle, you would be bent together like a 'V'.An obtuse angle measures more than 90° and is open more than a right angle. Obtuse angles have a larger measurement. If you were to sit inside a obtuse angle, you would be leaning back as if you were lounging in a beach chair by the pool.A straight angle measures exactly 180° and forms a straight line. If you were to sit inside a straight angle, you would actually have to lay down flat on your back.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Constructions and Angles

Unit Overview

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Use a protractor and ruler.
Identify different types of triangles and quadrilaterals and their characteristics.

Lesson Flow

After an initial exploratory lesson involving a paper folding activity that gets students thinking in general about angles and figures in a context, the unit is divided into two concept development sections. The first section focuses on types of angles—adjacent, supplementary, complementary, and vertical—and how they are manifested in quadrilaterals. The second section looks at triangles and their properties, including the angle sum, and how this affects other figures.

In the first set of conceptual lessons, students explore different types of angles and where the types of angles appear in quadrilaterals. Students fold paper and observe the angles formed, draw given angles, and explore interactive sketches that test many cases. Students use a protractor and ruler to draw parallelograms with given properties. They explore sketches of parallelograms with specific properties, such as perpendicular diagonals. After concluding the investigation of the angle types, students move on to the next set.

In the second set of conceptual development lessons, students focus on triangles. Students again fold paper to create figures and certain angles, such as complementary angles.

Students draw, using a protractor and ruler, other triangles with given properties. Students then explore triangles with certain known and unknown elements, such as the number of given sides and angles. This process starts with paper folding and drawing and continues with exploration of interactive sketches. Students draw conclusions about which cases allow 0, 1, 2, or an infinite number of triangles. In the course of the exploration, students discover that the sum of the measure of the interior angles of a triangle is 180°. They also learn that the sum of the measures of the interior angles of a quadrilateral is 360°. They explore other polygons to find their angle sum and determine if there is a relationship to angle sum of triangles. The exploration concludes with finding the measure of the interior angles of regular polygons and speculating about how this relates to a circle.

Lastly, students solve equations to find unknown angle measures. Using their previous experience, students find the remaining angle measures in a parallelogram when only one angle measure is given. Students also play a game similar to 20 Questions to identify types of triangles and quadrilaterals. Having completed the remaining lessons, students have a four-day Gallery to explore a variety of problems.

The unit ends with a unit assessment.

In this Cyberchase video segment, Harry tries to snowboard and learns how to measure and identify many common angles.