Circles is one of my favorite units to teach! (If you’ve read my other interactive notebook posts, you may realize that this is a theme. I just love teaching geometry!) Circles is always among the last of my units to teach. Oftentimes, students struggle because there are so many properties and so much vocabulary to remember. For this unit, I try to break topics up as much as possible. Read more to see how our circles geometry interactive notebook unit develops.
Circles Geometry Vocabulary
Most of what students learn in our circle vocabulary lesson is actually review from middle school. They already know about the difference between the radius and diameter (in fact, I rely on that prior knowledge during our volume unit). In this lesson, we deepen their understanding of circle, center, radius, diameter, and chord, and elevate their definitions to high school. (This is where we could also include a mini lesson on locus.) Words that are new to students, in terms of circles, are tangent and secant. We also discuss semicircles, minor arcs, and major arcs, practice their notation, and talk about the most basic circle postulates and theorems. This year, for distance learning, we also included a sorting practice activity.
Equations of Circles
In the classroom, I often cover basic circle equations the same day we cover circle vocabulary. We gain a basic understanding of how circle equations function, and then the next day we learn about circle equations in the general form. For the second lesson, we start by reviewing completing the square. By this point, students typically forget how to complete the square, but remember it as one of their least favorite factoring methods. I don’t dwell on this too long before we look at an example of completing the square to convert a circle equation from general to standard form. We practice problems finding the standard form, the center, and the radius of a circle when given the equation in general form. Since we have a class set of ti-nspire calculators, we also spend time learning how to graph circles in general form and finding the center and radius using the calculator’s tools.
Tangent Theorems
When it comes to tangent theorems, we stick with the basics – a tangent is perpendicular to a circle at its radius, and tangent segments formed from a common external point to the circle are congruent. We complete practice problems for these theorems in our notes, and using task cards. This year we got to use digital task cards.
Chord Theorems
Chord theorems are a bit more cumbersome. There are four that we focus on: congruent chords and intercepted arcs, the perpendicular bisector of a chord (and its converse), chords that are equidistant from the center, and parallel chords. We have two examples for each theorem in our notes, and then we have task card practice. Again, this year, we got to practice with digital task cards.
Circles Geometry Interactive Notebook: Central & Inscribed Angles
After tangents and chords, we move on to angles. We start with a definition and practice for central angles, and then move on to inscribed angles. We use practice problems to develop the theorems for inscribed angles that intercept the same arc, and angles inscribed in semicircles. Then we talk about the definition of an inscribed polygon and circumscribed circle before we discuss the inscribed quadrilaterals theorem. Students love completing the practice for inscribed quadrilaterals. We practice this topic with a maze and (digital) task cards.
(Circle Angles) Angles On, Inside, & Outside of Circles
Next, we move on to angles on, inside, and outside circles. We spend time discussing a formula for each, and then work on practice problems. We complete a maze for more practice.
Circle Segments
Our next topic is circle segments. We look at “formulas” for solving problems involving two chords, two secants, and a tangent and secant combo. For this topic, we do a lot of highlighting to help students see the different segments and make sense of what needs to be multiplied. We complete practice problems in our notes, and then practice with a maze.
Area of Sectors & Arc Length
Our final topic of the unit is area of sectors and arc lengths. For this topic, I emphasize that we are looking at a portion (or a fraction) of a circle, and this helps students derive the formulas. After we confirm the formulas, we complete practice problems in our notes. For arc length, we take the time to distinguish between arc measure and arc length. To practice, we complete task cards.
Circles Geometry Interactive Notebook
Are you looking for materials to teach this unit? Look no further! All of the pages you see in my Geometry Interactive Notebook: Circles are now available. Prior to uploading these pages for your use, I taught each lesson as described above. Some of the pages may not look exactly as they do in this post because they have all been edited and updated. Also, a full answer key for each page is included. New this year, I created a digital circles geometry interactive notebook!
Looking for more resources? Check out my interactive notebook resources page!
