Circle Basics Unit (Part 1)

We split up our circles unit into 2 parts (Part 1: Circle Basics, Circumference & Area, Area of Shaded Regions, & Tangent Lines; Part 2: Arcs, Central Angles, Chords, Sector Area, Arc Length, and Segment Area). I know a majority of schools teach circles as one big unit but I don't think that most of my special education students could remember all of those theorems and rules and be successful. For those that teach circles as one big unit and your students are successful, can you show me a sample of your unit outline? :)

Day 1: We used the foldable below to learn about the basic parts of a circle. I LOVE this foldable and have used the same one for the past 3 years. Students choose one color to represent each vocabulary word and color-code accordingly. I found that this helps students out A LOT! I really emphasized the difference between a secant and a chord. Also, when listing chords, some students forget to write down the diameter down so I reminded students that the diameter is the longest chord in a circle. Identifying all the radii in the circle helped students realize that even though a line is not drawn, it is still a radius! After the notes on our foldable, I told students to close their foldable and attempt the blue sheet (vocabulary review) by themselves. I told them to read through the definition and draw a picture. About 85% matched the vocabulary word with the definition correctly with the most common mistakes of switching tangent and secant.

I had too much time left in class so I decided to start circumference and area notes. I labeled the purple sheet with the students before introducing the flip-book. On the purple sheet I had students write down d=2•r and r = 1/2•d (even though it is not shown in the pictures). We only went through the vocabulary, circumference, and area sections of their flip-book. These examples were easy and a quick review of what they already know about circumference and area. Overall, the vocabulary, circumference, and area section took about 15 minutes to complete (and most students finished the examples before I was even done!)

 

After the notes, I handed them the following homework to complete over circle basics. I did have to to remind students again that the diameter is a chord in problem #4. 

Day 2: Students walked in and opened up to their circumference and area foldable. Before we got started, I cold called on several students and asked them questions over circumference and area. Some sample questions that I asked students were, "If the diameter of a circle is 10m, then what is the length of the radius?" "If the circumference of a circle is 56⫪, then what is the radius of the circle?" "If the area of a circle is 49⫪m², then what is the circumference of the circle?" After I had several students answer my questions, we started on the more circumference and more area sections in our flipbook. Many students got stuck/had questions on the square inscribed in the circle problem (on finding the diameter).

After the notes, I handed students the following circumference and area homework. Students had the most questions on the diameter on question #8 since we have not practiced 45-45-90 triangles in a minute :)

Day 3: Students walked in and cut out their area of shaded regions foldable and taped it down next to their review of area formula chart. I am so glad that I made this review of area formula chart to place next to their area of shaded regions foldable because many students referenced this when we got to the homework. In many of my classes, I have to tell students how to find the area in very clear and concise ways or I will lose/confuse many of them. For example, I told students that to find the area of the shaded region in example 4 we will use the following formula: "area of the big circle - area of medium circle - area of the small circle."

After the notes, I had students complete the following area of shaded regions homework. Again, most students had questions on how to find the diameter of the circle in question 4 (just like circumference & area) so in my lower level classes, we went over question #4 together. 

Day 4: Today we did the following tangent lines foldable together as a class. We completed the foldable first and then summarized our findings on the blue graphic organizer. Students really understood the concept of tangent lines after this lesson. Question #3 was definitely my favorite question on this foldable :)

After the foldable, we completed the following worksheet over tangent lines and students did GREAT on this formative assessment. Most of my special education students could complete #5 correctly, even though there was not a question like this on our notes (big deal in my class).  

Here are some of the files that I used: 

• Circle Basics Foldable
• Circles Vocabulary Review
• Circumference & Area Foldable
• Circumference & Area Graphic Organizer
• Area of Shaded Regions Foldable
• Review of Area Formula Chart
• Tangent Lines Foldable
• Tangent Lines Graphic Organizer