Lesson Plan

Circle Segment Theorems - Secant Tangent

Using the Secant Tangent Theorem
Betsy P.
Lexington High School
Lexington, United States
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My Grades 9, 10, 11, 12
My Subjects Math

Students will be able to:

-Identify a secant segment on a circle.

-Identify a tangent segment on a circle.

-Given a secant and tangent intersecting outside the circle, find the missing segment length.


Grades 9 – 12
All Notes
Teacher Notes
Student Notes

1 Sponge

The teacher will have the sponge question displayed on the whiteboard when students enter the room. 

After the students have had time to answer, the teacher will go over the sponge question with verbal responses from the students. 

Using google docs to collect the sponge questions each day allows the teacher to have easy access to the document to comment and check on a daily or weekly basis. 

Using the applet allows the students a quick hands-on experience. 

Student Instructions

The students will use their previous knowledge of the definitions of tangent, secant, and chord to answer the sponge question on their own participation google document.

Sponge: Using the applet, drag the points on the circle. What do you notice about the segment when the points coincide? Why does that make sense? What's the difference between a secant and a tangent segment?


2 Direct Instruction

The teacher will use her school-issued iPad and the app neu.Annotate+ PDF to annotate the pdf student version of the notes (pg 820/821). The Apple TV will be used to display the notes.

Filling in the student notes of the curriculum allows the students to follow along while the teacher is teaching. It, also, allows them to listen instead of having to continually write down information. 

If a student is absent, the teacher will be able to e-mail the annotated notes to them.

Student Instructions

Since the school is 1:1 with iPads, the students can choose to take notes using an annotation app on the iPad, printing off the student notes to fill in paper/pencil, or writing their notes down paper/pencil in their notebooks.

3 Guided Practice

The teacher will use Kahoot via the Apple TV as guided practice for the students. The teacher will go over the new theorem prior to starting the Kahoot game.

Also, the teacher will go over the correct answers by working out the problem that way the students who didn't get the correct answer now know how to do the problem correctly.

The teacher will, also, discuss common errors that students may make to get the incorrect answer. 

The link to the Kahoot: https://play.kahoot.it/#/k/f5bbac46-5a38-4e35-87c5-f44bb5326646

Kahoot allows for a quick response to the questions, so it's a quick assessment.  It allows the teacher to see if the students do or do not understand the topic. If at this point there is a majority of students getting the problems incorrectly, the teacher can pause and reteach.  Also, Kahoot is interactive for the students. It engages them by adding competitiveness along with learning. 

Student Instructions

Using their iPads, the students will play the Kahoot game using the website in order to demonstrate their knowledge. 

The students should be working out each problem instead of guessing or copying from another student. 

4 Independent Practice

The teacher will have the homework assigned electronically prior to the start of class. 

Whether the student chooses to use the HMH player or HRW website, the students will be able to benefit by doing the homework online. The student is able to check the answer when doing the homework online. If they are incorrect, they are given the option to try the problem again. Also, the student can look at a similar example to help them solve the current problem. One other option is to do the problem step-by-step where the student is guided step-by-step on how to complete the problem correctly.

Also, by doing the homework electronically, a unique set of problems is created for each student. Each student will have a similar problem, but not exactly the same. Typically, the problems looks the same, but have different numbers.  Thus, the assignment is automatically being differentiated. 

If a student prefers to work the assignment on paper rather than electronically, the student may do so. 

Having students complete the homework online, allows the teacher to be able to run reports considering many factors such as individually, by assignment, or by learning objective. When looking at a quick report, the teacher can see the scores of all the students, as well, as which problems were missed (Ex: #12 missed by most students). These reports allow the teacher to tailor the teaching to the needs of the students. 

Student Instructions

The student will use the HMH iPad application or the HRW website to complete the homework online. The student should have a workpage for all problems. The assignment is due 10 minutes after the start of class the following day. 

5 Exit Ticket/Extension

The teacher will ask the students to respond verbally on the "Find the Error" Powerpoint over the Secant Tangent Circle Segment Theorem displayed on the whiteboard.

Lastly, the teacher will have the students work the problem correctly. The teacher will walk around the room to monitor the students to help any student who needs assistance.  The students will then share their answer verbally.

By having the students find a common error, it can be eye-opening to some common mistakes.  It allows them not only to do the problem themselves but to critically think about why the other person did incorrectly. It adds a higher level of learning.

Student Instructions

The students will respond verbally to the powerpoint slides.