
Lesson Plan Template:
Confirmatory or Structured Inquiry

Learning Objectives: What will students know and be able to do as a result of this lesson?
 Students will be able to describe and use the segment length relationships between two chords that intersect in the interior of a circle.
 Students will be able to describe and use the segment length relationships between two secants that intersect exterior to a circle.
 Students will be able to describe and use the segment length relationships between a secant and tangent that intersect exterior to a circle.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know all the vocabulary associated with circles: Circle Vocabulary and Definitions
 circle
 major arc
 minor arc
 semi circle
 diameter
 radius
 center of a circle
 secant
 chord
 tangent to a circle
 inscribed angle
 central angle
 interior of circle
 exterior of circle
To be certain the students have this knowledge they will participate in a game of "Pictionary" in their heterogeneous groups. The teacher will write the vocabulary terms on index cards, with one term on each card.
 Each group will be given a set of cards with the vocabulary terms on them.
 Students will shuffle the cards and put them face down.
 Taking turns, each student will draw a card and without letting the other students see the word, draw it on their white board while their teammates guess the word.
The teacher will circulate while the teams play and note terms that students have difficulty with.
After students have played the game for 10 minutes or so, the teacher will bring the group together and review the vocabulary terms until the students are proficient in using them.

Guiding Questions: What are the guiding questions for this lesson?
While the students are working, the teacher will ask:
 What would you call those segment (lines)?
 answer: chord, secants, tangents
 What relationships do you see?
 answer: the last two columns are the same
 Does it always work?
 What is the rule that explains that?
 answer: see answer key for handout
For enrichment the teacher might like to make connections between other knowledge and the new knowledge discovered:
 What is the connection between the inscribed angle of a minor arc compared to a major arc?
 How do you think the angles will compare that are formed by the chords (or secant, or tangent)?
 How might the fact that all circles are similar connect to the relationships we are finding between the segment lengths?

Introduction: How will the teacher introduce the lesson to the students?
The teacher will tell the students, "Now that we have learned about the various lines and segments that are related to circles, we will discover if there are some relationships that can be found." Students will then be given a worksheet to help guide them in this discovery. They will be given three GeoGebra files that will be used to give them data to help determine those relationships. (The teacher will need to check with the IT person at their campus to be sure the free software from GeoGebra.org is installed on all the computers the students will be using. The three files could be added to the class website or Edmodo group for easy access by students. Another way to have the students access these files is to ask the IT person to place on the desktop of each computer.) The teacher will point out to the students that the files are numbered and to access them in order so that the information matches the charts. The teacher will point out to the students that the points they will move are colored blue on the files.

Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be used to answer the question(s)?
The students will be investigating the following questions:
 What is the relationship between the lengths of the two halves of two chords that intersect on the interior of a circle?
 What is the relationship between the segment lengths of portions of two secants that intersect on the exterior of a circle?
 What is the relationship between the segment lengths of portions of a tangent and a secant that intersect on the exterior of a circle?
The students will be provided with a worksheet:
Seeking Segments Discovery Handout
Seeking Segments Discovery Handout Answers
The students will be given three GeoGebra files. They are in attachments and called Discovery1.ggb, Discovery2.ggb, Discovery3.ggb.

Analyze: How will students organize and interpret the data collected during the investigation?
The students will use the charts and guided questions in the handout to help them determine commonalities between the various sets of data they have recorded. They will work in pairs and justify their rules until they come to a consensus.

Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
At the end of the activity the teacher will call the group back together and ask random students to give their rule for the first discovery. Then the students will have a class discussion, led by the teacher trying to reach a consensus on the best wording for the rule. Then this rule will be recorded in the end of the handout where space has been provided. This process will be repeated for the next two discoveries. During this discussion it might be helpful to begin by recording rules given by groups called at random. After about a half dozen have been written on the board, questions to students like:
 What do the different rules have in common?
 What differences do you notice?
 Do you agree with number___?
 What might be a better way to put that?
 Is that always true?
 How do you know?
This is a good time for the teacher to use the formative assessment information gathered to strategically call on the students who were making connections during the discovery. Leading to the rules included on the answers to the worksheet (or equivalent) would be the goal of this discussion.

Summative Assessment
Students will apply the knowledge they have learned about circles and segment lengths the next class period during a bellwork assignment. The teacher will collect and grade this assignment as a determination of how student understanding has developed toward the learning goals.
Summative Bellwork
Summative Bellwork with Answers
This will be only one of numerous lessons that address these Standards/Benchmarks. Similar methods could be used to help students discover the other parts. Geogebra is very user friendly and many lessons and applets are available for free on their Wiki.

Formative Assessment
Opening: The teacher will circulate the room while students do a group activity to review vocabulary. The teacher will observe student knowledge and fill in gaps in knowledge during the introduction to the activity.The teacher will look for common misconceptions among the students regarding the terms and also which student have a good grasp of the vocabulary so they can be called on to explain to the class.
During Discovery Activity: The teacher will walk around the room while the students complete the discovery phase and keep students on task. Teacher will listen for the connections students are making and correct any misconceptions that might derail the thought process with guiding questions. While the teacher is hoping to hear students have "ah ha" moments about the relationships of circle segments the teacher must guard against leading too much. Try using guiding questions to keep the students thinking and working.
 What would you call those segment (lines)?
 answer: chord, secants, tangents
 What relationships do you see?
 answer: the last two columns are the same
 Does it always work?
 What is the rule that explains that?
 answer: see answer key for handout
There is a fine line between guiding them to make their own discoveries and giving them the answers. Eventually of course the connections must be made and the teacher will want to note which students can be called upon during the class discussion to explain the connections.

Feedback to Students
Opening: The students are in their heterogeneous groups where they will coach and assist each other with this review activity. The students will also receive feedback from the teacher regarding their prior knowledge during the introduction to the activity.
During Discovery: Students will work with a partner to assist and coach one another.
Discussion: Students will receive feedback and clarification from the teacher during the discussion after the activity.