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 accurately use the relationships between arcs and angles formed by secants, tangents, and chords of a circle to find unknown values.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know vocabulary related to circles: Circle vocabulary and definitions
- Minor Arc
- Major Arc
- Semi Circle
- Inscribed Angle
- Intercepted Arc
- Angle Measure
- Arc Measure
- Interior of Circle
- Exterior of Circle
Guiding Questions: What are the guiding questions for this lesson?
As the teacher walks around while the students are working they can ask:
- Do you notice any relationships between the arcs of the circle and the angles?
- Answer: Yes, depending on the chart they are filling out either the intercepted arc is double the inscribed angle, the angle whose vertex is in the interior of the circle is half the sum of the arcs, or the angle whose vertex is located outside the circle is half the difference of the two arcs.
- How could you generalize this information? How could you explain that angle?
- Answer: The formulas listed above. The teacher could help the students arrive at the equations that the intercepted arc is double the inscribed angle, the angle whose vertex is in the interior of the circle is half the sum of the arcs, or the angle whose vertex is located outside the circle is half the difference of the two arcs.
Introduction: How will the teacher introduce the lesson to the students?
To begin the lesson students will participate in a "Win-Lose-Draw" game to review vocabulary words needed in the lesson.
How to play "Win-Lose-Draw":
- Write each of the vocabulary words above on index cards. One word per index card.
- Each group of four students are provided a set of cards.
- The students shuffle the cards and place them face down in the center where everyone can reach.
- Have one student select the top card from the deck, and, without revealing the card to their team mates, draw concept represented by the word without using words.
- The other team members attempt to guess the word from the drawing.
- The student continues to draw until the group guesses the word.
- The next student clockwise will select the next card and play continues.
- The teacher should circulate the room looking for misconceptions or incorrect definitions.
- To make the game more competitive the teacher could add that the students receive the index card when they guess the correct answer. The student with the most index cards wins.
After about 10 minutes, the teacher will bring the class back together to review any vocabulary words with which the students struggled.
The teacher will, then, explain that the students are being tasked with finding relationships. Their goal is to look at the circles provided on the discovery sheet, and in groups of two students, find relationships that exist in circles. Today they are to explore angles created on the circle, in the interior of the circle, and exterior to the circle.
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)?
Analyze: How will students organize and interpret the data collected during the investigation?
The students will fill out the provided discovery sheet, organizing their data in charts. They will be prompted to look at the data through investigative questions.
Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Once the students have completed the discovery worksheet the teacher will bring the students back together. As a class they will discuss the findings, affirm valid answers, and develop relationships that will be helpful in the future.
Seeking Circle Angles discovery sheet answers
Summarize the material in the box provided on the sheet for the students to reference in the future.
If time allows the teacher could provide students with white boards and ask questions that apply the discovered relationships.
White board sample questions
White board sample questions answers
The following day the students will complete a short quiz on the relationships between arc measures and angle measures.
Bellwork with Answers
Students will participate in a group activity of "Win-Lose-Draw". The teacher will circulate the room to ensure that the students are participating and understanding the vocabulary.
Throughout Discovery Activity
The teacher will walk around and observe the students as they work through the discovery activity. The teacher will only prompt students to keep them engaged and on task. The teacher will look for the connections that the students are making and relationships they are discovering. The teacher will note and correct the misconceptions with guiding questions.
Feedback to Students
Students will correct and coach each other's knowledge of the vocabulary, and the teacher will intervene if necessary.
Throughout Discovery Activity
The students will coach and challenge each other's ideas. The teacher will circulate to correct any misconceptions through guiding questions.
The teacher will lead a discussion to ensure that the students understand the intended relationships.