Summary
In this lesson, students will be introduced to all four conic sections, first by manipulating light to create the conics, then by participating in a card sort to match graphs, key features, and their equations. Next, students will formalize their knowledge through a flow chart and an informational video before participating in an expert stay-and-stray strategy, where they will teach their peers about conic sections. The lesson concludes with a check for understanding to ensure that students can graph and identify key features given the equation of each conic section.
Essential Question(s)
How do the key features of conic sections help in constructing the equations and graphs?
Snapshot
Engage
Students use a flashlight and table to create conic sections with the light.
Explore
Students use a card sort to group equations, graphs, and key features with each conic section.
Explain
Students complete a flowchart to determine conic sections and watch a video to formalize their knowledge of each conic section.
Extend
Students practice differentiating key features of each conic section through the Expert Stay and Stray strategy.
Evaluate
Students complete practice problems and review and correct peers' responses.
Materials
Lesson Slides (attached)
Playing with Light (attached; one per student)
Card Sort (attached; one per group)
Card Sort Answer Key (attached)
Classifying Conics Flowchart (attached; one per student)
Classifying Conics Flowchart (Answer Key) (attached)
Conic Sections Key Features (attached; one per student)
Conic Sections Key Features (Sample Responses) (attached)
Conic Sections Practice Problems (attached; one per student)
Conic Sections Practice Problems (Answer Key) (attached)
Flashlight (one per group)
Cardboard boxes (Optional)
Engage
5 Minute(s)
Use the Lesson Slides to guide the lesson. Introduce the lesson by asking the essential question and explaining the objectives on slides 2-4.
Split the class into groups of 2-4 students, provide each group with a Playing with Light handout (attached) and flashlight, and use slide 5 to introduce the activity to the class. Explain to students that when you turn on your flashlight and point it towards the wall, you can see a cone of light, with the tip of your cone being your flashlight and the base of your cone being the plane that it intersects. When you hold the flashlight at a different angle to the wall (or plane), the shape of the light will change. Tell students that with their groups, they will investigate these changes and record them on their handout.
Dim the classroom lights to the best of your ability and instruct the groups to complete the table on their handout. Encourage students to utilize the word bank as necessary.
Explore
20 Minute(s)
Keeping students in the same groups from the Engage, transition to slide 6, and give each group a set of the prepared Card Sort. Explain to the class that they will work with their groups to match the five equations, graphs, and key features together for each conic section.
Explain
20 Minute(s)
Transition to slide 14 and give each student a copy of the Classifying Conics Flowchart. Using prior knowledge and the card sort, have the groups work together to complete the flowchart.
When complete, ask the students to take a picture of their completed card sort to reference later. Shuffle and rubber band the cards together, and return the card to a specific place in the classroom.
Review correct responses for the Flowchart on slide 15 and encourage students to keep the flowchart in a place to refer to in the future. If students have a math notebook or folder, consider gluing or stapling it in.
Display slide 17 to share the Introduction to Conic Sections video for students to formally learn about each conic section and the key features of its graph.
Extend
30 Minute(s)
Show slide 18 and pass out Conic Sections Key Features handout (attached) to introduce the next activity to the class. Inform students that they will identify key features of their conic section before sketching the graph and writing an equation based on an existing graph.
Once groups have completed their conic section, transition to slide 19, introduce the Expert Stay and Stray strategy, and provide each student with the remaining conic section pages.
Assign all students a number 1 through 4. Ask students assigned number 1 to be the first expert while the other group members rotate to the next table. Start a class timer of 5 minutes or use the timer on slide 19 and instruct students to listen carefully to the expert talk about their conic section while they fill in their notes.
Once the timer is complete, ask a different student to stay at the table group to become the new expert, and all other students move to the next table.
Repeat this process a total of 4 times.
Once all students have had the opportunity to learn about all 4 conic sections from their classmates, instruct the students to return to their seats and place their note pages in a place like their notebooks or binders to refer to later.
Evaluate
20 Minute(s)
Transition to slide 20 and give each a copy of the Conic Sections Practice Problems handout (attached). Tell students not to write their names on this paper. Instruct students to use their notes, graphing technology, and any other tools to help them solve the four problems on their paper in the time provided.
Start a class timer for 10 minutes or use the timer on slide 20 and walk about the room while students work. Answer questions and keep students on task.
When the timer has elapsed, ask the class to turn in their paper without their name written on it to a predetermined location in the classroom. Once all papers have been collected, shuffle them and randomly hand back one paper per student.
Transition to slide 21 and ask the students to write their names at the top of this piece of paper, start the class timer for 10 minutes, and instruct students to use this time to review the work on the paper, make corrections, and complete any work.
When the time has finished, ask the students to turn in their paper to a predetermined location in the classroom to be graded.
Resources
K20 Center. (2021, September 21). K20 Center 5 minute timer. [Video]. YouTube. https://www.youtube.com/watch?v=EVS_yYQoLJg
K20 Center. (2021, September 21). K20 Center 10 minute timer. [Video]. YouTube. https://www.youtube.com/watch?v=9gy-1Z2Sa-c
K20 Center. (n.d.). Card sort. Strategies. https://learn.k20center.ou.edu/strategy/147
K20 Center. (n.d.) Expert stay and stray. Strategies. https://learn.k20center.ou.edu/strategy/2650
K20 Center. (n.d.) Stand up, sit down. Strategies. https://learn.k20center.ou.edu/strategy/1771
K20 Center. (2025, January 23). Hooked on Conics [Video]. YouTube. https://www.youtube.com/watch?v=XYWF2yPJdGE
MathLawes. (2023, April 18). How to Visualize and Model Conic Sections with a Flashlight (90 sec.) [Video]. YouTube. https://www.youtube.com/watch?v=DMehuSl2hsc