Summary
In this lesson, students will use legal, game, and content based methods to understand how to create proofs.
Essential Question(s)
How can we use our knowledge of definitions, theorems, and postulates to justifying our reasoning?
Snapshot
Engage
Students use Chat Stations to discuss how they argue and how arguments can be made stronger and weaker.
Explore
Students watch a movie clip of a court scene and work as partners to construct the line of questioning and the corresponding reasons in a table. The whole class discusses the argument in the movie clip and determines how effective it is.
Explain
Students complete guided notes over the types of proofs, list reasons for proofs, and practice answering proofs.
Extend
Students work in small groups to complete a card matching activity to complete proofs.
Extend — ICAP
Students watch a video interview to understand how the legal field uses proofs.
Evaluate
Students use the GUS strategy to complete a proof on their own.
Materials
Lesson Slides (attached)
Writing utensil
Sticky notes
Opening Statements Posters (attached)
Witness Testimony handout (attached; one per student)
Witness Testimony Sample Response document (attached)
Evidence Guided Notes handout (attached; one per student)
Evidence Guided Notes (Model Notes) document (attached)
Cross-Examination Card Sets handout (attached; one per group)
Cross-Examination Records handout (attached; one per group)
Cross-Examination Key document (attached)
Closing Arguments Task Cards (attached; one card per student)
Closing Arguments Task Cards Teacher’s Guide (attached)
UNO cards (optional)
Engage
20 Minute(s)
Use the attached Lesson Slides to guide the lesson. Review the essential question and learning objective on slides 3 and 4.
Transition to slide 5 and introduce the Chat Stations strategy. Place students into groups of three to four and have each group stand by one of the attached Opening Statements Posters and provide each student with three sticky notes.
Have each group discuss the question on their poster, write their answer on a sticky note, and place it near the poster.
Next, have students rotate to the next poster and repeat the process. After each group has answered all the questions, have them return to the poster at which they started. Have students to read all of the sticky notes and organize them by similar ideas.
Ask each group to share what the sticky notes at their poster say and what they notice about the responses.
When all groups have shared, have students return to their seats.
Explore
20 Minute(s)
Display slide 7 prepare to show the Legally Blonde scene to students. Set the scene by explaining that the lead character, Elle, is a law student and is defending her client, who is accused of murder. Inform students that in this part of the scene, Elle is asking a witness questions to prove that her client is not guilty of murder. Ask students to evaluate Elle’s argument by listening for strong points she makes and places she could have improved.
After playing the video, move to slide 8 and have students get into pairs.
Pass out a copy of the attached Witness Testimony handout to each pair and give time for students to work through the handout.
Display slide 9 to write in information for students or walk around the room and assist as needed.
When students are finished, transition through slides 10-13 and facilitate a whole-class discussion over the four questions.
Explain
30 Minute(s)
Display slide 20 and give each student a copy of the attached Evidence Guided Notes handout. Using the attached Evidence Guided Notes (Model Notes) document for guidance, review the definition of “proof” and “justify” with students and ask them to write these definitions on their handout. These two terms are related because a student writes a proof by “laying out their mathematical thoughts and processes step by step” in order to prove a statement is true.
Move to slide 20 and explain that proof writers will categorize proofs based on the class that type of math is taught in. For example, algebraic proofs contain math and reasons commonly taught in algebra classes, while geometric proofs contain math and reasons commonly taught in geometry classes. These classifications serve no purpose other than to guide student towards possible reasons to use in their proof.
Move to slide 21 and review the definitions that explain the difference between two-column and paragraph proofs. Have students write the types of proofs on their handout.
Move to slide 22 and show the examples of both types of proofs. Point out that a two column proof and paragraph proof contain the same information, but differ in structure. Ask students the following questions to guide them in understanding these differences:
Look at the first statement and reason in the two-column proof. Where does that information appear in the paragraph proof?
Does the information appear in the same order in both the two-column proof and the paragraph proof?
Look at the last two sentences of the paragraph proof. Would you make any changes?
Which type of proof do you prefer? Why?
Display slide 23 and direct students to look at the same information on their handout. Ask them to put a check mark next to all of the vocabulary words that they remember, and put a star next to any terms they do not know. Walk around the room and determine if any terms need to be reviewed.
Move to slide 23 and informally review any terms needed by asking the students to define it and describe how it is used.
Move to slide 24 and repeat this process with the terms “postulates” and “theorems”.
Transition through slides 25-26 and use the statements to ensure that students understand where reasons come from and why proofs can look different before moving on to examples.
Display slide 27 and ask students to solve the algebra problem. Ask them to list each step in the equation in the left column of the provided table.
After students have had an opportunity to solve the problem, transition through slides 27-31 and help students make the connection between solving the problem and constructing the proof.
Transition through slides 32-39 and explain the steps of creating a proof.
After students construct a two-column proof, give them time to transfer the same information into a paragraph format. Each student's paragraph can differ slightly as long as it contains the same information as the two-column proof.
If time allows or students need more practice, unhide slides 40-45 and allow students to complete more proofs.
When students are finished, have them add their work to their math notebook if that is a classroom norm.
Extend
30 Minute(s)
Have students move into groups of three or four. Display slide 46 and pass out a copy of the Cross-Examination Card Sets and Cross-Examination Records handouts to each group. Introduce the Card Matching strategy and have students match the missing statements and reasons with the provided cards. Direct groups to record their results on the handout.
As groups match the cards, use the attached Cross-Examination Key document to check students' work and ask them to look back at any proofs that are not correct.
If time allows, move to slide 47 to show students the video interview with a criminal defense attorney to understand how proofs are used by the justice system.
Evaluate
15 Minute(s)
Display slide 48 and give each student one task card from the attached Closing Arguments Task Cards handout. Instruct students to complete the proof on their task card. They can use the back of the card or on a separate sheet of paper if additional space is needed.
After students have completed their proofs, move to slide 49 and have them use the GUS Method to share their feelings about the answer that they have provided. Have students add their GUS response under their proof.
Resources
K20 Center. (n.d.). Card Matching. Strategies. https://learn.k20center.ou.edu/strategy/1837
K20 Center. (n.d.). Chat Stations. Strategies. https://learn.k20center.ou.edu/strategy/944
K20 Center. (n.d.). Elbow Partners. Strategies. https://learn.k20center.ou.edu/strategy/116
K20 Center. (n.d.). GUS Method. Strategies. https://learn.k20center.ou.edu/strategy/76
K20 Center. (2022, September 22). K20 ICAP - Prove Me wrong [Video]. YouTube. https://www.youtube.com/watch?v=RW4SVMW5pgg
Movieclips. (2015, November 30). Legally blonde (2001) - Elle wins! scene (11/11) | Movieclips [Video]. YouTube. https://www.youtube.com/watch?v=GSu7BGbyJqc