Summary
In this lesson, students explore the differences between inductive and deductive logic and how to use that reasoning to draw logical conclusions.
Essential Question(s)
How can we use facts and patterns to draw logical conclusions?
Snapshot
Engage
Students discuss their methods for finding the next figure in a pattern to introduce the idea of reasoning.
Explore
Students use given information to draw conclusions about what is going to be on the lunch menu, unknowingly exploring inductive and deductive logic.
Explain
Students formalize their understanding of inductive and deductive reasoning.
Extend
Students predict the sum of the interior angles of a 13-gon using both inductive and deductive reasoning and an interactive GeoGebra activity.
Evaluate
Students create their own inductive or deductive problem and then find the logical conclusion of their peer’s problem.
Materials
Lesson Slides (attached)
What’s for Lunch? Red handout (attached; one per group; print two-sided)
What’s for Lunch? Blue handout (attached; one per group; print two-sided)
Inspecting Interior Angles handout (attached; one per student; print two-sided)
Pencils
Paper
Calculators
Student devices with internet access
Engage
10 Minute(s)
Introduce the lesson using the attached Lesson Slides. Slide 3 displays the lesson’s essential question. Slide 4 identifies the lesson’s learning objective. Review each of these with your class to the extent you feel necessary.
Display slide 5 and introduce the Give Me Five strategy. Then, ask the class what they notice about the three figures on the slide.
After two minutes of “think time” (or wait time), ask five students to share their thoughts.
Transition to slide 6 and facilitate a discussion to come to a consensus about what the next iteration (Figure 4) of the pattern should look like. Use this time to help students practice communicating their reasoning.
Explore
30 Minute(s)
Show slide 7 and split students into groups of 2–3. Provide half of the groups with a copy of the attached What’s for Lunch? Red handout and the other half with a copy of the attached What’s for Lunch? Blue handout. Here students are given information about how the menu at the cafeteria is determined, but the same information is presented differently on the two handouts—do not yet share this information with the class.
As groups complete their handouts, walk around and monitor their work. Help students who are struggling, but be careful not to give them any answers.
Consider asking questions like the following:
Why do you think that?
Does the whole group agree?
What have you tried already?
After groups have completed their work, have them partner with another group that had the opposite handout to discuss their results.
Explain
20 Minute(s)
Display slide 8 and ask a group to present their results and share how they reached their conclusions. Make sure they explain their reasoning. Do not affirm or correct the answers. After one group has shared, ask the class if anyone else had different answers or different reasonings. As needed, use the hidden slide 9 for what should be on the menu.
Show slide 10 and lead a class discussion on the following questions:
Whose reasonings were more convincing?
Which handout do you think was easier? Why?
Which handout was more difficult? Why?
Did you change anything when you worked with the group who did the other handout?
Display slide 11 and use the slide to share the definitions of inductive and deductive reasoning.
Inductive Reasoning: the process of observing data, recognizing patterns, and making generalizations about those patterns
Deductive Reasoning: the process of showing that certain statements follow logically from agreed-upon assumptions and proven facts
Have students work in their groups to determine which reasonings presented used inductive reasoning and which used deductive reasoning.
Show slide 12 and read the prompt from the slide: “The first four numbers in a sequence are 3, 6, 9, and 12. What is the fifth number in the sequence?” Ask students to come to a logical conclusion and then decide whether they use inductive or deductive reasoning.
Repeat this using slides 13–15 with the following prompts:
Ruthie takes a nap every afternoon. The time is 1:45 p.m., what is Ruthie doing?
Amir got to school at 7:59 a.m. on Monday, at 8:01 a.m. on Tuesday, and at 8:03 a.m. on Wednesday. What time will he get to school on Friday?
If I get to work on time, I will be assigned to a better station. I got to work on time today.
Extend
30 Minute(s)
Display slide 16. Give each student a copy of the attached Inspecting Interior Angles handout and calculator. Provide students with the link to the GeoGebra activity: k20.ou.edu/7g. Here students use the provided tools to create polygons and effortlessly find the angle measures of the interior angles. Have students follow the directions on their screen, and then use their results and calculators to complete the “Measure the Angles” portion of their handout. Students are to use this information to answer the questions in the “Find the Pattern” portion and predict the sum of the interior angles of a 13-gon.
Once several students are done with Parts A and B, move to slide 17. The directions are also on the handout for students to be able to easily work ahead. Students are directed to navigate to the “Use the Facts” portion of the GeoGebra activity to complete the corresponding portion of their handout. Again, they are asked to predict the sum of the interior angles of a 13-gon, but this time they are given the formula.
Evaluate
15 Minute(s)
Display slide 18 and introduce the Commit and Toss strategy. Ask students to take out a half-sheet of paper and create their own inductive or deductive reasoning problem like they saw during the Explain phase of the lesson. Remind students that they need to give enough information that someone could use either inductive or deductive reasoning to answer their question. Give students approximately 5 minutes to complete this task.
Move to slide 19 and have students crumple their papers and gently toss them into the middle of the room. Then have students pick up a paper, other than their own, and answer the question on the paper.
Use student responses to determine if additional practice is needed.
Resources
K20 Center. (n.d.). Elbow partners. Strategies. https://learn.k20center.ou.edu/strategy/116
K20 Center. (n.d.). Commit and toss. Strategies. https://learn.k20center.ou.edu/strategy/119
K20 Center. (n.d.). GeoGebra. Tech tools. https://learn.k20center.ou.edu/tech-tool/2352
K20 Center. (n.d.). Give me five. Strategies. https://learn.k20center.ou.edu/strategy/150
K20 Center. (n.d.). Inspecting interior angles [Web app]. GeoGebra. https://www.geogebra.org/m/ca3cxmcz