Reasoning Roots Worksheet Reasoning Roots
Lesson 1: Deductive vs. Inductive Reasoning
Logic Lab / Unit 01
Name:
Date:
CASE FILE: THE MISSING MASCOT
The school mascot's costume disappeared from the gym locker room between 3:00 PM and 4:00 PM on Tuesday. Security footage shows only three students entered that hallway: Alex, Jamie, and Sam.
Evidence Clip A
Jamie was seen wearing blue sneakers in the hall at 3:15 PM. Blue sneaker prints were found inside the locker room where the costume was kept.
Question: Does this clue PROVE Jamie is the culprit, or just SUGGEST it?
Evidence Clip B
The thief had to use a key card to enter the gym. The system log shows that Sam's key card was the ONLY one used between 3:00 PM and 4:00 PM.
Question: Does this clue PROVE Sam is the culprit, or just SUGGEST it?
Deductive Reasoning
Moves from general rules to a specific, certain conclusion.
Conclusion is 100% guaranteed if the starting points are true.
Focuses on certainty .
"Top-down" logic.
Inductive Reasoning
Moves from specific observations to a general, probable conclusion.
Conclusion is likely, but not guaranteed.
Focuses on probability .
"Bottom-up" logic.
Analysis Practice
Identify each statement as D (Deductive) or I (Inductive). Explain your reasoning.
"Every time I go to the mall on a Saturday, it is crowded. Today is Saturday. Therefore, the mall will probably be crowded today."
"All high school students must take an English class. Leo is a high school student. Therefore, Leo must take an English class."
"I've watched three movies by this director, and they were all sci-fi. Her next movie will likely be a sci-fi movie too."
Reasoning Roots Answer Key Teacher Resource
Reasoning Roots
Answer Key & Teacher Guide
Logic Lab / Unit 01
CASE FILE SOLUTIONS
Clue A (Blue Sneakers)
Inductive Reasoning (SUGGESTS)
Reasoning: Having blue sneakers and finding blue prints is evidence, but not proof. Many people could own blue sneakers. It is probable but not certain .
Clue B (Key Card Log)
Deductive Reasoning (PROVES)
Reasoning: If only one card was used, and that card belongs to Sam, it necessarily follows (within the logic of the scenario) that Sam entered the gym. It is a matter of certainty based on the defined rule.
Analysis Practice Key
I
"Every time I go to the mall on a Saturday, it is crowded. Today is Saturday. Therefore, the mall will probably be crowded today."
Note: Uses past patterns to predict future probability. The word "probably" is a major clue.
D
"All high school students must take an English class. Leo is a high school student. Therefore, Leo must take an English class."
Note: Conclusion follows necessarily from the general rule. There is no room for probability.
I
"I've watched three movies by this director, and they were all sci-fi. Her next movie will likely be a sci-fi movie too."
Note: Generalizes from a small sample size to predict a likely outcome.
Facilitation Notes
Common Misconception: Students often think "deductive" just means "smart detective work." Remind them that Sherlock Holmes actually uses induction most of the time (making smart guesses from clues)!Keyword Search: Encourage students to look for words like always, must, necessarily (Deductive) vs. likely, probably, usually (Inductive).The "Certainty" Test: Ask: "Is it possible for the premises to be true but the conclusion to be false?" If yes, it's Inductive. Syllogism Skeleton Slides The Syllogism Skeleton
Anatomy of a Perfect Argument
Lesson 02 Logic Lab
What is a Syllogism?
A deductive argument with three categorical propositions that link two terms through a third.
Formal Definition
"A discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so."
— Aristotle
The Three Bone Structure
Major Premise
The broad rule. It contains the Major Term (the predicate of the conclusion).
Minor Premise
The specific case. It contains the Minor Term (the subject of the conclusion).
Conclusion
The logical result that connects the specific case to the broad rule.
Skeleton Dissection
Classic Case
1
All humans are mortal.
Major Premise
2
Socrates is a human.
Minor Premise
3
Therefore, Socrates is mortal.
Conclusion
Standardizing Language
Logic needs clear labels. We convert messy English into Categorical Form :
Natural Speech
"Dogs always chase cats."
Categorical Form
"All dogs are cat-chasers."
Avoid verbs other than "is" or "are". Convert actions into nouns or categories.
Syllogism Skeleton Worksheet The Skeleton Lab
Lesson 2: Syllogism Dissection & Standardization
Logic Lab / Unit 01
Name:
Date:
PART 1: THE DISSECTION
Label each part of the syllogism: Major Premise , Minor Premise , or Conclusion .
All mammals have backbones.
Label here...
A blue whale is a mammal.
Label here...
Therefore, a blue whale has a backbone.
Label here...
No reptiles have fur.
Label here...
All lizards are reptiles.
Label here...
Therefore, no lizards have fur.
Label here...
PART 2: STANDARDIZATION
Rewrite the following casual statements into Categorical Form (All A are B, No A are B, Some A are B).
"Every student in this room loves pizza."
"Not a single cat can bark."
"People who live in Seattle usually own an umbrella."
Hint: Use "Some" for "usually"
End of Skeleton Lab Workshop
Truth and Structure Slides Truth vs. Structure
Validity & Soundness
Lesson 03 Logic Lab
The Green Cheese Debate
1. All satellites are made of green cheese.
2. The moon is a satellite.
Therefore, the moon is made of green cheese.
Is this "Good" Logic?
Structurally? Yes. No.
This argument is VALID but not SOUND.
Validity
What it is:
The logical structure . If the premises WERE true, the conclusion WOULD HAVE TO be true.
The Test:
Can you imagine a world where the premises are true but the conclusion is false?
If NO, then it is valid.
Soundness
The "Golden Standard" of Logic
Perfect Validity
True Premises
=
SOUND ARGUMENT
An argument is sound if and only if it is valid AND all of its premises are actually true in the real world.
Spot the Problem
Argument:
"All billionaires are astronauts. Elon Musk is a billionaire. Therefore, Elon Musk is an astronaut."
Valid?
YES
The structure follows perfectly.
Sound?
NO
Premise 1 is factually false.
Truth and Structure Worksheet The Soundness Check
Lesson 3: Evaluating Validity vs. Soundness
Logic Lab / Unit 01
Name:
Date:
PART 1: THE EVALUATION
For each argument, determine if it is Valid (structurally correct) and if it is Sound (factually true). Explain your choice.
All birds can fly.
Valid?
Yes
No
Sound?
Yes
No
Explain:
All fruits are healthy snacks.
Valid?
Yes
No
Sound?
Yes
No
Explain:
PART 2: THE ALCHEMIST
Construct your own syllogism that is VALID but UNSOUND . This means the logic must work, but at least one premise must be false.
Major Premise (The False Rule):
Minor Premise (The Specific Case):
Conclusion (Must follow logically):
Critical Reflection
Why is it dangerous to accept an argument just because it "sounds logical" (is valid)?
Mapping the Mind Slides Mapping the Mind
Venn Diagrams for Logic
Lesson 04 Logic Lab
Can You See the Truth?
Sometimes syllogisms get complicated. Venn Diagrams allow us to map categories and see if the logical "boxes" actually fit together.
"If the conclusion is already 'drawn' just by mapping the premises, the argument is valid."
Category A
Category B
Drawing "All A are B"
The Method:
Draw two overlapping circles (A and B).
Shade out the part of A that is NOT in B.
Shading means "This area is empty."
B A
"All A are B"
The 3-Circle Test
To test a syllogism, we use three overlapping circles (one for each term):
Argument:
All Humans are Mortal.
Mortal
Humans
Greeks
If the "Greeks" circle is pushed entirely into the "Mortal" circle by the first two rules, it's valid!
Visual Mastery
Grab your practice sheet. We are going to map the relationships between:
Draw Circles
Shade Areas
Verify Results
Mapping the Mind Worksheet The Visual Logic Lab
Lesson 4: Testing Validity with Venn Diagrams
Logic Lab / Unit 01
Name:
Date:
Shading Rules
All A are B: Shade the part of A that is not in B.No A are B: Shade the overlap between A and B.Some A are B: Place an 'X' in the overlap between A and B.SHADING means the area is EMPTY.
The Validity Test
Map the Major Premise and the Minor Premise . After mapping both, look at the diagram. If the Conclusion is already drawn (shaded or X-ed), the argument is VALID .
Case 01
All Humans (H) are Mortal (M).
Result:
Valid
Invalid
M H G
Case 02
All Dogs (D) are Animals (A).
Result:
Valid
Invalid
A D C
Visualizing Logic Reflection
In Case 02, why did the argument look logical at first glance, but fail the Venn diagram test? What part of the diagram showed the "gap"?
Argument Architect Worksheet The Argument Architect
Lesson 5: Constructing & Peer Reviewing Syllogisms
Logic Lab / Unit 01
Name:
Date:
1
Blueprints: Drafting Your Argument
Topic Ideas: School cell phone policy, grading systems, sports requirements, or current local news.
Major Premise (The General Rule):
Example: All student-athletes must maintain a 2.0 GPA...
Minor Premise (The Specific Case):
Example: Jordan is a student-athlete...
Conclusion (The Logical Result):
Example: Therefore, Jordan must maintain a 2.0 GPA.
2
Structural Inspection (Peer Review)
Architect's Name:
Inspector's Name:
Standardized?
Does it use clear "All/No/Some" language? Does it use "is/are" as the verb?
Valid Structure?
Does the conclusion necessarily follow from the premises? (No logical gaps!)
Sound Argument?
Are the premises actually true in the real world?
Inspector's Verdict & Feedback:
Write suggestions for improvement here...
Argument Architect Teacher Guide Teacher Resource
Argument Architect
Evaluation Guide & Mastery Rubric
Logic Lab / Unit 01
Mastery Standards
Criteria Mastery (3) Developing (2) Starting (1) Standard Form Uses All/No/Some. All verbs are "is/are". Language is clear and noun-based. Uses quantifier, but verbs are inconsistent. Some phrasing is messy. Uses natural language. Missing clear categorical terms. Validity Conclusion is mathematically certain based on the premises. No logical gaps. Conclusion is likely but contains a structural flaw (e.g., Undistributed Middle). Premises and conclusion are unrelated or conclusion is non-sequitur. Soundness All premises are factually true in the real world. Argument is grounded in fact. One premise is questionable or subjective but logically defended. Premises are demonstrably false or purely fictional.
Watch for "Gaps"
Students often create Invalid arguments that "feel" true. Point out the undistributed middle:
All cats are mammals.
Mastery Tip
Ask students to use the Venn Diagram Test from Lesson 4 on their own draft before they hand it to a peer. This self-correction phase dramatically increases the quality of the final arguments.
Suggested Pacing: 15 mins Drafting, 15 mins Peer Inspection, 10 mins Final Revisions.
