Investigating a Mathematical Statement
Statement of Inquiry: Mathematicians use logic to understand mathematical relationships and thereby generalize how multiplication functions across number types when making scientific calculations.
Concept Question: Is it always true that multiplication increases a value?
Suggested length: 1 hour
Learning objectives:
- Objective B: Investigating patterns
- ii. describe patterns as relationships and/or general rules consistent with findings
- iii. verify and justify relationships and/or general rules.
| Concepts | Global Context | ATL Skill |
|---|---|---|
| Logic Relationships Generalization Validity | Scientific and technical innovation: Patterns in mathematics | Critical thinking: Draw justifiable conclusions and generalizations |
Resources and Preparation
- Set up a Kialo discussion around the concept question with the thesis: “Multiplication always increases a value.”
- (Alternative questions can be found at the end of the downloadable lesson plan.)
- Use Tasks and Small Group Mode to structure the discussion, if appropriate.
- Share the discussion with students.
Introduction
Display the statement: Multiplication always increases a value.
Think-pair-share: Ask students to discuss for two minutes and note down their thoughts.
Gather students’ initial ideas.
Concept Formation
Discuss the following questions with students:
What does the logic of multiplication tell us about how the operation behaves with different types of numbers?
How does the relationship between the multiplicand and the multiplier affect the outcome?
Main Activity
Students will work in small groups in their own copy of the Kialo discussion responding to the thesis: Multiplication always increases a value.
Explain that students can use PROS to support the statement and CONS to challenge it, building their argument using claims, examples, and explanations.
Model the following example before students begin:
- Claim: Multiplying increases a value when you multiply by any whole number greater than 1.
- Example: 5×3=15 — 15 is greater than 5.
- Explanation: When you multiply by a whole number greater than 1, you are adding that number to itself multiple times.
- Example: For example, 5×3 is the same as 5+5+5, which increases the value.
Reflection Activity
Discuss the following questions in open discussion or exit ticket format:
- Generalization: Can you generalize a rule about what happens when you multiply by numbers greater than 1, less than 1, or equal to 0 or 1?
- Validity: Is the statement “Multiplication always increases a value” valid in all situations? If not, under what conditions is it valid or invalid?
