Solving Systems by Graphing
Students will solve systems of linear equations by graphing both lines and identifying their intersection point.
Key Questions
- Critique the limitations of solving systems by graphing, especially with non-integer solutions.
- Design a process for accurately graphing two linear equations on the same coordinate plane.
- Assess the visual representation of a system's solution when lines are parallel or coincident.
Ontario Curriculum Expectations
About This Topic
The Law of Conservation of Mass is a cornerstone of physical science, stating that matter cannot be created or destroyed in a chemical reaction. Students learn to balance chemical equations to reflect this reality, ensuring that the number of atoms for each element remains constant. This topic connects to Ontario's emphasis on quantitative relationships and the predictive power of science.
By mastering equation balancing, students develop the skills needed for stoichiometry and environmental chemistry. This topic particularly benefits from hands-on, student-centered approaches where students use physical counters or digital simulations to 'balance' the reactants and products, making the abstract math visible.
Active Learning Ideas
Inquiry Circle: The Sealed Bag Lab
Students mix vinegar and baking soda inside a tightly sealed heavy-duty bag on a digital scale. They observe that despite the fizzing and gas production, the total mass remains unchanged.
Stations Rotation: Equation Balancing Puzzles
Stations feature unbalanced equations and physical 'atom' tokens. Students must arrange the tokens to match the equation and then determine the correct coefficients to balance the reaction.
Think-Pair-Share: Where Did It Go?
Show a video of a candle burning on a scale where the mass appears to decrease. Students discuss in pairs where the 'missing' mass went and how to prove it still exists.
Watch Out for These Misconceptions
Common MisconceptionMass is lost when a gas is produced in an open container.
What to Teach Instead
The gas has mass but has escaped into the atmosphere. Performing reactions in both open and closed systems helps students see that the 'loss' is just a measurement limitation.
Common MisconceptionYou can change the subscripts in a chemical formula to balance an equation.
What to Teach Instead
Changing subscripts changes the substance itself; only coefficients can be adjusted. Using molecular model kits helps students see that H2O and H2O2 are entirely different molecules.
Suggested Methodologies
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Frequently Asked Questions
How can active learning help students understand conservation of mass?
Why do we balance chemical equations?
What is a coefficient in a chemical equation?
What happens to atoms during a chemical reaction?
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
unit plannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
rubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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