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Geometric Relationships and Construction · Term 2

Angles in Triangles

Discovering and applying the triangle sum theorem and exterior angle theorem.

Key Questions

  1. Justify why the interior angles of any triangle always sum to 180 degrees.
  2. Predict the measure of an exterior angle of a triangle given its remote interior angles.
  3. Construct a proof or demonstration of the triangle sum theorem.

Ontario Curriculum Expectations

7.G.B.5
Grade: Grade 7
Subject: Mathematics
Unit: Geometric Relationships and Construction
Period: Term 2

About This Topic

This topic explores the science of solutions, focusing on how substances dissolve and the factors that influence solubility. Students learn to distinguish between the solute (the substance being dissolved) and the solvent (the substance doing the dissolving). They investigate how temperature, agitation, and particle size affect the rate at which a solution forms, which are key concepts in the Ontario curriculum.

Students also explore the concept of saturation, the point at which no more solute can be dissolved in a solvent. This has practical applications in everything from cooking to industrial manufacturing and environmental science. This topic particularly benefits from hands-on, student-centered approaches where students can experiment with different variables to see how they change the dissolving process.

Active Learning Ideas

Watch Out for These Misconceptions

Common MisconceptionWhen something dissolves, it disappears or turns into a liquid.

What to Teach Instead

The solute is still there; it's just broken down into particles too small to see. Massing the solvent and solute before and after mixing helps students see that the matter is conserved.

Common MisconceptionA saturated solution is 'full' and has no more space.

What to Teach Instead

It's more about the balance between dissolving and re-crystallizing. Using a simulation that shows particles constantly moving in and out of solution helps students understand this dynamic equilibrium.

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Frequently Asked Questions

What is the difference between a solute and a solvent?
The solute is the substance that is being dissolved (like salt or sugar), and the solvent is the substance that does the dissolving (like water). In most cases, the solvent is present in a larger amount than the solute.
How does temperature affect solubility?
For most solid solutes, increasing the temperature of the solvent increases solubility. This is because the particles are moving faster and have more energy to break the bonds of the solute. However, for gases, solubility usually decreases as temperature increases.
What does it mean when a solution is 'saturated'?
A solution is saturated when it contains the maximum amount of solute that can be dissolved at a given temperature. If you add more solute to a saturated solution, it will simply settle at the bottom and not dissolve.
What are the best hands-on strategies for teaching solubility?
Inquiry-based labs where students choose their own variables are highly effective. Instead of following a recipe, asking students to 'find the fastest way to dissolve this' forces them to apply their knowledge of particle theory. This approach encourages them to experiment with temperature, surface area, and stirring, leading to a deeper understanding of the 'why' behind the results.

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