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Ratios and Proportional Reasoning · Term 1

Ratio Tables and Equivalent Ratios

Using tables to represent and solve problems involving equivalent ratios.

Key Questions

  1. Explain how to determine if two ratios are equivalent using different mathematical strategies.
  2. Construct a ratio table to find missing values in a proportional relationship.
  3. Analyze the patterns within a ratio table that indicate proportionality.

Ontario Curriculum Expectations

6.RP.A.3.A
Grade: Grade 6
Subject: Mathematics
Unit: Ratios and Proportional Reasoning
Period: Term 1

About This Topic

Physical Changes in Daily Life focuses on how matter changes state and shape without changing its chemical identity. Students investigate melting, freezing, evaporation, condensation, and sublimation, linking these processes to the particle theory. This topic is highly practical, as it explains everything from how we preserve food to how the Canadian climate shapes our landscape through the freeze-thaw cycle.

In the Ontario curriculum, students are encouraged to look at the industrial applications of physical changes, such as the distillation of maple syrup or the manufacturing of glass and metal products. They also explore the water cycle as a massive, natural example of physical changes in action. This topic particularly benefits from hands-on modeling where students can observe and measure changes in state in real-time.

Active Learning Ideas

Watch Out for These Misconceptions

Common MisconceptionBoiling water 'disappears' when it turns into steam.

What to Teach Instead

Explain that the water has just changed into an invisible gas (water vapor) and is still present in the room. Using a cold plate to catch steam and turn it back into liquid droplets provides immediate visual proof.

Common MisconceptionPhysical changes are always reversible.

What to Teach Instead

While many are (like melting ice), some physical changes like shredding paper or breaking a rock are very difficult to reverse. Peer discussion about 'reversibility vs. identity' helps students understand that the substance remains the same even if the shape is permanently altered.

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Frequently Asked Questions

What is the difference between a physical and chemical change?
In a physical change, the substance stays the same even if its state or shape changes (like ice melting). In a chemical change, a brand new substance is formed (like wood burning into ash). Grade 6 focuses primarily on physical changes.
How can active learning help students understand changes of state?
By conducting experiments like making 'slushies' with salt and ice or observing dry ice (sublimation), students see these changes happen before their eyes. Active learning encourages them to measure variables like time and temperature, turning a simple observation into a data-driven investigation that reinforces the particle theory.
What is sublimation?
Sublimation is when a solid turns directly into a gas without becoming a liquid first. A common example is 'dry ice' (solid carbon dioxide) or snow disappearing on a very cold, sunny day in the Canadian winter.
How does the water cycle use physical changes?
The water cycle is a series of physical changes: evaporation (liquid to gas), condensation (gas to liquid in clouds), and freezing/melting (snow and ice). It is the ultimate example of how energy from the sun drives changes in matter.

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