math · Grade 12 · Calculus
Limits Values and Rates
Distinguish a limit from a function value in selected examples.
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Explore the related learning targets, foundations and possible next connections.
Learning goals
- Distinguish a limit from a function value in selected examples.
Before you begin
Understand the words and representations introduced in the Explore activity.
Age and grade do not measure readiness. Adjust reading or adult support to preserve the intended learning goal.
Follow the sequence
Complete practice
Practice previewLimits Values and Rates
Practice · Independent · 25 min
Distinguish a limit from a function value in selected examples. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.
1. Explore
Practice previewLimits Values and Rates: Explore and Explain
Explore · Independent · 10 min
Distinguish a limit from a function value in selected examples. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.
2. Practice
Practice previewLimits Values and Rates: Practice Independently
Practice · Independent · 10 min
Distinguish a limit from a function value in selected examples. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.
3. Apply
Practice previewLimits Values and Rates: Apply and Create
Apply · Independent · 15 min
Distinguish a limit from a function value in selected examples. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.
Download the unit pack
Numbered activities, separate answer keys and a teaching guide in one ZIP. The pack uses the focused sequence; the complete practice sheet above is an alternative.
Teaching and response guide
- Begin with: Simplify f(x) and state the excluded x value.
- Connect the response to: Is f(1) defined by the original formula?
- Ask students to apply the idea: Find the average rate of change of x² from x = 2 to x = 3.
Watch for: Accepting an answer without checking whether it uses the material and satisfies the requested relationship or criteria.
Check the answer criteria for each task. A supported explanation may have more than one acceptable response. These activities offer evidence to discuss; completing a sheet alone does not establish mastery.