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Rate of change

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Look Inside · 7 pages

Title slide for a calculus lesson with the stated objective to understand the meaning of a rate, from Maths Support
Opening slide that sets the lesson objective
Calculus introduction: tangent line problem recap, then f(x) as fuel in a tank or car distance, with x as time
Lecture slide for introducing the concept
Instantaneous versus average rate of change of f(x) at x = a, with the ARC formula as change in f(x) over change in x
Notes slide to copy down the ARC formula
Velocity as a rate: average velocity as a difference quotient of s(t), and instantaneous velocity v(a) as a limit
Bridges the formulas to motion for direct teaching
Worked Example 1: instantaneous velocity at t = 0 for a spring weight with s(t) = sin t, solved with a limit
Model solution to walk through step by step
Worked Example 2: instantaneous rate for balloon volume V(t) = t^3 - 6t^2 + 35 at 5 hours, solved by factoring a limit
Second modeled example, with factoring and cancelling
Worked Example 3: thermostat temperature T(t) = 0.4t^2 - 4t + 70, with the rate at midnight found as -1.6°F per hour
Third example for applying the limit to a real context
Attributes
Subject

Math, Calculus

Grades

Grade 12

Types

Teacher Tools, Lesson Plans

File

Microsoft PowerPoint

Editable
No
Author
Maths Support Centre
Rating
Add To Collection
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About This Product

PowerPoint presentation, 8 slides explaining how To understand the meaning of rate of change and solve problems.

What's Included

PowerPoint presentation, 8 slides

Resource Tags

calculus rate of change

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