Investigation 3: Inverse Variation

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Presentation transcript:

Investigation 3: Inverse Variation Chapter 1: Thinking with Mathematical Models

3.1 Rectangles With Fixed Area Focus Question: When the product of two variables is some fixed number, what is the pattern of change and how is that pattern of change reflected in tables and graphs of the relationships? 3.1 Rectangles With Fixed Area

Launch What is area? How do you find the area of a rectangle? How can you write this area as a formula? If you know the area of a rectangle, how can you find possible lengths and widths? Launch

A rectangle with an area of 100 square units. It’s length is 8 units A rectangle with an area of 100 square units. It’s length is 8 units. What is it’s width? 12.5 units I’m thinking of…

Focus Question: What examples using distance, rate and time show one variable inversely related to another? Launch Video If you are on a car trip and driving at 60 mi/h, what two variables might you be interested in? What equation relates distance and time? Is this a linear relationship? How do you know? Suppose you are going on a car trip of 60 miles. How long will the trip take if you travel at 60 mi/h? What would the time be if you traveled more slowly, at 30 mi/h? 3.2 Distance, Speed & Time

In this problem, you are going to consider what happens if the distance, rather than the rate is fixed. The variables will be rate and time instead of distance and time.