- A great way to do this is to put them in groups of 2 or 3 and place rectangles of the pieces of the cut out shaded area on the desk (Can be made of paper, poster board is better).
- Then have a piece of poster board on the desk (the coordinate plane can be pre-drawn for less advanced students).
- Have them try to find the Area of each Rectangle by placing each rectangle under the curve you gave them. They will get the side lengths from where they are placed on the coordinate plane. Have them place the shape on the coordinate plane given restraints that you give them. So that there is only one correct place to put each.
- Then have them estimate the area of the shape using the guide lines you gave them. Obviously you will want them to start basic but you can make the shapes however complicated you want as long as they don't require integration.
- Use common curves
- Make the spacing of all of the rectangles for all groups and all curves the width of a yard stick so they are consistent
- Set small boundaries at first (ie: 0 to 10 where the width of one rectangles is 1 unit)
- Once they have an estimate for the curve with boundaries ask them what would happen if you went 0 to 100 or 0 to 1000? Leading them to 0 to infinity!
Approximating the Area Under the Curve Using Sigma Notation
Real World Uses for Area Under a Curve
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