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Comparing and contrasting gives the student opportunity to learn the vibrant deeper

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Finding x

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I think breaking it down like this will help students better connect and understand the concept and representations.

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What to do if the lower limit of integration isn't 0 and how to find the expression for x.

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I love how this steps the students through the process to get the limit of the Riemann sum. The fill-in-the-blanks are great.

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Why did the upper limit in the sigma notation change from a 3 to a 6 in the simplification step? Is that just a typo?

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How to find the x value and the notation.

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Guided and scaffolded question gives students of all levels an entry point for success.

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Not understanding the notation with respect to area of infinite rectangles.

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I love the way it walks the student through discovery with little changes.

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You could start the lesson doing a quick summation notation question from algebra 2, just to remind the students what summation/ sigma notation is. If students can remember that summation notation is nothing more than adding different values, it might make it easier for them when we are adding areas.

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You could start the lesson doing a quick summation notation question from algebra 2, just to remind the students what summation/ sigma notation is. If students can remember that summation notation is nothing more than adding different values, it might make it easier for them when we are adding areas.

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Agreed. The x-value

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How to find x value

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These worksheets would help understand how limits of Riemann Sums and definite integrals are related.

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Finding the x value is the most difficult part for my students.

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Finding the x value is the most difficult part for my students.

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This lesson would be great to help the students organize their ideas and see how everything goes together.

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I believe the discovery lesson will help students better make the connection between the integral and the summation notation.

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My students struggle with understanding the expression needed to plug in for the "x" value, especially if it is not a right sum.

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Do students need to know how to calculate the summation? By hand or calculator? ... I didn't think they needed to do that but I just wanted to make sure!

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For the Ap test, should we only stress the right Riemann Sum when using Sigma Notation? Or should we include left and midpoint? I know the right sum is the "easiest" and that is what most text books stress but didn't know if college board expected students to know/understand all forms.

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My students always have a tough time with this and I think the discovery aspect will help them to take ownership and really understand the topic. Great idea!

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I love lessons that allow students to discover!

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I think that finding the expressions for x and delta-x are the most difficult for students.

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Students sturggle with the connection between the summation of the areas of the rectangles and the integral showing the areas of the rectangles. I don't think they readily think in terms of areas when looking at the sigma notation.

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The process is well scaffolded

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Most kids struggle with the numerator being 3.  

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Most kids struggle with the numerator being 3.  

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I love how students are in charge of their discovery of the pattern of Riemann Sums

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I love how students are in charge of their discovery of the pattern of Riemann Sums

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Chart enables them to see patterns.

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They have difficulty understanding the "x-value".

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Students get a chance to discover how elements in the integral correspond to elements in limit.

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They struggle understanding what 'i' represents

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They struggle understanding what 'i' represents

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I like that the activity connects a physical learning with computation.