AP Calculus AB Lesson 2.1 Share by NMSI Training https://padlet.com/NMSITTT/732t30o81ux5os4w Thoughts about the limit of Riemann sum discovery lesson en-us 2022-04-08 01:48:23 UTC 2023-09-14 18:07:51 UTC hello@padlet.com They struggle understanding what 'i' represents NMSITTT https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2135853005 2022-04-08 05:45:36 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2135853005 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2249940316 Students get a chance to discover how elements in the integral correspond to elements in limit.]]> 2022-07-26 13:08:37 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2249940316 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2250040988 They have difficulty understanding the "x-value".]]> 2022-07-26 16:16:41 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2250040988 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2250041258 Chart enables them to see patterns.]]> 2022-07-26 16:17:18 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2250041258 I love how students are in charge of their discovery of the pattern of Riemann Sums https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2250043007 2022-07-26 16:21:25 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2250043007 Most kids struggle with the numerator being 3. https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2250043223 2022-07-26 16:21:52 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2250043223 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2252546554 The process is well scaffolded]]> 2022-08-01 03:48:03 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2252546554 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2252547177 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.]]> 2022-08-01 03:49:03 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2252547177 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2254200488 I think that finding the expressions for x and delta-x are the most difficult for students.]]> 2022-08-03 14:42:36 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2254200488 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2254200614 I love lessons that allow students to discover!]]> 2022-08-03 14:42:50 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2254200614 Love the matching activities. https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2264521088 2022-08-18 15:39:03 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2264521088 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2267380641 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!]]> 2022-08-22 13:15:57 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2267380641 Only Right? https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2267383079 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.]]> 2022-08-22 13:18:15 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2267383079 Finding Summation value? https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2267386516 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!]]> 2022-08-22 13:20:11 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2267386516 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2267388617 My students struggle with understanding the expression needed to plug in for the "x" value, especially if it is not a right sum. ]]> 2022-08-22 13:22:03 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2267388617 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2301791630 I believe the discovery lesson will help students better make the connection between the integral and the summation notation. ]]> 2022-09-18 18:06:34 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2301791630 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2321169418 This lesson would be great to help the students organize their ideas and see how everything goes together.]]> 2022-09-30 14:41:38 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2321169418 Finding the x value is the most difficult part for my students. https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2321170206 2022-09-30 14:42:10 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2321170206 Riemann Sums https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2591656811 These worksheets would help understand how limits of Riemann Sums and definite integrals are related.]]> 2023-05-15 17:14:27 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2591656811 Riemann Sums https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2591909791 How to find x value ]]> 2023-05-15 21:03:17 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2591909791 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2640559198 I like that the activity connects a physical learning with computation.]]> 2023-07-07 15:52:32 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2640559198 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2640559445 Agreed. The x-value]]> 2023-07-07 15:53:31 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2640559445 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. https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2641892853 2023-07-10 14:45:43 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2641892853 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2642034613 I love the way it walks the student through discovery with little changes.]]> 2023-07-10 19:40:23 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2642034613 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2642034857 Not understanding the notation with respect to area of infinite rectangles.]]> 2023-07-10 19:41:09 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2642034857 Guided Questions https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2650303751 Guided and scaffolded question gives students of all levels an entry point for success. ]]> 2023-07-24 15:47:18 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2650303751 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2652759900 How to find the x value and the notation.]]> 2023-07-28 20:19:08 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2652759900 First example in the table https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2666387345 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?]]> 2023-08-19 13:30:17 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2666387345 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2666387609 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.]]> 2023-08-19 13:31:21 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2666387609 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2666387953 What to do if the lower limit of integration isn't 0 and how to find the expression for x.]]> 2023-08-19 13:32:40 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2666387953 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2669051993 I think breaking it down like this will help students better connect and understand the concept and representations.

]]> 2023-08-22 17:21:54 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2669051993 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2669052721 Finding x]]> 2023-08-22 17:22:41 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2669052721 https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2704657810 Comparing and contrasting gives the student opportunity to learn the vibrant deeper]]> 2023-09-14 18:07:51 UTC https://padlet.com/NMSITTT/732t30o81ux5os4w/wish/2704657810