Unit 3: Implementation in Geometry and Algebra II Topics
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Introduction
As you've begun to learn in Unit 2, opportunity to incorporate probability and statistics exists in our current mathematical curriculum. In this Unit, you will now take a look at an example in Geometry and an example in Algebra II that successful connected a course standard with a concept in probability and/or statistics. As a result of this Unit, you will be able to modify an existing Geometry lesson to incorporate probability and/or statistics.
Lesson 1: Geometric Probability with Darts
Creating a meaningful connection to probability in a Geometry class is quite simple... because Geometric Probability exists! Although it is not explicitly stated in the Geometry NYS standards, probability can really easily be implemented.
About the Lesson
Students will be calculating areas of a sectors that exist on a dart board in order to determine the probability of throwing a dart at random and it landing in those various areas. This can be simplified to an archery board if students are not yet comfortable calculating the area of many sectors, but are comfortable calculating the area of the entire circle.
This lesson targets the GEO-G.C standard: Find arc lengths and areas of sectors of circles. (5) Using proportionality, find one of the following given two others: the center angle, arc length, radius, or area of sector.
As you will see when reviewing the lesson, it will also target the SP.S.MD standard: Calculate expected values and use them to solve problems.
The lesson can be found by clicking here.
Reflect
Please answer the following in your Ongoing Learning Journal: How is this lesson effectively implementing probability? If you were teaching Geometry, could you see yourself using this lesson? Explain why or why not.
Lesson 2: Building Exponential Models
Of course you must see an example for an Algebra II course too. After reviewing this finally example lesson, you will have reviewed a possible lesson for Pre-Algebra I, Algebra I, Geometry, and Algebra II.
About the Lesson
Students will be creating an exponential model for the bounces created by a racquetball ball. They will be collecting the data themselves, analyzing the data, and answer questions based on the exponential model that they create.
This lesson targets the AII.F.IF standard: Interpret functions that arise in applications in terms of the context. (4) For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities; and the AII.F.BF standard: Build a function that models a relationship between two quantities.
As you will see when reviewing the lesson, it will also target the AII.S.ID standard: Represent bivariate data on a scatter plot, and describe how the variables' values are related. (a) Fit a function to real-world data; use functions fitted to data to solve problems in context of the data.
The lesson can be found by clicking here.
Reflect
Please answer the following in your Ongoing Learning Journal: How is this lesson effectively implementing statistics? If you were teaching Algebra II, could you see yourself using this lesson? Explain why or why not.
Lesson 3: Analyzing and Modifying a Geometry Lesson
After reviewing an example of a Geometry and an Algebra II lesson that connects to probability and/or statistics, let's see if you can modify another lesson such that it connects to a Probability & Statistics standard.
Link to the NYS Common Core Standards (scroll to the Probability & Statistics section)
Activity
Make a copy of the original Geometry Lesson, it will automatically be created in our Shared Google Drive. Name your copy as follows, FirstLastU3L3. Choose one of the Probability & Statistics standards to tie to this lesson and modify it such that the standard better fits. This could be as simple as adding in an extra question or as complex as changing an entire section of the lesson. Insert a page at the start of the Google Doc. On this page, please state the standard you are implementing and why you chose to implement it.
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