Name: Brandon Harvill                                                                                

 

Title of lesson:

 

Mean, Median, and More!

 

Date of lesson:

Early on in project

 

Length of lesson:

 50 minutes

Description of the class:

                     Name of course: Algebra I or II

                     Grade level: 9th or 10th                                                             

                     Honors or regular: Probably regular

 

Source of the lesson:

                     I came up with this lesson on my own

TEKS addressed:

 

(2)  Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students study algebraic concepts and the relationships among them to better understand the structure of algebra.

(A1)    

(A)  describe independent and dependent quantities in functional relationships;

(B)  gather and record data and use data sets to determine functional relationships between quantities;

(A2)

(D)  collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

 

 

I.       I.      Overview

For our project it will be really important that the students are able to analyze the results they are getting to determine whether or not their results have significance. At the very least we want to make sure they have the basic tools required such as calculating the mean and median of data and drawing conclusions from that so that they can be successful in the project. 

II.  Performance or learner outcomes

            Students will be able to take data or groups of data and figure out what the average is and what the median value is. From there they will be able to determine more about the accuracy of their data.

   

III. Resources, materials and supplies needed

 Students could do this on a graphing calculator after they know how to calculate it themselves.

 

IV. Supplementary materials, handouts.

For the actual lesson I would use worksheets with data of things they like, such as the season stats of NBA All stars or the time it takes for cars to go from 0-60.         

 

Five-E Organization

Teacher Does                     Probing Questions                      Student Does       

Engage:

I plan to ask some simpler questions designed to get students excited about averages and how they can use them a lot in their everyday lives.

 

      

 

 

 Ask anything about clothes, cars or sports where kids have to calculate averages, such as “If Kobe Bryant scores 81 points in a game, how many points did he average each quarter?

 Or, Katie goes shopping at Hollister with her gift card of 150$ and gets 7 shirts. About how much did each shirt cost?

 Students will calculate the averages and reply.

                                                   

Explore:

Now we get into the more advanced portions of the lessons.

 

 

 

 

      Can anyone tell me what the mean of something is?

 

What about the median?

 

How do we find them?

Isn’t that the same thing as the average of something?

 

Some students may not know the difference but it is important that they figure out the differences between the two.

 

If students don’t explain to me how to find them then I will explain it for them. Then they will work on the worksheets with the statistical data on them.

 

 

    

Explain:

Learning Experience(s)

 

 

 

Students will then enter the data into a graphing calculator and make it into a stat plot so they can see all of their data and analyze it graphically.

 

 

I would also want to ask questions that may give them more trouble and require them to think a little more. For example, I would want to have a question where the average would indicate one thing (such as the overall success of a company) but the median would indicate something else (where one or two stores are having lots of success and the rest aren’t) so that the data ends up skewed. This is all building to the importance of the significance of their data collection on bugs and how to avoid drawing the wrong conclusions about data.

Some students may have problems with this portion so I will help them with it. I will also show them how it can calculate mean and median on its own

                                               

Extend / Elaborate:

Learning Experience(s)

 

      

 

I’d really like to get into quartiles and whether or not they are looking at data that is skewed or has outliers (values way above or below the median value) if they are handling everything well. This would help the students determine if their data is skewed one way or another. For example, if we took the average income of everyone in a room and Bill Gates was in the room, everyone on average becomes a millionaire, but the median could be about 20,000 dollars, telling us that Bill Gates is really messing up the average a whole lot. 

What do we do when there are 2 medians?

 

Why is the difference between the two important?

 

 

   

  Evaluate:

I would either ask them the questions in the next column or provide a new set of data for them to analyze. 

 

 

       

 

So how do we find the average of something?

 

And the median?

 

What about quartiles?

 

 

Students will respond.