Organizing and Calculating Data with Matrices

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Objective

SWBAT organize Data into Matrices to Solve Problems Involving Addition, Subtraction, and Scalar Multiplication.

Big Idea

To understand the vocabulary of Matrices including rows, columns, and addresses to set up a Real World Problem. As well as perform Multi-step Operations to that problem.

Warm Up

15 minutes

I begin the lesson with this Warm up. It is an Introduction to the vocabulary that students will need to understand to know how to work with Matrices.  Students need to know how to name a Matrix, use it to organize data, identify the correct location of an element, and perform calculations.  For Algebra One, the focus is going to be on finding the sum, finding the difference, and finding the product of scalar multiplication.  The sum and difference of a Matrix can only be found if the dimensions are the same, and I relate scalar multiplication to students' prior knowledge of the Distributive Property.

I expect the Warm Up to take about 15 minutes for the students to complete and for me to review with the class.  I demonstrate reviewing some of the problems from the Warm Up in the video below.

Partner Activity

20 minutes

After reviewing the Warm Up with the students, I hand each set of table partners a Snowfall Activity.  In this activity, students use a table showing the snowfall in 2012-2013 for 12 given U.S. cities and the Average Snowfall per year for each city.  The units for the snowfall in both cases is inches per year.    

The snowfall data is from the website below:

http://www.weatherwise.org/Archives/Back%20Issues/2014/January-February%202014/snow-report-full.html (last accessed 7-08-71)

 

The task the students are to complete is the following:

  • Organize the data given in the table into a matrix
  • Find the difference of the Given Snowfall and the Average Snowfall per year 
  • Create a third column in the matrix to show the difference
  • Find the expected 20% decrease of snowfall in 2014 

 

As students complete the task, I have two sets of table partners begin discussing their work. Students may make changes based on this feedback and discussion or not.  Then, I ask for a few student volunteers to share their responses under the document camera.  During the presentation of student work, I emphasize the criteria below:

1.  The matrix to organize the table data may be a 12 x 2 or a 2 x 12 matrix.

2.  A positive difference means that the snowfall in 2012-2013 was above the average            snowfall.

3.  A negative difference means that the snowfall in 2012-2013 was below the average            snowfall.

4.  The scalar of 20% needs to be changed to the decimal .20 and then multiplied to each        element  to find the expected decrease of 20% in 2014.

 

At the end of the class discussion, I take any questions that the students may have, and then I hand each student an Exit Slip to complete individually.

Exit Slip

15 minutes

After completing the Snowfall Activity, I hand each student an Exit Slip.  The students are to work the Exit Slip individually because I use it as a formative assessment to check for individual student progress.  I want to be able to identify students that are still struggling, and may need extra help. This allows me to set up different partners for peer tutoring, or provide them with one to one help from me while they are working the next day.  

The Exit Slip is about how many different sizes and types of pizza the Pizza Place sells on Friday, Saturday, and Sunday. I am assessing students ability to do the following:

1.  Organize data into a Matrix

2.  Perform addition and subtraction operations with Matrices

3.  Perform scalar multiplication with Matrices involving percent

Students answer the questions on the back of the Answer Document from the Snowball Activity, or on their own paper.  I have students hand in the Exit Slips for me to assess before leaving class.  I do not want students to take this Exit Slip home for homework to ensure that the student works the problem individually.