##
* *Reflection: Intrinsic Motivation
Organizing and Calculating Data with Matrices - Section 3: Exit Slip

In this sample of student work, the student presents two different ways to solve the problem on their own. The student first shows a decrease of 35% on Sunday sales by multiplying .35 by the Sunday Matrix, and then subtracting it from the original matrix. The student then shows a second method below by multiplying the Sunday Matrix by .65 to get the same answer. This shows me that Common Core is changing the way our students think even without our request of them. Students are starting to look for and see more than one way to solve problems.

Not all students take the extra initiative to show me more than one method, but the class culture is changing for more and more students to go above and beyond the minimum. This kind of class culture rubs off on students who might of otherwise just sat back and not used their thinking skills to their highest potential.

*Intrinsic Motivation: Student Presents Two Ways to Solve the Problem on Their Own*

# Organizing and Calculating Data with Matrices

Lesson 1 of 10

## 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.

*50 minutes*

#### Warm Up

*15 min*

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.

#### Resources

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#### Partner Activity

*20 min*

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.

#### Resources

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#### Exit Slip

*15 min*

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.

*expand content*

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Organizing and Calculating Data with Matrices
- LESSON 2: Introduction to Statistics
- LESSON 3: Outliers and their Effect on the Central Tendencies
- LESSON 4: Dot Plots, Box Plots, and Histograms! (Day 1 of 2)
- LESSON 5: Dot Plots, Box Plots, and Histograms! (Day 2 of 2)
- LESSON 6: Dispersion of Data (Day 1 of 2)
- LESSON 7: Dispersion of Data (Day 2 0f 2)
- LESSON 8: What is the Shape of the Data and What Can We Infer?
- LESSON 9: Analyzing Box and Whisker Plots in a Real World Context
- LESSON 10: Compare Two Data Sets Using Box and Whisker Plots