##
* *Reflection: Connection to Prior Knowledge
The Purrrrrfect Cat Toy Company - Section 2: Share and Summarize

For one of the questions on today's in-class worksheet, students were asked to recall what they already know about matrices. Here is a list that we generated as a class. My students' prior knowledge mainly focused on operations with matrices.

There were two interesting things that came up from this list - that you can perform any operation with corresponding entries of two matrices and that you can divide two matrices. These will definitely be addressed as we progress through the unit.

One student also wrote that matrices have "a bunch of numbers." This seemed trivial to most of the class but to me it was the most important part of matrices! If we only had one entry, there would be no need to use a matrix. The essential quality is that it is a powerful tool where a computer or calculator can perform tons of operations with one matrix equation.

*Connection to Prior Knowledge: Prior Knowledge Inventory*

# The Purrrrrfect Cat Toy Company

Lesson 1 of 16

## Objective: SWBAT interpret, add, and subtract matrices.

## Big Idea: Matrices are perfect for large data sets - monthly sales for cat toys are analyzed and matrix operations are introduced.

*50 minutes*

#### Launch and Explore

*15 min*

After working with trigonometry for the last few units, we are going to switch gears and work with something completely different – matrices. I won’t tell my students too much about them at first. We will be exploring Matrices for the next few days. However, I do think it is important to let them know that we will be working with something different than trigonometry.

I chose these introductory matrix tasks because I can give them to the class with no preface. As students work and we discuss their work, we will pick up important information about working with matrices.

I decided to introduce matrices using a rather large data set since that is primarily the advantage to using them – Matrices allow us to perform many operations very quickly. I also chose a context that we can revisit throughout the unit. The **Purrrrrfect Cat Toy Company** will be used as we explore other matrix topics.

I give my students these tasks and have them work on them with their table groups for 10-15 minutes. While circulating around the room I will make note of the conversations they are having and what their struggles are. I will pay particularly close attention to whether or not they can interpret these matrices correctly. Even really young students can add matrices, but it will be more important for students to understand what these matrices mean in the context of this problem.

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#### Share and Summarize

*15 min*

I usually make the decision whether to go over questions #1a through #1d based on what I observe; usually I find that it is not necessary. It is a good idea to discuss #1e to see what they already know about matrices. I find that matrices are a polarizing topic in my classroom – some students know a lot while other students know very little. It is helpful to assess this informally at the start of the unit.

Question 2 is the heart of this worksheet – seeing whether or not students can add matrices and make sense of their meaning. I will choose a group that completed this correctly and have them share their thinking. It is important to get at the meaning of *E + W* as the total sales for both regions.

When discussing the dimensions of the matrix *E + W*, students may list them as 3 by 12 or 12 by 3. I establish the norm of **rows by columns **so that we are consistent with the way math texts describe matrices. When we discuss why *E + W* has the dimensions of 3 by 12, I want students to think about that the context –** if we are adding the sales of the East and West regions, we are not adding any additional months and we are not adding any additional products**. Thus, the dimensions will still be 3 by 12. We can generalize to say that with matrix addition the dimensions must always match up and the sum will have the same dimensions.

Technology has to be an important part of this unit since it will allow us to perform matrix operations very quickly. I lay the foundation for this today by showing students how to enter the matrices on the calculator and how to add two matrices. Here is an online matrix calculator that student can use if they do not have a graphing calculator. Unfortunately, the online calculator can only go up to ten rows or columns.

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#### Extend

*20 min*

After our initial work with matrices, I give students this worksheet as a homework assignment. They can begin it in class and can work with their table groups on any issues that they have. In the homework assignment students will be introduced to matrix subtraction. Like today’s tasks, the overall emphasis will be on interpreting matrices since the calculation are fairly simple.

In the video below I talk about a problem on the assignment that introduces a relation matrix to students.

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
- UNIT 9: Sequences and Series
- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: The Purrrrrfect Cat Toy Company
- LESSON 2: Forecasting Sales and Calculating Revenue - Day 1 of 2
- LESSON 3: Forecasting Sales and Calculating Revenue - Day 2 of 2
- LESSON 4: Digital Images
- LESSON 5: Jet-Setting to the Purrrrrfect Cat Toy Offices
- LESSON 6: Market Research with a Markov Chain
- LESSON 7: Formative Assessment: Matrices
- LESSON 8: Manufacturing Cat Toys (Day 1 of 2)
- LESSON 9: Manufacturing Cat Toys (Day 2 of 2)
- LESSON 10: Hop on the Carousel
- LESSON 11: Partial Fraction Decomposition
- LESSON 12: Building Cat Furniture: An Introduction to Linear Programming
- LESSON 13: More Linear Programming
- LESSON 14: Formative Assessment: Systems of Equations and Inequalities
- LESSON 15: Unit Review and Cryptography
- LESSON 16: Unit Assessment: Matrices and Systems