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### Overview

The lesson will introduce the concept of a matrix. The matrix is labeled by its rows and columns. This lesson will teach the concept of adding, subtracting, scalar multiplication, and multiplication of matrices. This lesson will be a prerequisite for solving systems of equations with matrices.

This lesson results from the ALEX Resource Gap Project.

## UP:MA19.A2.4

### Vocabulary

• Appropriate dimensions

### Knowledge

Students know:

• The aspects of a matrix with regard to entries, rows, columns, dimensions, elements, and subscript notations.

### Skills

Students are able to:

• Strategically choose and apply appropriate representations of matrices on which arithmetic operations can be performed.

### Understanding

Students understand that:

• Matrix addition and subtraction may be performed only if the matrices have the same dimensions.
• Matrix multiplication can be performed only when the number of columns in the first matrix equal the number of rows in the second matrix.
• There are many contextual situations where arithmetic operations on matrices allow us to solve problems.

### Body

1. Add, subtract, and multiply matrices of appropriate dimensions.

### Evidence of Student Attainment

Students: <br>
Given two matrices,
<ul><li>Determine whether arithmetic operations (add, subtract, multiply) are defined.
</li><li>Perform arithmetic (add, subtract, multiply) operations to form new matrices.</li></ul>
[Note: New field. Currently this information is displayed as "additional connections" along with primary objectives]

### Primary Learning Objectives

The student will be able to multiply a scalar by a matrix.

The student will be able to add matrices.

The student will be able to subtract matrices.

The student will be able to multiply matrices.

### Procedures/Activities

Before:

As the students enter the classroom, the teacher will place the bell ringer, "Bell Ringer Matrices", from the attachment section on the interactive whiteboard. The teacher will give the students 3 minutes to complete. The teacher will give the students 1 minute to talk with a partner. The teacher will ask for suggestions from the class. The answers are in white. The teacher will highlight below “Answers” and change the color to reveal the answers.

During:

1. The teacher will start the first presentation from Khan Academy: https://www.khanacademy.org/math/precalculus/precalc-matrices/multiplying-matrices-by-scalars/v/scalar-multiplication. The teacher will continue through the entire lesson, if necessary. The teacher will do informal assessments while working the interactive examples from the website.
2. The teacher will use the textbook for more examples of scalar multiplication. The teacher will call on students to work on the interactive whiteboard.
3. The teacher will start the second presentation from Khan Academy: https://www.khanacademy.org/math/precalculus/precalc-matrices/adding-and-subtracting-matrices/v/matrix-addition-and-subtraction-1. The teacher will continue through the entire lesson, if necessary. The teacher will do informal assessments while working the interactive examples from the website.
4. The teacher will use the textbook for more examples of adding and subtracting matrices. The teacher will call on students to work on the interactive whiteboard.
5. The teacher will start the third presentation from Khan Academy: https://www.khanacademy.org/math/precalculus/precalc-matrices/multiplying-matrices-by-matrices/v/matrix-multiplication-intro. The teacher will continue through the entire lesson, if necessary. The teacher will do informal assessments while working the interactive examples from the website.
6. The teacher will use the textbook for more examples of matrix multiplication. The teacher will call on students to work on the interactive whiteboard.
7. The teacher will hand out the worksheet from Math-Aids,

Multiplying Matrices

8. The students will work with partners. The teacher will select students to write answers on the interactive whiteboard. The teacher will monitor student work for an informal assessment.

After:

The teacher will use the exit slip from Math-Aids,

Exit Slip

### Assessment Strategies

Informal:

The teacher will solicit questions while the students are watching Khan Academy. The teacher will ask students to answer the interactive questions. The teacher will monitor the students as they work with a partner.

Formal:

The teacher will grade the exit slip from the material section from Math-Aids.

### Acceleration

Worksheet for Accelerated Students: copy as needed

https://www.mathworksheets4kids.com/matrices/multiplication/18.pdf

### Intervention

The students will work with partners and the teacher will do one-on-one instruction as needed.

### Total Duration

61 to 90 Minutes

### Background/Preparation

Teacher:

The teacher will need to preview the videos and other materials on the Khan Academy website. The website has interactive sessions after the introduction. The teacher can pick and choose the problems and material according to the skill level of the class.

Student:

The student needs to know that matrices are labeled by their dimensions like pieces of wood. An example is a 4 x 8 piece of plywood. The student needs to be able to write linear equations in standard form.

### Technology Resources Needed

Desktop computer/Interactive Whiteboard

Graphing Calculator, if available