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Precalculus and Advanced Topics Module 1, Topic C, Lesson 21

Classroom Resource Information

Title:

Precalculus and Advanced Topics Module 1, Topic C, Lesson 21

URL:

https://www.engageny.org/resource/precalculus-and-advanced-topics-module-1-topic-c-lesson-21

Content Source:

EngageNY

Type:

Lesson/Unit Plan

Overview:

In this lesson, students will:

represent linear transformations of the form L(x,y) = (ax + by, cx + dy) by matrix multiplication.
recognize when a linear transformation of the form represents rotation and dilation in the plane.
multiply matrix products of the form.

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 9-12
Algebra II with Statistics

2. Use matrices to represent and manipulate data.

Unpacked Content

Evidence Of Student Attainment:

Students:

Given a contextual situation, represent the data in a matrix and interpret the value of each entry.

Teacher Vocabulary:

Matrix/Matrices
Data
Elements
Dimensions
Rows
Columns
Subscript notation

Knowledge:

Students know:

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

Skills:

Students are able to:

Translate data into a matrix.

Understanding:

Students understand that:

A matrix is a tool that can help to organize, manipulate, and interpret data.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
ALGII.2.1: Define matrix.
ALGII.2.2: Organize data into a matrix using rows and columns.

Prior Knowledge Skills:

Identify a row.
Identify a column.
Add complex numbers.
Subtract complex numbers.

Mathematics
MA2019 (2019)
Grade: 9-12
Algebra II with Statistics

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

Unpacked Content

Evidence Of Student Attainment:

Students:
Given two matrices,

Determine whether arithmetic operations (add, subtract, multiply) are defined.
Perform arithmetic (add, subtract, multiply) operations to form new matrices.

Teacher 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.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
ALGII.4.1: Multiply matrices of appropriate dimensions.
ALGII.4.2: Subtract matrices of appropriate dimensions.
ALGII.4.3: Add matrices of appropriate dimensions.

Prior Knowledge Skills:

Recognize rows.
Recognize columns.
Recognize the distributive property.

Tags:

algebra II, data, dilation, linear transformation, matrices, matrix, multiplication, rotation

License Type:

Custom Permission Type
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https://creativecommons.org/licenses

Accessibility

Text Resources: Content is organized under headings and subheadings

Comments

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site.

This resource provided by:

Author:

Hannah Bradley

ALEX Classroom Resource

Precalculus and Advanced Topics Module 1, Topic C, Lesson 21