## The Power of Matrices - Section 1: Launch

# Digital Images

Lesson 4 of 16

## Objective: SWBAT understand how matrices are used in computer graphics.

*25 minutes*

#### Launch

*5 min*

**Note:** Today is a half day with an abbreviated class period, so we will be looking at just a little about digital images and their connection to matrices. In this video I talk about why I like this lesson so much.

Most of my students have Instagram or know what it is. The app has transformed photo sharing by taking a user's photograph and applying artistic filters to enhance its aesthetics. But how can the software so easily modify your photograph? I start the class by asking my students this question and showing them this image. Then I will have them to discuss with their table groups. We will share out with the entire class. Some students will correctly hypothesize that it has something to do with matrices since that is what unit we are in.

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#### Explore

*15 min*

This worksheet is an investigation of how digital images are manipulated using computers. Students are introduced to the concept of a pixel and how a corresponding matrix can be used to represent many pixels.

For questions a) through d) students are to investigate how the matrix can be changed to make the image lighter, darker, more contrasting, or more clear. At this point in the unit we have looked at matrix addition, subtraction, and multiplication, so students must choose which operation will produce the indicated change. I find that students have an easier time with questions a) and b) than the remaining two. Some students don't know what it means for an image to have more contrast, so you may have to explain to them that it makes the light shades lighter and the dark shades darker.

The back of the worksheet gives students some actual practice with analyzing an image using these values to represent the darkness of each pixel. Although we are doing math, students sometimes comment that it doesn't feel very "math-y." This is a good opportunity to talk about how the applications of matrices can be far-reaching and go beyond the traditional topics we associate with mathematics.

#### Resources

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#### Summarize

*5 min*

For the last few minutes of class, I will go back to the image of the Instagram filter that students saw at the beginning of class and discuss what changes are made.

Since we are working in color, it adds a new layer of complexity to the problem. Some students may know that a printer used magenta, cyan, and yellow ink to print all colors. Teachers may know that a standard television had pixels that were red, green, or blue to create all colors. For this specific image, students may understand that the hue has changed because one color component has changed more than the others.

#### Resources

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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

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- 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