Matrix Operations

Pass out copies of the attached Guided Notes handout and display slide 8. Complete the front side of the handout as a class.

After completing only the front side of the handout, direct students to set it aside. Students complete the back side later in the lesson.

Display slide 9 and give each student a copy of the attached Problem Solved handout. Have students work in pairs to solve each equation using the matrix operations learned during the Explain 1 portion of the lesson. Encourage students to use their Guided Notes handout for reference.

When students finish, transition through slides 10–11 and allow students time to check their work. If time allows, ask for volunteers to explain their process for solving each equation. Use student responses to identify any misconceptions.

Show slide 13. Start completing the back side of the Guided Notes handout as a class by teaching students how to multiply matrices using the information at the top of the page and in example 3.

Before starting example 4, read the following to the class to introduce the example:

Sports are an excellent source of data. Think about all of the numbers used to describe a basketball player’s performance, like their offense, defense, and rebounding. These data can be used to rank players. For example, EA Sports uses data for rankings in NBA 2K video games. But how do they do it? When processing that amount of data, computers are performing the calculations using matrices. They multiply the players’ ratings by the weights of the categories to yield the overall player ranking.

Complete example 4 as a class. Have students add their completed Guided Notes handouts to their math notebooks if that is a classroom norm.

Direct students to get into groups of four or assign students to groups. Show slide 14 and pass out a copy of the attached Transformation Matrices handout and a set of Transformation Cards to each group. Direct students to read and follow the steps on the handout. Here students are to select a figure, select four transformation cards, and use matrix multiplication to transform their selected figure.

As students work, circulate around the room. Once you notice most students are on the back side of the handout, transition to slide 15. This slide helps clarify step 5 by showing students how to write their vertices as matrices to use for matrix multiplication.

After students finish multiplying their transformation matrix, instruct them to use the graph paper to draw their original figure and their new figure. As students finish their sketches, share slide 16 and direct them to use their devices to access the GeoGebra activity: geogebra.org/m/re5ajfet. Students should click the transformation buttons in the order in which they want them applied. Remind students that this order is the opposite order of how they multiplied their matrices.