Lesson 3: Column-Major Traversal

In the previous units, we worked with data to find information for a user and to create abstract data art.

Discuss: Use the Retrieve-Pair-Share strategy to discuss the prompt.

• How would 2D arrays have made it easier to store and process that data?

Discussion Goal: Students share examples of datasets they used in the previous units and how 2D arrays would have allowed them to store related values of the same type in a table.

Students may have worked with data of different types in their unit projects, so a 2D array would not have been beneficial in those scenarios. Ask students to consider how this might have changed if their values were of the same data type.

In the previous lesson, we learned how to traverse a 2D array in row-major order. We can also traverse a 2D array in column-major order.

Do This: Review the lesson objectives.

Do This: Direct students to Level 1 on Code Studio to predict the program's outcome, then run the program to compare their predictions to the actual outcome.

Discuss: Click through the animated slide to display the prompts.

• What do you notice about the code in this program?
• What do you wonder about the code in this program?

Discussion Goal: Students notice the outer loop traverses each column, and the inner loop traverses each row. Students also notice that the syntax for accessing an individual element is still the same. Students may wonder when they would traverse a 2D array in column-major order.

Display: Show the video – Column-Major Traversal.

Do This: Click through the animated slide to demonstrate a column-major traversal.

Group: Place students in pairs.

Distribute: Give each pair a copy of the Tracing Column-Major Traversals handout.

Do This: Have students complete the Tracing Column-Major Traversals handout.

You can choose to model completing the first few rows of the trace table as a class first, then have students work with their partners to complete the remaining rows.

We can traverse a 2D array in row-major order or column-major order depending on how we want to access the information. Both approaches have several similarities and differences.

Discuss: Use the Hold That Thought strategy to discuss the prompt.

• What are the differences between the row-major and column-major order traversal algorithms?

Discussion Goal: Students note that the for loop headers are swapped. In row-major order, the loop variable in the outer for loop is used as a row index, and the loop variable from the inner for loop is used as a column index. Conversely, in column-major order, the loop variable in the outer for loop is used as a column index, and the loop variable from the inner for loop is used as a row index.

Do This: Explain use cases for each traversal approach.

In the previous lesson, we modified a standard 1D array algorithm to find the sum of all values in a 2D array. Let's modify this algorithm to find the sum of each column in a 2D array.

Do This: Have students write pseudocode to find the sum of each column in a 2D array.

Do This: Direct students to Level 2 on Code Studio to complete Levels 2, 3, and 4. Students debug the program on Level 2, then continue to Level 3 to implement their algorithm. Students complete a choice level on Level 4 to apply a standard 1D array algorithm to a 2D array using the console or The Theater.

We have learned a lot about 2D arrays and applying standard 1D array algorithms to 2D arrays. Let's recap some of the key concepts we have learned.

Discuss: Click through the animated slide to display the prompts.

• What are some similarities between creating and traversing 1D arrays and 2D arrays? What are some differences?
• What are some scenarios you have encountered before where 2D arrays would have been useful?
• What were you confident about in this lesson? What would you like to practice?

Discussion Goal: Students identify similarities and differences in the syntax for creating and traversing arrays. Students suggest examples of scenarios where 2D arrays would have been useful for storing and organizing data. Students share concepts they are confident about and that they need more practice.

Do This: Review the concepts covered in this lesson.

Display: Key Vocabulary

Check For Understanding Question(s) and solutions can be found in each lesson on Code Studio. These questions can be used for an exit ticket.

To assign questions from the AP Classroom Question Bank that align with this lesson, create a custom quiz in AP Classroom by searching the Question Bank for the Essential Knowledge statements listed at the top of this lesson plan. You can find instructions and video demonstrations to do this on AP Central.