Unit 10: Post-AP Exam Projects (4–5 weeks)

Lesson 4.05: Shifting Values & Arrays of Objects

Overview

Objectives — Students will be able to…

  • Shift elements within an array

  • Construct arrays of objects

Assessments — Students will…

  • Complete Practice questions

  • Model memory manipulation using array whiteboards

Homework — Students will…

  • Read BJP 7.4 “Nested Arrays” and BJP 7.5 “Rectangular Two-Dimensional Arrays”

  • Complete self-check questions #27-29 and exercise #4

Materials & Prep

If your classroom structure allows it, arrange array whiteboards and markers at stations where students can gather around them to model the concepts you teach during your intro. Ideally, students will be standing huddled around the arrays, actively moving and rearranging items.

Pacing Guide: Day 1

Section

Total Time

Bell-work and attendance

5min

Introduction & small-group practice

20–25min

Practice Questions

25–30min

Error-checking algorithm (see below)

10min

Pacing Guide: Day 2

Section

Total Time

Bell-work and attendance

5min

CS Awesome Array Algoritms 6.4

35–45min

Procedure 1

Hook your class today by having them in small groups with the array whiteboards during your Introduction. As you write out the code samples on the whiteboard, pause at different stages to model what is happening to the elements stored in memory. As the introduction progresses, ask students to model the changes for the whole class, with you and the other groups replicating their manipulations. The key to this introduction is to have students working through the examples in physical space, so make sure that all groups are working along with their array whiteboards.

Bell-work and Attendance [5 minutes]

Introduction & Small-Group Practice [10 minutes]

  1. Introduce your example array called metroCardRides (or dailyDrive, milesWalked, whatever represents your students’ commute to school), and hold up an array of ints:

  2. Briefly ask your students to direct you in constructing and initializing this array object, then ask students for some ideas as to how to move the 5 from the first element of the array to the last element, so that we end up with [4][3][2][1][5].

    Give students a minute to try moving numbers around their whiteboards. Most numbers can be moved by shifting down the line with a for loop, but the first element will need to be removed to allow “space” for the shift.

  3. Ask students how to store that first element (value 5) into a local variable, then write that code on your main whiteboard.

    int first = metroCardRides[0];

    Redirect students to the task of shifting the rest of your values on your array. As a class, discuss what you need the code to do, then ask the groups to draft some code and test that code on their array by tracing the code and checking for errors.

  4. The correct loop for this loop looks like this:

    for (int j = 0; j < metroCardRides.length – 1; j++) {
    metroCardRides[j] = metroCardRides[j + 1];
    }

    If students use metroCardRides.length instead of metroCardRides.length – 1, walk through the loop on your array whiteboard, demonstrating that metroCardRides.length causes Java to run off the end of the loop since there is no element at index 5. Alternatively, remind students about zero indexing, and see if they catch their own mistake.

  5. Ask students to remind you (in pseudocode) what all the steps are that are needed to successfully shift the numbers in the array.

    • Model on your array whiteboard what steps have already been successfully written, and ask students what is left to do now that your array looks like this:

    • Select a group to give you the last step that re-inserts the first element at index 4, and ask the class to finish up the complete method, so your final method looks like this:

      public static void firstToLast (int[] metroCardRides) {
      int first = metroCardRides[0];
      for (int j = 0; j < metroCardRides.length – 1; j++) {
      metroCardRides[j] = metroCardRides[j + 1];
      }
      metroCardRides[metroCardRides.length – 1] = first;
      }
  6. If all students understand this method, move the last element to the first position, shifting the other elements one position to the right.

    • Direct students to start working on this challenge by re-setting their whiteboards and modeling the different steps that need to occur.

    • Walk around the room, checking that students are on the right path. Students should recognize that they need to temporarily store the last element as a variable now that they’re shifting array elements in the other direction.

  7. Once students have written the code they think is correct, have them trace their own code and manipulate the arrays in their whiteboard.

    Encourage students to divide up this task so one student reads the code and another student moves the elements on the whiteboard. All members should be engaged in error checking.

  8. The correct final code looks like this:

    public static void firstToLastRight (int[] metroCardRides) {
    int last = metroCardRides[metroCardRides.length – 1];
    for (int j = metroCardRides.length – 1; j >= 1; j--) {
    metroCardRides[j] = metroCardRides[j – 1];
    }
    metroCardRides[0] = last;
    }
  9. Spot check student code for an off-by-one error; starting the loop at 0 asks Java to look for a value at index -1, which doesn’t exist. (If students are modeling their code execution with the array whiteboards, they should catch this.)

    • If students “correct” this error by starting the loop at 1, ask them to model the code execution with their array white boards for you. The loop overwrites the value at j – 1 with the value at j, so the array will start filling in with all 5s as the loop repeats itself:

    • The solution to this is tricky! It might be worth discussing/working as a class if groups are getting stuck on this. The loop needs to shift values right by starting at the left and running backwards. See if you can get students to brainstorm this solution by manipulating the values on their whiteboards first.

    • Now add back in the temporarily-stored value 1 at index 0.

  10. Collect the array whiteboards (or have students set them aside) and briefly introduce arrays of objects.

    • This is an optional extension. Since we haven’t studied objects yet, you might want to leave this out if it is too far beyond your students’ zone of proximate knowledge.

    • Arrays of objects store reference to objects instead of a primitive type value. Drawing something like this might help student comprehension:

    • Ask students leading questions, getting them to tell you that because the array and the array contents are both objects, both need to be constructed.

    • Work through an example together as a class; ask students to help you construct an array of points. Your code should look something like this:

      Point[] points = {
      new Point(3, 7),
      new Point(4, 5),
      new Point(8, 2),
      new Point(7, 5),
      new Point(2, 8)
      };

Practice Questions [25-30 minutes]

  1. Depending on the mood and frustration levels in the class, you may choose to have students workin pairs.

    a. If students are really having a rough time, work through the first Practice question together as a whole group.

    b. Put soft, soothing (but upbeat) music on in the background to encourage work

  2. Have students complete the following Self Check practice problems at the back of the chapter.

    a. Self-Check 7.22: arrayCodeTracing3 b. Self-Check 7.23: arrayCodeTracing4 c. Self-Check 7.25: arrayMystery2 d. Self-Check 7.26: arrayMystery3 e. Self-Check 7.30: isPalindrome

  3. If more 25% or more of the class is struggling, return to whole group with the stipulation that students who understand the task may continue working independently. Otherwise, encourage peer tutoring, or using the textbook or notebooks for help.

Error-Checking Algorithm [10 minutes]

At the end of class, if time permits, have students draft an algorithm for error-checking (see below for details).

Accommodation and Differentiation

If your class needs additional challenges, make the arrays in your examples a bit more sophisticated. Change the values or add “tricks” to the code, and include some mistakes in your delivery (written or conceptual) to let the students “catch” you. If they don’t catch you (and you’re a good actor), fumble your way into revealing the mistake in logic or code, and let them catch you so you can model a positive attitude towards error checking.

If students finish this lesson early, have them draft an algorithm or checklist that will help students check their loop code when shifting values in an array (what are common errors to look for?).

If the checklist is thorough, brief, and complete, have students create a handout or poster that you can hang up or share with the class.

To adjust for reading/comprehension challenges in the ELL classroom, consider having students work in small groups with the array whiteboards. Give each group/student a print out with the questions, and have them turn in the worksheets at the end of class.

Procedure Day 2

This lesson continues with array algorithms with examples from the College Board AP CS A examps free response questions using CS Awesome's Lesson 6.4 Array Algorithms.

Bell-work and Attendance [5 minutes]

CS Awesome Array Algoritms 6.4 [35-40 minutes]

The student lesson for Part 2 uses CS Awesomes Lesson 6.4: Array Algorithms. There you will find the lesson plan and activities to check for student understanding. The teacher lesson plans are accessible by joining the Teaching CSAwesome google group and navigating to 6.4. Array Algorithms. The slide deck for this lesson are located on Dr. Long Nguyen GitHub at For Loops

College Board Topic Questions

After this lesson, students will be able to answer questions from the College Board Unit 6 Topic Questions 6.4 Developing Algorithms for Arrays.

Video

Forum discussion

Lesson 4.05 Shifting Values & Arrays of Objects (TEALS Discourse account required)