Lesson 1: Algorithms Solve Problems

Have your students complete these questions independently some time before starting this unit.

Pre-Unit Pulse Questions: The answers to these questions can provide insights into the preferences, strengths, and motivations of your students. If you'd like to adapt the questions or add in your own, you may want to make a copy of this Google Form which already has the existing questions populated.

For more tips and ideas of how to use these questions, check out the CSP Guide to Pre-Unit Pulse Questions

Distribute: Give each student a copy of the Unit 10 Journal (Digital/Interactive Notebook) or have students set up this unit's section in their CSP journals.

Discuss: What makes two pieces of code “the same”? Could there ever be two pieces of code that you consider to be “the same” even if they aren’t identical?

Discussion Goal: This is an optional discussion. If you are able to move directly to the main activity you should do so. This discussion should get students thinking about the themes of the lesson.

There are no "wrong answers" here though you should expect answers that focus on the fact that often there's lots of ways to write code that does the same thing.

Have students think about their answers on their own, then share with a partner, and then finally discuss responses with the entire room.

Today we are going to kick off a short unit about how computer scientists think about problem solving. A really important skill will be recognizing patterns and similarities.

Distribute: Ask students to take out their journals or give them some blank paper for working on the following problems

Show the slides for the ten problems students will need to solve.

Circulate: Ask students to review the problems for one minute, and then let them move around the room collecting information needed to solve the problems. This may take them several minutes.

Discuss: Which problems did you need to do something similar in order to solve them?

Discussion Goal: This discussion should focus on what made the problems that students solved similar to one another. You likely will want to put the problems back on the screen to make it easier to talk through. Here are some connections you may pull out though there are more students may make.

• Problems 1 and 2 are very similar. As soon as you find one person who meets the criteria you know you're done.
• Problem 3 and 4 are very similar but you need to talk to every other student to answer it. You only need to keep track of the closest birthday you've heard so far, however.
• Problem 5 is easy to solve as soon as you've solved problems 3 and 4.
• Problem 6 - 10 require you to have written down everyone's birthday, likely in order.
• Problems 7 - 9 are the same problem but for different numbers of people. Whatever strategy you use for one of those would be helpful to solve the others
• Problem 10 is a different version of problem 7 but instead of finding the smallest gap you're finding the largest.

Have students discuss the prompt with a neighbor before asking them to share with the room. Lead a discussion on their experiences.

The first thing that we need to think about as computer scientists is what is a "problem". We just looked at 10 problems, but as we discussed, a lot of them are similar. If we solve one problem we may actually solve another, or at least have a good idea for how to start solving another. As computer scientists it's important to ask "have I seen this problem before" or "how is this problem similar to others I've solved?"

We just thought about whether problems are similar. Now we're going to look at whether we're actually solving the same problem.

Discuss: Which of these algorithms are “the same” as one another?

Discussion Goal: This discussion should focus on what made the algorithms the same. While they are designed to fall into two categories, ideally a number of points should come out of this discussion.

• Algorithms 1, 3, and 4 draw a square while 2, 5, and 6 draw a rectangle
• Algorithms 4 and 6 are written using a flowchart while 1, 2, 3, and 5 are written in the AP Pseudocode
• Some of these algorithms turn the robot right by turning left three times. It's debateable whether we can really call these algorithms "the same"
• Some of these algorithms create lists or variables to store information. Depending on the context we may not be able to call these algorithms "the same"

Circulate: Ask students to review the algorithms with a partner and group them into categories. Move around the room making sure students are not getting stuck. If they finish early push them to see if they can think about the problem in a different way.

Discuss: Discuss with another group. which of these algorithms are “the same” as one another?

Have students discuss with another before asking them to share with the room. Lead a discussion on their experiences using tips from the discussion goal at the side.

Create Performance Task Written Response Practice

In order to help prepare students for the new component of the AP Create Performance Task, there will be several opportunities throughout the curriculum to practice creating written responses aligned with the learning objectives that might be assessed on the exam.

Sample Prompt: What makes two pieces of code “the same”? Could there ever be two pieces of code that you consider to be “the same” even if they aren’t identical?

Unit Journal Template

Sample Response for Instructors

Journal: Students add the following vocabulary words and definitions to their journals: problem, algorithm, sequencing, selection, iteration.

Discuss: How did today’s activities change the way you think about algorithms and problems?

Have students think about their answers on their own, then share with a partner, and then finally discuss responses with the entire room.

Discussion Goal: Use this discussion to reinforce vocabulary introduced in the slides and check in on whether students have begun the transition towards thinking on a higher level about algorithms and problems.

Computer scientists don't just think about "code", they think about problems and the algorithms that solve them. In this unit we're going to explore what makes two problems, or two algorithms, similar or different from one another, and the way computer scientists talk about them. Not only will you be a better programmer, but you'll get to work on some really interesting problems along the way.

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.

Question: In your own words explain the difference between a problem and an algorithm.