AP CSP Day 2 - Binary Representation of Numbers

Course Information

• Course: AP Computer Science Principles
• Unit: Big Idea 3 - Data & Information (DAT)
• Lesson: Day 2 (50 minutes)
• Learning Objective: DAT-1.A - Explain how data is represented in computing systems

Learning Objectives

Primary Goals

Students will be able to:

1. Explain binary representation of numbers
2. Identify integer and floating-point representations
3. Apply binary conversion techniques
4. Analyze the impact of binary representation on data processing

AP Exam Alignment

• Big Idea 3: Data & Information (27-36% of AP Exam)
• Essential Knowledge: DAT-1.A.1, DAT-1.A.2, DAT-1.A.3
• Computational Thinking Practice: 2.B - Represent data using multiple encoding schemes

Lesson Structure (50 minutes)

Opening Hook (10 minutes)

2.1 Welcome & Lesson Preview (5 minutes)

Teacher Activities:

• Welcome students to Day 2
• Review previous lesson's key concepts
• Introduce today's focus on binary representation of numbers

Student Activities:

• Review previous lesson's materials
• Think about: "What is binary representation?"

2.2 Quick Binary Conversion Challenge (5 minutes)

Activity: "Convert Decimal to Binary"
Instructions:

• Groups of 4-6 students
• Convert decimal numbers to binary
• Discuss the process

Purpose: Activate thinking about binary conversion

Core Content Instruction (20 minutes)

3.1 What is Binary Representation of Numbers? (10 minutes)

Definition (DAT-1.A.1):

Binary representation involves encoding numbers in base-2 format.

Key Concepts:

• **Integer representation: Whole numbers in binary
• **Floating-point representation: Decimal numbers in binary
• **Bit and byte: Units of binary data

Case Study: The representation of integers in binary

• Representation process: Converting whole numbers to binary
• Outcome: A basic understanding of integer encoding

3.2 Types of Number Representations (5 minutes)

Types:

• **Integers: Whole numbers
• **Floating-point: Decimal numbers
• **Bit and byte: Binary units

Examples:

• E-commerce app: Integer representation for product IDs
• Calculator app: Floating-point representation for calculations

3.3 Importance of Binary Representation (5 minutes)

Why is it important?:

• Efficiency: Compact data storage
• Interoperability: Standardized data exchange
• Accuracy: Precise data interpretation

Discussion Questions:

1. How does binary representation work for integers?
2. What are the differences between integer and floating-point representations?
3. Why is binary representation important for data processing?

Hands-On Activity (15 minutes)

4.1 Group Project: Binary Conversion Practice (15 minutes)

Activity: "Convert Numbers to Binary"
Instructions:

• Groups of 3-4 students
• Convert various numbers to binary
• Discuss the process and its applications
• Present findings

Materials:

• **List of numbers to convert
• **Conversion worksheet
• **Access to coding environment

Learning Goals:

• **Understand binary conversion
• **Identify number representations
• **Apply conversion techniques
• **Present ideas effectively

Assessment:

• **Group participation
• **Conversion accuracy
• **Use of conversion tools
• **Presentation clarity

Closure & Preview (5 minutes)

5.1 Key Concepts Review (2 minutes)

Today's Learning Highlights:

1. ✅ Understanding binary representation of numbers
2. ✅ Identifying integer and floating-point representations
3. ✅ Applying binary conversion techniques
4. ✅ Analyzing binary representation impact

AP Exam Connection:

• These concepts will appear in AP exam multiple choice questions
• Understanding binary representation is crucial for the Explore Performance Task

5.2 Next Class Preview (3 minutes)

Day 3 Topic: "Binary Representation of Text"

• Learning Objective: DAT-1.A - Explain how data is represented in computing systems
• Activity: Practicing text encoding techniques
• Homework: Think about a recent program you used. What binary representations did it use? What could be improved?