Day 1: Introduction to Data Representation

Learning Objectives

• DAT-1.A: Explain how data can be represented using bits.

Essential Questions

• How is all digital data represented at the lowest level?
• Why is binary used as the foundation of digital data representation?

Materials Needed

• Presentation slides on data representation
• Binary conversion handouts
• Binary cards (cards with powers of 2) for hands-on activity
• Exit ticket templates

Vocabulary

• Bit
• Binary
• Decimal
• Digital data
• Representation
• Base-2
• Base-10

Procedure (50 minutes)

Opening (10 minutes)

1. Welcome and Introduction (5 minutes)

   • Introduce the Data Big Idea in AP CSP
   • Explain that this is the second of five big ideas in the course
   • Share the learning objectives for the unit

2. Activating Prior Knowledge (5 minutes)

   • Ask students: "What types of data do you interact with daily?"
   • Create a class list of data types (text, images, video, sound, etc.)
   • Ask: "How do you think computers store this information?"

Main Activities (30 minutes)

3. Mini-Lecture: Introduction to Binary (10 minutes)

   • Explain that all digital data is represented as sequences of bits (0s and 1s)
   • Discuss why computers use binary (electrical signals, on/off states)
   • Show the powers of 2 and how they relate to binary positions
   • Demonstrate converting simple decimal numbers to binary

4. Guided Practice: Binary Conversion (10 minutes)

   • Walk through converting decimal numbers to binary step-by-step
   • Have students practice converting 3-4 numbers together as a class
   • Introduce converting binary back to decimal
   • Show shortcuts and patterns to look for

5. Activity: Binary Representation Hands-On (10 minutes)

   • Distribute binary cards to students (cards with 1, 2, 4, 8, 16, 32, etc.)
   • Call out decimal numbers and have students hold up the appropriate cards to represent that number in binary
   • For each number, have students explain their reasoning
   • Reverse the activity: show binary patterns and have students convert to decimal

Closing (10 minutes)

6. Demonstration: Beyond Numbers (5 minutes)

   • Brief overview of how text, images, and sound are represented in binary
   • Show examples of:
     • ASCII table for text representation
     • Simple black and white image as a grid of bits
     • Waveform of sound and its digital sampling
   • Explain that we'll explore these representations in depth in upcoming lessons

7. Exit Ticket (5 minutes)

   • Students convert a decimal number to binary (e.g., 25 to binary)
   • Students explain in 1-2 sentences how the conversion process works
   • Bonus question: Name one type of data and how it might be represented in binary

Assessment

• Formative: Participation in binary conversion activities
• Exit Ticket: Accuracy of binary conversion and quality of explanation

Differentiation

For Advanced Students

• Convert larger decimal numbers to binary
• Introduce hexadecimal and have them convert between decimal, binary, and hex
• Ask them to research and explain how negative numbers are represented in binary

For Struggling Students

• Provide a binary conversion chart
• Use smaller numbers for conversion practice
• Allow use of calculators for decimal calculations

Homework/Extension

• Complete a worksheet with 10 decimal-to-binary and binary-to-decimal conversions
• Research one interesting fact about binary representation in computers
• Create a binary "cheat sheet" with conversion tips and examples

Teacher Notes

• Emphasize that understanding binary is fundamental to all computing concepts
• Watch for students who struggle with the powers of 2 and provide additional support
• Make connections to students' everyday experiences with digital devices
• Preview that binary representation will be the foundation for the next several lessons