Number Systems

Grade Level 9-12 (can be adapted for 6-8)

Timing: Two 90 minute lessons (1 for Engagement and Exploration, 1 for Explanation, Elaboration and Evaluation)

Content Objectives:

Students will

  • know how binary and hexadecimal number systems work.

  • understand how abstraction plays a role in computers.

  • be able to explain how to convert between decimals, binary and hexadecimal number systems

  • compare and contrast the different number systems

Inquiry Abilities, Understandings and Process Skills:

Students will

  • Use appropriate tools to gather, analyze and interpret data

  • Develop descriptions, explanations, predictions and models using evidence

  • Think critically and logically to make relationships between evidence,

  • Current knowledge and understanding guide investigations

  • Formulate explanations using evidence, models, principles and theories

  • Communicate procedures and explanations

Materials: String, Play dough, paper, cups, paper tubes, tape, makers, scissors, copy of the flippy do instructions, card stock to make flippy dos, large paper 11x17 for hexadecimal flippy do

Technology: Computers are needed for students (Can be paired). See links within the lesson for recommended websites.

Engagement:

Time: 40 minutes

What is a number system? How does a computer represent data?

Materials needed: String, Play dough, paper, cups, paper tubes, tape, makers, scissors

Diagnostic Assessment: Have students answer the following questions on Poll Everywhere to record their answers do not display answers until most people have answered give 1-2 minute per question to answer.

  • What is your personal definition of information?

  • What is a number system?

  • How many ways can you represent the number 5?

Introduction activity (adapted from code.org, 2017)

  • In pairs have students develop a binary system using things they find around the classroom. Explain to them that they will not be able to talk or write to each other during the activity. They will be across the room from each other, and no projectiles. Give them 10 minutes to develop the plan and construct.

    • Ask a binary question and have them communicate to their partners

    • Discuss afterward if their devices would still work

        • If you couldn't see their partner?

        • If their partner was not paying attention?

        • If you needed to display four choices could you adapt quickly?

        • More choices?

Watch the video on Discovery Education: Chalk Talk Binary (NSF, 2014). This explains why computers still use binary numbers. Alternate viewing of the video.

Exploration

Time: 15 minutes

  • Students will play the binary game by Cisco (10 minutes)

      • Ask the following questions:

        • How does it work? how does binary work?

        • How do decimals work? What is expanded form of a number?

Explanation

Time: 30 Minutes

  • Students can work in groups on Kahn Academy's lessons to further develop their knowledge if needed. (30 min). Formative assessment is Kahn's questions built in the lesson.

      • Have students work through both binary and hexadecimal lessons

      • Students who need extra help can use a flippy do from code.org

  • Replay the binary game. Did they get better?

  • Have students post questions, reference information, etc on the Padlet.

  • Create a graphic organizer for number systems and computer science using Google Draw, Slides or any graphic organizer app. Using the Padlet.

Elaboration

Time: 30 minutes

Students should do the following in small groups. They should be able to provide evidence and explain their work. Have a whole group discussion the last 10 minutes regarding each of these questions.

  • Make a flippy do for Hexadecimal numbers.

  • Color is represented in RGB values since the computer screen is made up of light. The values go from 0-255. Can you explain why? What would the values in binary look like? In hexadecimal? How does this relate to abstraction? Provide evidence.

  • Review Graphic organizers, and have students comment on Padlet.

  • Is the video below a computer?

Evaluation

Time (60 minutes)

  • Project: Students should work in pairs on one of these

      • Design a cartoon using hexadecimal and Binary code

      • Design a Hexadecimal and binary calendar

      • Create a simple Hexadecimal/Binary/Decimal Game

  • Students will self-reflect on their knowledge in a 1-3 minute Flipgrid of what they have learned and how this knowledge impacts computer science.

  • Students will look at questions involving number systems and abstraction at the end of big data unit (AP Prep).

Technology to be used: Canva, Adobe Illustrator/ InDesign, Scratch, Processing

Rubrics

Rubrics

References:

Binary Numbers. (n.d.). Kahn Academy. https://www.khanacademy.org/computing/computers-and-internet/xcae6f4a7ff015e7d:digital-information/xcae6f4a7ff015e7d:binary-numbers/a/bits-and-binary

Cisco Learning Network. (n.d.). Binary Game. https://learningnetwork.cisco.com/s/binary-game

Code.org. (2017). How to make a Flippy Do. https://docs.google.com/document/d/1QnD9khmPUz1az3ZLc5L8vavR6lU0uScspotRhORnHxE/edit

Code.org. (2017). Lesson 2: Sending Binary Lessons. https://curriculum.code.org/csp-1718/unit1/2/

Flipgrid. (2022).. https://info.flipgrid.com/

Fung, K. (2012, June 4). Music Wagon -Amsterdam, Holland 2012 [Video]. YouTube. https://www.youtube.com/watch?v=w8nwq7KV9HI

Hexadecimal Numbers. (n.d.). Kahn Academy. https://www.khanacademy.org/computing/computers-and-internet/xcae6f4a7ff015e7d:digital-information/xcae6f4a7ff015e7d:hexadecimal-numbers/a/hexadecimal-numbers

National Science Foundation(NSF), (2014) Chalk Talk: Binary. [Full Video]. Available from https://www.discoveryeducation.com

Padlet. (2022). https://padlet.com/

Poll Everywhere. (2022). https://www.polleverywhere.com/