Decoding Decimal, Binary & Octal: Number System Adventures

By Angela Smart, Heritage College

Decoding Decimal, Binary & Octal: Number System Adventures

At a Glance

Discipline

  • Mathematics

Instructional Level

  • College & CEGEP

Course

  • Mathematics of Computer Science and Information Technologies

Tasks in Workflow

Social Plane(s)

  • Group
  • Whole Class

Type of Tasks

  • Creating & designing
  • Analyzing
  • Collecting & seeking information

Technical Details

Class size

  • Small (20-49)

Time

  • Single class period (< 90 mins)

Inclusivity & Accessibility

  • Diversity of engagement

Instructional Purpose

  • Application & knowledge building
  • Consolidation & metacognition
  • Preparation & knowledge activation

Overview

The purpose of this activity is for students to explore the binary and octal number systems. In this activity, teams of two to three students will be given a binary converter and asked what they see. Once they’ve identified the characteristics of the binary system, students will then be asked “Why do we need base 2 in computing?” Students will then connect what they’ve learned to answer the question “How many symbols in base 10?” To conclude, students will be asked to explore and make suggestions on how they could create an octal, or base 8, converter.

By engaging in this activity, students can learn how an abstract mathematical concept, the binary system, applies to the real-world.

This activity takes place in-class during the first week of class. The strategy used is problem-based learning which allows students to solve a problem through direct experience while being grounded in real-world application.

Instructional Objectives

Students will be able to:

  • Identify and analyze the characteristics of a binary number system
  • Analyze how the characteristics of binary and decimal systems are related
  • Identify and analyze characteristics of an octal system

Workflow & Materials

Workflow

Activity Workflow

View on CourseFlow

Key Points for Activity

Angela Smart

Interactive media

3D Binary Converter

Angela Smart

Contributor's Notes

Benefits
Challenges
Tips
Benefits
  • Linking to real-world experiences: students can understand the value of learning abstract mathematical concepts and how these may impact their daily life.
  • Motivation: students can engage with a physical tool and be motivated to participate in creating a new tool.
  • Engagement: Having a tactile way to physically change quickly as the numbers change and therefore have immediate feedback and be able to adjust in response.
  • Active learning lesson: students are always more engaged in active learning which allows the students to think about ideas, discuss with peers, and have the opportunity to be heard.
Challenges
  • Access to a 3D printer: cegeps and public libraries can have access to 3D printers. If the instructor doesn’t have access to a 3D printer, a binary converter can be made using construction paper.
  • Time to prepare the material: allot enough time to print the 3D converters or create them with construction paper.
Tips
  • Sticking point: If the groups are stuck, bring it back together and walk through as a whole class.
  • Engagement: keep the group work short to keep students engaged.
  • Distractions: the binary converters can become fidget toys for students. Have the students put them aside during class discussion.

Applied Strategies

Problem-Based Learning

Teamwork and collaboration