Question

number system lesson​

Answer 1

Answer:

The four most common number system types are:

1. Decimal number system (Base- 10)
2. Binary number system (Base- 2)
3. Octal number system (Base-8)
4. Hexadecimal number system (Base- 16)
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Answer 2

Answer:

Overview

Students will explore the properties of number systems by effectively inventing a base-3 number system using circles, triangles and squares as the symbols instead of arabic numerals. Students are asked to create rules that explain how each arrangement of symbols can be generated or predicated as an orderly, logical series. The objective is to understand that you can represent any number with any agreed-upon set of symbols that appear in an agreed-upon order. This is as true for circles, triangle and squares as it is for the digits 0-9, or the number systems we commonly see in computer science (binary and hexadecimal).

Purpose

In computer science it’s common to move between different representations of numbers. Typically we see numbers represented in decimal (base-10), binary (base-2), and hexadecimal (base-16). The symbols of the decimal (base-10) number system - 0 1 2 3 4 5 6 7 8 9 - are so familiar that it can be challenging to mentally separate the written symbols from the abstract values they represent. As a result, using the digits 0 and 1 can be a distraction when learning binary initially, so we don't in this lesson.

We want to expose the fact that numbers themselves (quantities) are laws of nature, but the symbols we use to represent numbers are an arbitrary, man-made abstraction. Sometimes students memorize conversions from one number system to another without really understanding why. By effectively inventing their own base-3 number system in this lesson the goal is for students to see that all number systems have similar properties and function the same way. As long as you have 1) a set of distinct symbols 2) an agreement about how those symbols should be ordered, then you can represent any number with them.

Agenda

Getting Started (5 mins)

How many ways can you represent "7"?

Activity (30 mins)

Circle-Triangle-Square Activity - Create a number system using symbols

Wrap-up

Present Student Circle-Triangle-Square Number Systems

Discuss the Rules Created for the Number Systems

Connect to Number Systems and Binary Numbers

Assessment

Extended Learning

Extend to a 4 digit numbering system

View on Code Studio

Objectives

Students will be able to:

Reason about permutations and symbols as arbitrary abstract concepts that can be used to represent numbers.

Invent their own “number system” with symbols and rules for getting from one permutation to the next