Representing Numbers: Tally Marks

Learning Objectives Define tally marks as a unary (base-1) system for representing numbers. Convert any number up to 30 into its tally mark representation. Convert a set of tally marks back into its standard decimal number. Explain the 'group of five' rule and why it makes counting more efficient. Identify tally marks as a simple form of data encoding. Describe the steps (algorithm) for creating tally marks for a given number. Ever tried to count votes for class president or keep score in a game? 🗳️ How do you keep track of a growing number without losing your place? We're going to explore one of the oldest and simplest ways to represent numbers: tally marks! You'll learn how this system works, why it's a basic form of data encoding, and how it rela...

TermDefinitionExample Tally MarkA single stroke ( | ) used to represent one item being counted. It's a simple way to keep a running total.To count three apples, you would draw three tally marks: ||| Data RepresentationThe different ways we can store or show information. Numbers can be represented as digits (7), words ('seven'), or tally marks (|||| ||).The number 5 can be represented as the digit '5' or as the tally mark group '||||'. EncodingThe process of converting information from one format into another. Computers do this all the time, like converting letters into binary code.Encoding the number 4 into the tally mark format gives you '||||'. Unary System (Base-1)A number system that uses only one symbol. To represent a number 'N'...

The One-to-One Rule 1 item = 1 tally mark ( | ) For every single item you count, you draw one single, vertical line. This is the most basic rule of tallying. The 'Group of Five' Rule The 5th mark is a diagonal slash across the first 4. When you get to the fifth item, you don't draw another vertical line. Instead, you draw a diagonal line through the previous four (||||). This creates a bundle that is easy to see and count. The Tallying Algorithm 1. For each item, draw a vertical mark. 2. If the count is a multiple of 5, make that mark a diagonal slash over the last four. 3. Start a new group for the next item. This is the set of steps, like a computer program, that you follow every time to make sure your tally marks are correct. It's a simple loop...