Number Formation Worksheet: Creating the Greatest and Smallest Numbers

Introduction

This worksheet is designed to strengthen number sense and logical reasoning by practicing the formation of the greatest and smallest possible numbers under different constraints. Learners explore how digit choice, position, and repetition affect numerical value.

What Is Number Formation

Number formation involves arranging given digits to create numbers that are either as large as possible or as small as possible, while strictly following the rules provided in each problem.

This skill plays a key role in understanding place value, comparison of numbers, and strategic decision-making in mathematics.

Overview of the Six Problem Scenarios

This worksheet includes six carefully designed problem types, each focusing on a different aspect of number formation.

1. Unique Digits Challenge

You are given a list of 3, 4, 5, or 6 single digits.

Use all the given digits without repetition to form:

• The smallest possible number
• The greatest possible number

2. Multi-Digit Mastery

You are provided with a list of 6 single digits.

From these digits, form the:

• Smallest and greatest 3-digit numbers
• Smallest and greatest 4-digit numbers
• Smallest and greatest 5-digit numbers

Digits must not be repeated in the formed numbers.

3. Digit Duplication Dilemma

In this scenario, you are given 3 single digits.

One digit must be used twice to construct:

• The smallest possible 4-digit number
• The greatest possible 4-digit number

4. Position Puzzle

A digit from 0 to 9 is fixed at a specific position such as ones, tens, hundreds, or thousands.

Using the remaining digits without repetition, your task is to form:

• The smallest possible 4-digit number
• The greatest possible 4-digit number

5. Digit Duplex

You are given two digits.

Each digit must be used an equal number of times to form either:

• A 4-digit number
• A 6-digit number

The required number of digits depends on the number of input boxes provided.

6. Extreme Number Hunt

You are presented with a list of 4-digit or 5-digit numbers.

Your task is to identify:

• The smallest number in the list
• The greatest number in the list

How to Approach These Problems

Carefully read the conditions of each problem before forming numbers.

Pay close attention to place value, digit repetition rules, and any fixed-position constraints.

Skills Developed Through This Worksheet

• Strong understanding of place value
• Improved logical and strategic thinking
• Accurate comparison of numbers
• Confidence working with multi-digit numbers

Online, Interactive, and Self-Correcting

This is an online, interactive worksheet where learners enter their answers directly into the input boxes.

Immediate feedback helps learners verify their reasoning and correct mistakes without delay. No printing or downloading is required.