Numbers 3B

Overview

In this Phlow, learners explore how the position of digits affects the size of a number. They are given sets of digits (e.g. 7, 8, 3 or 3, 6, 1) and must decide how to arrange them to make the largest or smallest possible 3-digit number, using each digit only once.

Forming the largest number from 7, 8, 3 → 873
Forming the smallest number from 3, 6, 1 → 136

Each step isolates one decision — choosing the first, second, and last digit — guiding students to reason systematically through place value. By starting with prompts like “Start with the first number,” then “Then the next number,” the learner experiences how the position of a single digit changes the overall value.

The design encourages reflective reasoning: to make the largest number, the biggest digit goes in the hundreds place; to make the smallest, the smallest digit goes there. This visual and interactive process strengthens the understanding that digit position determines value, a foundation for comparing, ordering, and rounding numbers at higher levels.

Learners also experience an early form of combinatorial reasoning — understanding that digits can form different numbers depending on order — which underpins future algebraic and logical thinking.

Step 1 / 6

Prerequisite Knowledge Required

Numbers 3A – Comparing 3-Digit Numbers.
Place Value 2B – Hundreds, Tens, and Ones.
Order 2A – Sequencing Numbers.
Understanding how digit position (hundreds, tens, ones) affects number size.
Ability to compare and order digits from smallest to largest.
Familiarity with constructing 2- and 3-digit numbers.
Comprehension of terms like largest, smallest, digit, number, next, and last.

Main Category

Number / Place Value & Number Construction

Estimated Completion Time

Approx. 10 seconds per screen (6 screens total) → 2–3 minutes total.

Cognitive Load / Step Size

Moderate — each screen isolates one decision (first, next, last digit), making reasoning sequential and easy to follow. Repetition deepens understanding of how digit order impacts magnitude.

Language & Literacy Demand

Moderate — sentences highlight key mathematical terms (largest, smallest, next, number, once) to reinforce reasoning. Phrasing scaffolds logical thought in clear, accessible language.

Clarity & Design

Digits are displayed separately from empty boxes for placement clarity.
Each step focuses on one position to avoid overload.
Purple highlights guide attention to the current decision point.
Immediate feedback (green highlight) reinforces correct reasoning.

Curriculum Alignment

Irish Mathematics Curriculum – Number Strand / Junior Cycle Strand 3: Number

Construct and compare numbers up to 999 using place value reasoning.
Understand that rearranging digits changes the size of a number.
Identify patterns and rules in forming the largest and smallest numbers.

Engagement & Motivation

High — the puzzle-like, step-by-step process keeps learners curious and engaged. Each successful placement gives a sense of progress, maintaining focus and flow.

Error Opportunities & Misconceptions

Reversing the rule (placing the smallest digit first when forming the largest number).
Repeating digits instead of using each once.
Confusing largest with smallest.

Consistent language and visual cues help correct these errors quickly.

Transferability / Real-World Anchoring

High — understanding how digits form numbers connects directly to reading prices, measurements, and numerical data, all of which rely on interpreting order and size correctly.

Conceptual vs Procedural Balance

Strongly conceptual — learners practise constructing numbers while internalising the deeper logic of positional value and magnitude.

Learning Objectives Addressed

Form 3-digit numbers from given digits.
Use place value to identify the largest and smallest possible number.
Recognise the effect of digit position on number value.
Strengthen sequencing, reasoning, and comparison skills.

What Your Score Says About You

Less than 15: Review place value — practise how digit order changes number size.
16–22: You understand the logic but need more accuracy when choosing the next digit.
23–29: Excellent grasp of place value reasoning and sequencing.
30 / 30: Perfect! You’ve mastered digit ordering — you’re ready for Numbers 4A, where you’ll apply place value in rounding and estimating larger numbers.