Mills Maths Tools

⭐Interactive maths tools for Years 7–10

Free, classroom-tested interactives inspired by the ELPSA cycle.

A growing collection of visual models to help students access key number and proportional-reasoning ideas. Developed by NSW Department of Education mathematics teacher Jeff Mills.

About this site

This site hosts a growing collection of classroom-tested visual mathematics tools designed to support deep conceptual understanding in Years 7–10.

The tools are intentionally aligned to the ELPSA learning cycle (Experience, Language, Pictorial, Symbolic, Application), providing multiple entry points for students and supporting movement from concrete experiences to formal mathematical reasoning.

Design decisions are also informed by Di Siemon’s Big Ideas in Mathematics, with an emphasis on structure, relationships, and multiplicative thinking rather than procedural shortcuts.

Make mathematical structure visible
Support discussion, reasoning, and representation
Reduce cognitive load while maintaining conceptual demand
Be usable flexibly for whole-class teaching, small groups, or independent exploration

Contact

Jeff Mills 📧 jeff.mills2@det.nsw.edu.au

Feedback, classroom reflections, and requests for new tools are welcome.

Tools

Search and filter to quickly find what you need.

🔍

Probability

🎰

Financial Expectation Spinner

Explore long-run outcomes and expected value using a simple spinner model. Designed to support discussions about probability, fairness, and financial expectation.

Stage 4 Stage 5 Probability Expected value

Ratio

➗

Divide a Ratio

Enter a total and a ratio to see how the quantity is shared. Supports part–whole reasoning and proportional splits in context.

Stage 4 Stage 5 Ratio Proportional reasoning

Ratio model

🧱

Stacked Bar Model – Ratio

A stacked bar visual that lets students represent and divide quantities in a given ratio. Great for making unit ratios, part–whole structure, and percentage links visible.

Stage 4 Stage 5 Ratio Visual model Proportional reasoning

Ratio bar

📊

Partition Splitter

A bar model that lets students partition a whole into ratio parts. Ideal for exploring equivalent ratios, scaling, and percentage contexts.

Stage 4 Stage 5 Ratio Visual model

Place value

🔢

Multiply / Divide by 10 Slider

A dynamic place value slider to model multiplying and dividing by powers of 10, including links to decimal representations and scientific notation.

Stage 4 Place value Powers of 10

Integers

➖

Negatives on the number line

Generate missing-value number line questions that include negative integers. Includes teacher controls (step + range) and quick Reveal/Next shortcuts.

Stage 4 Stage 5 Integers Number line Negative numbers

Relevant links