Financial Expectation Spinner
Explore expected value and long-run outcomes.
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Welcome to Mills Maths Tools
Free, classroom-tested interactives inspired by the ELPSA cycle.
Visual models supporting deep number, ratio and proportional reasoning. Built by NSW 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 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 informed by Di Siemon’s Big Ideas in Mathematics, with an emphasis on structure, relationships, and multiplicative thinking.
- 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
Tools
Grouped for quick scanning.
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Probability
chance, long-run thinking
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Ratio & Proportion
structure, scaling, equivalence
Divide a Ratio
Visualise proportional sharing.
Open →Stacked Bar Model – Ratio
Make ratio structure visible.
Open →Partition Splitter
Explore equivalent ratios and scaling.
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Number & Integers
place value, direction, operations
Multiply / Divide by 10
Dynamic place-value modelling.
Open →Negatives on the Number Line
Missing-value integer reasoning.
Open →Integer Addition
Visualise and reason about integer addition.
Open →Vector Integer Addition
Add integers using vector (directed) movement on the number line.
Open →Factor Circles
Build fluency with factors using circle models and quick generation.
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Measurement
area, perimeter, dimensions
Rectangles - Perimeter & Area
Explore area and perimeter relationships using rectangle models.
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Algebra
expressions, structure, simplification
Collecting Like Terms (1)
Practice collecting like terms using grouped visual models.
Open →Collecting Like Terms (2)
Simplify algebraic expressions by identifying and combining like terms.
Open →One step Equations - Double Number Line
Solve one-step equations using a visual double number line model.
Open →Contact
Feedback, classroom reflections, and requests for new tools are welcome.
Want more updates when new tools are added?
Follow the Mills Maths Tools Facebook Page for announcements and classroom ideas.
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