◆ Swift Playgrounds Curriculum

Geometry,
through code.

A six-chapter curriculum that teaches geometry concepts using Swift — from drawing simple shapes to building a complete suburban scene — with Maths connections throughout.

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Requires Swift Playgrounds 4 on iPad or Mac

Geometry Playground running in Swift Playgrounds on iPad

Getting started

How to Get Started

Getting the playground onto your device takes under a minute.
Here's how it works.

Install Swift Playgrounds

Download Swift Playgrounds 4 for free from the App Store on iPad or Mac. It's the app you'll use to open and run all the code in this curriculum.

Tap Subscribe

Press the Subscribe in Swift Playgrounds button on this page. It opens a deep link (developer.apple.com/ul/sp0) that registers this feed directly in the app.

Open your library

The Geometry Playground appears in your Subscriptions section inside Swift Playgrounds. Tap it once to download the full playground file.

Stay up to date

Swift Playgrounds checks the feed periodically. When a new version is published a badge appears — tap once to update. No re-subscribing needed.

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The curriculum

Six chapters. One complete picture.

Each chapter builds on the last — introducing a new programming concept alongside the geometry it makes possible.

Chapter I of VI

Coordinate Geometry with Sequences

Meet the Pen API. Draw squares, rectangles, triangles, and stars one command at a time — laying down sequences of lines and turns to build geometric intuition.

10 sections2 tutorials8 exercises

Chapter II of VI

Shape Properties with Variables

Store side lengths, colours, and coordinates in var and let, then reuse them to build diamonds, crosses, snowflakes, and rhombuses while exploring symmetry and shape properties.

21 sections3 tutorials18 exercises

Chapter III of VI

Polygon Patterns with Loops

Harness the for loop to draw regular polygons, spirals, and stars. Derive the interior-angle formula from nothing but a few lines of Swift.

9 sections1 tutorial8 exercises

Chapter IV of VI

Sorting Shapes with Conditionals

Use if, else, and Boolean logic to sort triangles, quadrilaterals, and angles by their properties. Meet Input() for live, interactive testing.

9 sections2 tutorials7 exercises

Chapter V of VI

Similarity with Functions

Define reusable functions with parameters, then call them at different scales to draw flags from around the world — exactly what similarity in geometry means.

21 sections2 tutorials19 exercises

Chapter VI of VI

Composite Figures in Action

Bring everything together. Combine functions, loops, and conditionals to build a house, a tree, a fence, a car — then compose them into a complete suburban scene.

10 sections1 tutorial9 exercises

Standards alignment · IM1 · IM2 · IM3

Integrated Maths

The Integrated Maths sequence is a three-part high school mathematics programme that weaves algebra, geometry, and statistics into a unified curriculum — rather than treating them as separate subjects. Each course builds on the last, progressing from visual geometric reasoning through proportional thinking to analytic and algebraic geometry.

Geometry Playground is designed to sit alongside IM1, giving students a hands-on coding context for the geometric concepts they are studying in class. Because the curriculum emphasises reasoning and abstraction, it also lays the conceptual foundations that students will formalise in IM2 and IM3.

Coordinate Geometry Polygon Properties Angle Relationships Shape Classification Functions & Abstraction Composite Figures

IM 1

Geometric Structure

Visual reasoning, transformations, congruence, and foundational measurement. Primary alignment for Geometry Playground.

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IM 2

Proportional Geometry

Similarity, trigonometry, circles, and formal deductive proof. Playground chapters on functions and scaling build early intuition here.

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IM 3

Analytic Geometry

Coordinate proofs, trigonometric identities, and mathematical modelling. The coordinate and composition work in early chapters echoes here.

Coverage at a glance — click a row to explore

Maths Concept	Ch01	Ch02	Ch03	Ch04	Ch05	Ch06
Coordinate Geometry IM1
Ch I Coordinate Geometry Plotting points on a Cartesian plane Direction vectors and angle from origin Computing distances between points Ch II Shape Properties Translating shapes using coordinate offsets Symmetry across axes Ch VI Composite Figures Positioning composite figures using anchor coordinates Scaling and translating sub-components
Polygon Properties IM1
Ch I Coordinate Geometry Perimeter of squares, rectangles, triangles Side lengths and proportions Ch II Shape Properties Area and perimeter of irregular polygons Lines of symmetry Ch III Polygon Patterns Interior angles of regular polygons: (n−2)×180° Exterior angles: 360°÷n Relationship between sides and central angle Ch VI Composite Figures Area of composite polygons Decomposing complex shapes into simpler ones
Angle Relationships IM1
Ch I Coordinate Geometry Angle measurement in degrees Turning angles to form closed shapes Complementary and supplementary angles Ch III Polygon Patterns Exterior angle theorem for polygons Rotational symmetry and central angles Ch IV Sorting Shapes Acute, right, obtuse angle identification Triangle angle sum = 180° Supplementary and vertical angles
Shape Classification IM1
Ch IV Sorting Shapes Triangle classification by side (scalene, isosceles, equilateral) Triangle classification by angle (acute, right, obtuse) Quadrilateral classification (parallelogram, rectangle, rhombus, square, trapezoid) Boolean logic applied to geometric properties
Variables & Expressions IM1
Ch II Shape Properties Naming and substituting values into expressions Side length as a variable Ch III Polygon Patterns Loop counter as a geometric variable (step, radius, angle) Expressing polygon angle formulas algebraically Ch V Similarity Parameters as variable inputs to geometric functions Evaluating expressions for different parameter values
Functions & Abstraction IM1–2
Ch V Similarity Function definition, parameters, and return values Geometric transformations as functions Scale and proportion in similar figures Drawing flags using parameterised shapes Ch VI Composite Figures Decomposition: breaking a scene into reusable components Function composition to build complex figures
Composite Figures & Area IM1
Ch I Coordinate Geometry Area of squares, rectangles, triangles Ch II Shape Properties Area of diamonds, crosses — decomposing into simpler shapes Ch VI Composite Figures Total area of a composite scene Real-world geometric modelling Perimeter of complex irregular shapes

Chapter-by-chapter breakdown

G-CO.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment.

G-GPE.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Angle Measure

Classify angles as acute, right, obtuse, or straight and use degree measure to construct shapes.

Area & Perimeter

Calculate and compare area and perimeter of squares, rectangles, and triangles drawn in code.

A-SSE.1

Interpret parts of an expression — use a variable to represent a side length and substitute values.

G-CO.3

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the symmetries.

Reflective Symmetry

Identify and draw lines of symmetry in shapes drawn with multiple pens.

Area of Polygons

Decompose irregular polygons (diamonds, crosses) into rectangles and triangles to find area.

G-CO.3

Describe rotational symmetry of regular polygons — the loop count equals the order of symmetry.

Interior Angles

Derive and apply the formula (n−2)×180° for the sum of interior angles of an n-sided polygon.

Exterior Angles

Each exterior angle of a regular n-gon = 360°÷n — used directly as the loop turning angle.

Iteration Pattern

Recognise and express a repeating geometric pattern algebraically, then encode it as a loop.

G-CO.10

Prove theorems about triangles — angle sum, base angles of isosceles triangles.

Triangle by Sides

Classify triangles as scalene, isosceles, or equilateral using side-length comparisons in code.

Triangle by Angles

Classify triangles as acute, right, or obtuse using conditional tests on angle measures.

Quadrilaterals

Apply properties of parallelograms, rectangles, rhombuses, squares, and trapezoids to classify shapes programmatically.

Angle Relationships

Use supplementary, complementary, and vertical angle relationships as classification conditions.

F-IF.1

Understand that a function assigns exactly one output to each input — mirrored in parameterised drawing functions.

G-SRT.1

Verify experimentally the properties of dilations — scale a shape by changing a parameter and observe proportional change.

Similarity

Two shapes are similar if one is a dilation of the other — functions make this relationship explicit through a scale parameter.

Geometric Transformations

Encode translation, scaling, and rotation as functions with parameters for distance, factor, and angle.

G-MG.1

Use geometric shapes, their measures, and their properties to describe objects — model a house, tree, or car with polygons.

G-GMD.3

Use volume formulas for cylinders, pyramids, cones, and spheres — introduced through 2D analogues in the scene.

Composite Area

Calculate the total area of a suburban scene by summing the areas of its geometric components.

Decomposition

Break a complex real-world object into primitive geometric shapes — the key problem-solving strategy of the chapter.

About

About the Developer

Daniel Budd

Apple Distinguished Educator · Apple Professional Learning Specialist
School-Wide Technology Team Leader, Hong Kong International School

Daniel is an Apple Professional Learning Specialist and Apple Distinguished Educator from Perth, Western Australia. At Hong Kong International School he spearheaded the design and development of an inclusive, modern Computer Science program by integrating it into the NCAS Media Arts Standards.

A strong advocate for the pedagogical integration of technology, Daniel focuses on the transformative potential of STEM education, robotics, and the evolving role of AI in shaping teaching and learning. As a speaker, author, and international educator, he has written extensively on coding, app development, and the impact of emerging technologies on education.

Daniel has delivered keynotes and workshops across Australia, South-East Asia, China, and the USA — inspiring educators worldwide to embrace innovation in their teaching practice.

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Documentation

Wiki & teaching notes