Illuminations Applet- and Video-Based Activities
Organized by Big Ideas in Mathematics

We all want our students to acquire a deep understanding of big mathematical ideas. These big ideas grow over time and throughout the curriculum. On this hyper-linked page you will find Illuminations activities at different grade levels related to the following big mathematical ideas.

Linear Functions

Grades 6-8

Constant Rate of Change (E-example 6.2)
Learning about Rate of Change in Linear Functions: Using Interactive Graphs
NCTM Standard: Algebra
Other NCTM Standards: Representation, Geometry, Connections, Data Analysis and Probability, Communication

Now-Next Recurrence Table Generator (Mathlet)

Grades 9-12

Linear Regression and Correlation (i-Math)
Investigating Linear Relationships: The Regression Line and Correlation
NCTM Standard: Data Analysis and Probability
Other NCTM Standards: Number and Operations, Algebra, Geometry, Reasoning and Proof, Representation

Linear Regression Residuals (E-example 7.4)
Understanding the Least Squares Regression Line with a Visual Model
NCTM Standard: Data Analysis and Probability
Other NCTM Standards: Algebra, Representation, Reasoning and Proof, Geometry, Communication, Number and Operations

Linked Lines (E-example 7.5)
Exploring Linear Functions – Representational Relationships
NCTM Standard: Problem Solving
Other NCTM Standards: Algebra, Representation, Reasoning and Proof, Geometry, Number and Operations, Connections

Now-Next Recurrence Table Generator (Mathlet)

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Exponential Functions   

Grades 6-8

Affine Recurrence Plotter (Mathlet)

Affine Recurrence Spreadsheet (Mathlet)

Now-Next Recurrence Table Generator (Mathlet)

Grades 9-12

Affine Recurrence Plotter (Mathlet)

Affine Recurrence Spreadsheet (Mathlet)

Eliminating Medicine from the Body (E-example 7.2)
Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body
NCTM Standard: Algebra
Other NCTM Standards: Representation, Geometry, Connections, Number and Operations, Problem Solving, Data Analysis and Probability, Communication

Light Intensity (i-Math)
Shedding Light on the Subject: Function Models of Light Decay
NCTM Standard: Algebra
Other NCTM Standards: Representation, Geometry, Connections, Problem Solving, Data Analysis and Probability, Communication, Reasoning and Proof, Measurement

Now-Next Recurrence Table Generator (Mathlet)

Trout Population (i-Math)
Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond
NCTM Standard: Algebra
Other NCTM Standards: Number and Operations, Data Analysis and Probability, Representation, Geometry, Problem Solving, Connections, Reasoning and Proof, Communication

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Rational Functions

Grades 9-12

Whelks (i-Math)
Whelk-Come to Mathematics: Using Rational Functions to Investigate the Behavior of Northwestern Crows
NCTM Standard: Algebra
Other NCTM Standards: Data Analysis and Probability, Representation, Problem Solving, Geometry, Number and Operations, Measurement, Connections, Reasoning and Proof, Communication

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Equivalence

Grades Pre-K–2

Shape Pan Balance (Mathlet)

Grades 3-5

Expression Pan Balance (Mathlet)

Shape Pan Balance (Mathlet)

Grades 6-8

Expression Pan Balance (Mathlet)

Grades 9-12

Expression Pan Balance (Mathlet)

Across the Grades

Equivalence (i-Math)
NCTM Standard: Algebra
Other NCTM Standards: Number and Operations, Measurement, Problem Solving, Reasoning and Proof, Connections, Geometry, Representation

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Rate of Change

Grades 3-5

Simulating Runners (E-example 5.2)
Understanding Distance, Speed, and Time Relationships Using Simulation Software
NCTM Standard: Algebra
Other NCTM Standards: Number and Operations, Geometry, Connections, Reasoning and Proof

Grades 6-8

Constant Rate of Change (E-example 6.2)
Learning about Rate of Change in Linear Functions Using Interactive Graphs
NCTM Standard: Algebra
Other NCTM Standards: Representation, Geometry, Connections, Data Analysis and Probability, Communication

Grades 9-12

Cardiac Output (i-Math)
Put the Heart into Mathematics: Cardiac Output, Rates of Change, and Accumulation
NCTM Standard: Measurement
Other NCTM Standards: Data Analysis and Probability, Problem Solving, Connections, Geometry, Representation, Algebra, Reasoning and Proof

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Fractions and Proportional Reasoning

Grades 3-5

One-Person Fraction Game (Mathlet)

Two-Person Fraction Game (E-example 5.1)
Communicating about Mathematics Using Games
NCTM Standards: Number and Operations, Communication
Other NCTM Standards: Reasoning and Proof, Representation, Connections, Problem Solving

Fraction Pie (Mathlet)

Pool Table (Mathlet)

Grades 6-8

Fraction Pie (Mathlet)

One-Person Fraction Game (Mathlet)

Learning About Fractions (and Area and Perimeter) (Inquiry on Practice)
Learning about Area, Perimeter, and Fractions with and from Peers
NCTM Standards: Number and Operations, Measurement
Other NCTM Standards: Communication, Reasoning and Proof, Geometry, Problem Solving

Pool Table (i-Math)
Analyzing Numeric and Geometric Patterns of Paper Pool
NCTM Standards: Number and Operations
Other NCTM Standards: Data Analysis and Probability, Geometry, Algebra, Communication, Measurement, Reasoning and Proof, Problem Solving

Pool Table (Mathlet)

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Recursion

Grades 3-5

Fractal Tool (Mathlet)

Grades 6-8

Affine Recurrence Plotter (Mathlet)

Affine Recurrence Spreadsheet (Mathlet)

Fractal Tool (Mathlet)

Now-Next Recurrence Table Generator (Mathlet)

Grades 9-12

Affine Recurrence Plotter (Mathlet)

Affine Recurrence Spreadsheet (Mathlet)

Fractal Tool (Mathlet)

Now-Next Recurrence Table Generator (Mathlet)

Light Intensity (i-Math)
Shedding Light on the Subject: Function Models of Light Decay
NCTM Standard: Algebra
Other NCTM Standards: Data Analysis and Probability, Reasoning and Proof, Problem Solving, Connections, Geometry, Representation, Measurement, Communication

Trout Population (i-Math)
Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond
NCTM Standard: Algebra
Other NCTM Standards: Number and Operations, Data Analysis and Probability, Representation, Geometry, Problem Solving, Connections, Reasoning and Proof, Communication

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3-D Geometry

Grades 3-5

Cubes (Mathlet)

Isometric Drawing Tool (Mathlet)

Spinning Polyhedra (i-Math)
Exploring Geometric Solids and Their Properties
NCTM Standard: Geometry
Other NCTM Standards: Algebra, Reasoning and Proof, Measurement, Communication, Data Analysis and Probability, Number and Operations

Students’ Understanding of Volume (Inquiry on Practice)
Gathering Evidence about Students’ Understanding of Volume
NCTM Standard: Measurement
Other NCTM Standards: Communication, Reasoning and Proof, Geometry, Algebra, Number and Operations, Problem Solving

Grades 6-8

Isometric Drawing Tool (Mathlet)

Spatial Reasoning (i-Math)
Spatial Reasoning using Cubes and Isometric Drawings
NCTM Standard: Geometry
Other NCTM Standards: Representation, Measurement, Algebra, Number and Operations, Reasoning and Proof, Data Analysis and Probability

Students’ Understanding of Volume (Inquiry on Practice)
Gathering Evidence about Students’ Understanding of Volume
NCTM Standard: Measurement
Other NCTM Standards: Communication, Reasoning and Proof, Geometry, Algebra, Number and Operations, Problem Solving

Grades 9-12

Isometric Drawing Tool (Mathlet)

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2-D Geometry

Grades Pre-K–2

Get the Turtle to the Pond – Navigation and Location (i-Math):
Developing Geometry Concepts Using Computer Programming Environments
NCTM Standard: Geometry
Other NCTM Standards: Problem Solving, Measurement

Ladybug – Navigation, Location, Rectangles (E-example 4.3)
Learning Geometry and Measurement Concepts by Creating Paths and Navigating
Mazes
NCTM Standard: Geometry, Measurement, Problem Solving
Other NCTM Standards: Connections, Communication

Polygons on Geoboards (E-example 4.2)
Investigating the Concept of Triangle and Properties of Polygons
NCTM Standard: Geometry
Other NCTM Standards: Connections, Communication, Reasoning and Proof

Tangram Activities (E-example 4.4)
Developing Geometry Understandings and Spatial Skills through Puzzlelike Problems with Tangrams
NCTM Standards: Geometry, Problem Solving
Other NCTM Standards: Reasoning and Proof, Number and Operations, Communication, Connections

Grades 3-5

Fractal Tool (Mathlet)

Shape Tool (Mathlet)

Properties of Rectangles and Parallelograms (E-example 5.3)
Exploring Properties of Rectangles and Parallelograms Using Dynamic Software
NCTM Standard: Geometry
Other NCTM Standards: Data Analysis and Probability, Reasoning and Proof, Measurement, Number and Operations, Communication, Connections

Grades 6-8

Congruence, Similarity, and Symmetry (E-example 6.5)
Understanding the Pythagorean Relationship Using Interactive Figures
NCTM Standard: Geometry
Other NCTM Standards: Algebra, Communication, Reasoning and Proof, Representation

Fractal Tool (Mathlet)

Learning About Area and Perimeter (and Division) (Inquiry on Practice)
Learning about Area, Perimeter, and Fractions with and from Peers
NCTM Standards: Measurement, Number and Operations
Other NCTM Standards: Communication, Reasoning and Proof

Length, Perimeter, Area, and Volume (E-example 6.4)
Understanding Congruence, Similarity, and Symmetry Using Transformations and
Interactive Figures
NCTM Standard: Geometry
Other NCTM Standards: Data Analysis and Probability, Measurement, Connections, Problem Solving, Reasoning and Proof, Communication

Pythagorean Theorem (E-example 6.5)
Understanding the Pythagorean Relationship Using Interactive Figures
NCTM Standard: Geometry
Other NCTM Standards: Algebra, Communication, Reasoning and Proof, Representation

Shape Tool (Mathlet)

Grades 9-12

Fractal Tool (Mathlet)

Ratios of Areas of Inscribed Figures (E-example 7.3)
Understanding Ratios of Areas of Inscribed Figures Using Interactive Diagrams
NCTM Standards: Geometry, Connections
Other NCTM Standards: Number and Operations, Measurement, Data Analysis and Probability, Problem Solving, Reasoning and Proof

Symmetries and Their Properties (i-Math)
NCTM Standard: Geometry
Other NCTM Standards: Connections, Algebra, Representation

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Vectors

Grades 6-8

Vectors and Cars (Mathlet)

Vectors and Planes (Mathlet)

Grades 9-12

Properties of Vectors and Vector Sums (E-example 7.1)
Learning about Properties of Vectors and Vector Sums Using Dynamic Software
NCTM Standard: Number and Operations
Other NCTM Standards: Geometry, Algebra, Connections

Translations (i-Math)
Symmetries and Their Properties - Part 3: Translations
NCTM Standard: Geometry
Other NCTM Standards: Connections

Vectors and Cars (Mathlet)

Vectors and Planes (Mathlet)

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Descriptive Statistics

Grades 3-5

Collect, Represent, and Interpret Data Using Spreadsheets (E-example 5.5)
Collecting, Representing, and Interpreting Data Using Spreadsheets and Graphing
Software
NCTM Standard: Representation
Other NCTM Standards: Data Analysis and Probability, Number and Operations, Reasoning and Proof

Investigating Data Using the Web (E-example 5.4)
Accessing and Investigating Data Using the World Wide Web
NCTM Standard: Data Analysis and Probability
Other NCTM Standards: Number and Operations, Representation, Reasoning and Proof, Connections

Grades 6-8

Compare and Contrast Mean and Median (E-example 6.6)
Comparing Properties of the Mean and the Median through the use of technology
NCTM Standard: Data Analysis and Probability
Other NCTM Standards: Number and Operations, Representation, Reasoning and Proof, Connections

Exploring Histograms (i-Math)
NCTM Standard: Data Analysis and Probability
Other NCTM Standards: Number and Operations, Geometry

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Probability

Grades 6-8

Simulating Probability (i-Math)
Simulating Probability Situations Using Box Models
NCTM Standard: Data Analysis and Probability
Other NCTM Standards: Representation, Reasoning and Proof

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Basic Skills

Grades Pre-K–2

Electronic Abacus (Mathlet)

Estimating Cranberries (E-example 4.6)
Developing Estimation Strategies by Making Connections among Number, Geometry,
Measurement, and Data Concepts
NCTM Standard: Connections
Other NCTM Standards: Number and Operations, Reasoning and Proof, Geometry, Measurement, Data Analysis and Probability, Communication, Algebra, Problem Solving

Number Properties Using 100 Boards and Calculators (E-example 4.5)
Learning about Number Relationships and Properties of Numbers Using Calculators
and Hundred Boards
NCTM Standards: Number and Operations, Reasoning and Proof, Communication
Other NCTM Standards: Algebra, Reasoning and Proof, Representation, Connections

Place Value – Child’s Development of Number Sense (Inquiry on Practice)
Understanding a Child’s Development of Number Sense
NCTM Standard: Number and Operations
Other NCTM Standards: Problem Solving, Connections, Communication

Grades 3-5

Factor Game (Mathlet)

One-Person Fraction Game (Mathlet)

Two-Person Fraction Game (E-example 5.1)
Communicating about Mathematics Using Games
NCTM Standards: Number and Operations, Communication
Other NCTM Standards: Representation, Connections, Reasoning and Proof, Algebra, Problem Solving

Fraction Pie (Mathlet)

Product Game (Mathlet)

Grades 6-8

Factor Game (i-Math)
NCTM Standard: Number and Operations
Other NCTM Standards: Problem Solving, Data Analysis and Probability, Algebra, Reasoning and Proof, Communication, Connections

Factor Game (Mathlet)

One-Person Fraction Game (Mathlet)

Fraction Pie (Mathlet)

Learning About Fractions (and Area and Perimeter) (Inquiry on Practice)
Learning about Area, Perimeter, and Fractions with and from Peers
NCTM Standards: Number and Operations, Measurement
Other NCTM Standards: Communication, Reasoning and Proof, Geometry, Problem Solving

Multiplication with Dynamic Area Model (E-example 6.1)
Learning about Multiplication Using Dynamic Sketches of an Area Model
NCTM Standard: Number and Operations
Other NCTM Standards: Geometry, Algebra, Representation

Product Game (i-Math)
NCTM Standard: Number and Operations
Other NCTM Standards: Connections, Geometry, Problem Solving, Reasoning and Proof, Communication, Algebra

Product Game (Mathlet)

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