| Investigating the Commutative and Associative Properties Using Geometric Shapes |  |   |
| Comparing One Measure of a Square (Side Length, Diagonal Length, Area, or Perimeter) to Another |  |   |
| | Finding √2 With a Computer Software Program |  |  |
| Investigating Linear Equations using a Real-World Scenario |  |   |
| | Understanding Modular Arithmetic With Analog Clocks (and Other Real-World Examples) |  |   |
| | Using Proportional Reasoning For Price Comparisons |  |  |
| Discovering Linear Relationships Between Time and Number of Bounces |  |  |
| | Extending Problems from Arithmetic to Algebraic Thinking |  |  |
| | Making Connections Among Different Classes of Polynomial Functions |  |  |
| | Solving the Mangoes Problem and Sailors and Coconuts in Several Different Ways |  |   |
| Exploring Number Concepts through Cryptology |  |   |
| | Determining How Many Squares of Any Size are on a Checkerboard |  |   |
| | Investigating Patterns That Lead to Functions |  |   |
| Investigating Conic Sections using a Double-Napped Cone
|  |   |
| | A Unique Way to Review Plotting Points |  |   |
| | Determining an Appropriate Function to Fit Data |  |   |
| | Exploring Arithmetic Sequences, Leading to the Factoring Pattern for the Difference of Squares |  |  |
| | Understanding and Solving Linear Programming Problems |  |  |
| | Representing Area of a Rectangle Using the Distributive Property |  |   |
| | Constructing Perpendicular Bisectors and Circumcenters to Explore Delivery Regions
|  |   |
| | Investigating Inverse Variation |  |  |
| | Describing the Domain of a Function with Graphs, Tables, Number Lines, Words, and Symbols |  |  |
| | Students will represent quadratic functions as a table, with a graph, and with words. |  |  |
| | Relating Linear Equations and Graphs in a Game of Ships and Attacks
|  |  |
| | Answering The Question, "When Will I Ever Need To Solve A System Of Equations?" |  |  |
| Building Algebraic Understanding |  |  |
| | Observing Relationships between Mass, Length, and Position of a Fulcrum |  |   |
| Using Expressions and Equations on the Pan Balance Tool |  |  |
| Playing a Numbers Game to Develop Computational Skills and Conceptual Understanding |  |   |
| Modeling Data From Car Repair Costs and Sports Contexts |  |   |
| Moving from Numeric to Algebraic Notation |  |  |
| Distinguishing Between Numbers With Many Factors and Numbers With Few Factors |  |  |
| | Using Cuisenaire Rods to Build Trains, Investigate Patterns, and Make Algebraic Connections |  |  |
| Using Hands-On Activity to Develop Understanding of Time and Distance |  |   |
| | Using Manipulative Blocks and Counters to Explore Equations such as 3x = 2x + 12
|  |  |
| | Extending the Fibonacci Sequence through an Algebra Exploration |  |  |
| | Making the Connection between Trigonometric Ratios and Graphs of Sine and Cosine Functions
|  |  |
| | Using Slope to Approximate Rate of Change on a Graph |  |    |
| | Determining the Equation of a Parabola |  |  |
| | Exploring Patterns, Systems of Equations, and Rates of Change While Finding the Area of a Triangle |  |   |
| Using a Mirror and Flashlight to Understand Rational Functions |  |  |
| | Points in the Coordinate Plane |  |  |
| | Exploring Linear Equations using Polygons on a Graphing Calculator
|  |   |
| | Exploring Magic Squares from an Historical and Mathematical Perspective |  |   |
| Using Beads and an Antifreeze Chart to Understand Mixture Problems |  |  |
| | Using Technology to Develop an Understanding of Functions and Modeling |  |  |
| | Using Movement to Analyze Linear Functions and Systems of Equations |  |  |
| | Using Algebra to Model Linear Relationships |  |  |
| | Curve-Fitting, Exponential Growth, and Percent Change |  |  |
| Using Measurement to Design A Fire-Wise Property |  |     |
| Seeing to the Horizon from the Top of Mount Everest |  |   |
| | How Knowledge of Exponential Growth Can Feed a Village |  |  |
| | Determining Altitude and Velocity |  |   |
| Analyzing Numeric and Geometric Patterns |  |   |
| | Investigating Properties of Perimeter and Area of Two‑Dimensional Shapes |  |    |
| | The Algebra of Gas Consumption |  |    |
| | Interpreting Slope as a Rate of Change |  |  |
| Bringing Archimedes’ Method to Life in the Geometry Classroom |  |   |
| | Plot Circumference and Diameter to Determine Pi |  |    |
| | Investigating the Geometry of an Origami Octagon that Changes Shape |  |   |
| | Solving Puzzles to Strengthen Understanding of Expanding and Factoring Polynomials
|  |  |
| Using Batteries as a Physical Model to Explore the Addition of Signed Numbers |  |   |
| Calculating Compound Interest with Savings Accounts and Credit Cards
|  |  |
| | Exploring the Relationships Among Lines, Slopes, and y‑Intercepts in the Context of Printing Their Algebra Textbooks |  |  |
| | Determining the Amount of Tax a Family Will Pay Based on a Certain Income |  |   |
| | Working With Fractions and Decimals to Design and Sell a House and Invest the Profits |  |  |
| | Creating Graphs and Rules from an Organized Chart |  |     |
| | Using Right Triangles to Determine the Slope of a Line |  |  |
| | Investigating How Sine Waves and Frequencies Cause Harmony and Dissonance |  |  |
| | Developing and Analyzing Exponential Models For The Behavior of Light Passing Through Water |  |  |
| | Examining the Factors that Influence a Forest-Fire Danger Rating Index |  |  |
| Using Dynamic Geometry Software to Discover the Law of Cosines |  |   |
| | Examining Numeric, Algebraic, and Graphical Representations of Composition of Functions |  |  |
| | Using a System of Linear Equations to finding the Equilibrium Point for Supply and Demand Problems. |  |  |
| | Exploring the Handshake Problem |  |  |
| | Examining the Relationship Between Tolls and Distance |  |   |
| | Choosing a Prepaid Cell Phone Plan Using Systems of Equations
|  |  |
| | Examining a Recursive Sequence in a Game Between the Devil and Daniel Webster |  |  |
| | Predicting When the World Population Will Reach 7 Billion |  |   |
| | Problem Solving using Systems of Equations
|  |  |
| | Exploring Varying Displacement, Velocity, and Acceleration |  |   |
| | Using a Visual Approach to Direct, Indirect, and Transitive Reasoning |  |   |
| | Using a Scale to Investigate x‑Intercepts and Negative Slope |  |  |