### Unit 0 – Getting Started with Modeling

**Lesson 0.1 School Population**- Students devise a plan to estimate their school’s student population.

**Lesson 0.2 BINGO Card**- Students consider methods to determine the number of squares on a BINGO card.

**Lesson 0.3 Skeleton Tower**- Students create models to represent and determine the number of cubes in a tower.

**Lesson 0.4 Coin Switcheroo**- Students represent the switching of coin positions to examine patterns for minimum moves.

**Lesson 0.5 Something’s Fishy**- Students use relationships described among its parts to find the length of a fish.

**Lesson 0.6 The Path of a Billiard Ball**- Students use a model of billiards to determine patterns based on the path of the ball.

### Unit 1 – Relationships Between Quantities and Reasoning with Equations

**Lesson 1.1 Trapezoid Trains**- Students investigate patterns related to pattern block perimeters and areas.

**Lesson 1.2 Paper Stacks**- Students create models to explore patterns that introduce exponential growth.

**Lesson 1.3 Toothpick Polygons**- Students relate mathematical models to physical patterns of making regular polygons.

**Lesson 1.4 A New Look at Equations**- Students use properties of operations and structures of expressions to simplify and solve equations.

**Lesson 1.5 Tile Tools**- Students represent algebraic expressions and equations with algebra tiles to model simplifying and solving them.

**Lesson 1.6 The Mighty Dollar**- Students keep track of money exchanges using different models and strategies.

**Lesson 1.7 Equation Extravaganza**- Students use and compare different methods of solving equations.

**Lesson 1.8 Measuring Cups**- Students devise a model to keep track of a sequence of pours with a given pair of different capacity containers to determine possible quantities that can be made.

**Lesson 1.9 Formulas for Success**- Students use a formula to model the relationship of a situation based on its context in order to solve a problem.

**Lesson 1.10 Adjusting Grades**- Students determine algebraic relationships based on arithmetic strategies and patterns.

**Lesson 1.11 Them Bones**- Students measure and compare lengths of specific body parts to model relationships between those parts.

### Unit 2 – Linear and Non-Linear Relationships

**Lesson 2.1 Make a New Puzzle**- Students examine ways in which relationships between original and new puzzle pieces are modeled.

**Lesson 2.2 Number Sequences**- Students model number sequences to decide whether they are arithmetic or geometric.

**Lesson 2.3 Interpreting Graphs**- Students interpret numberless graphs to match the model with an appropriate context.

**Lesson 2.4 Rods and Spools**- Students look for patterns from models based on structures made of rods and spools.

**Lesson 2.5 Pizza Puzzler**- Students decide how many of various types of pizzas should be made for a fundraiser.

**Lesson 2.6 Stories and Graphs**- Students examine graphs to determine information about a bike trip and the number of drinks in a vending machine.

**Lesson 2.7 Grains of Rice**- Students start with the premise of one grain of rice on a chessboard square and double the number of grains on subsequent squares resulting in a significant amount of rice.

**Lesson 2.8 Waiting for Rock Concert Tickets**- Students examine how the number of people in line for a rock concert grows over time.

**Lesson 2.9 Painted Cubes**- Students consider relationships for the number of cubes with paint on 3, 2, 1, or 0 faces if a larger cube is painted and cut into 1-inch cubes.

**Lesson 2.10 Tables, Graphs, and Stories**- Students match tables, words, and graphs of relationships.

**Lesson 2.11 Going Viral**- Students explore situations to decide whether the scenarios are “going viral.”

**Lesson 2.12 Families of Lines**- Students use the graphs of lines in
*y*=*mx*+*b*form to see the relationship between values of the linear coefficient and the constant with slope and the*y*-intercept.

- Students use the graphs of lines in
**Lesson 2.13 Design-a-Box Contest**- Students determine how the size of squares cut from the corners of a piece of paper affects the volume of the open box formed.

**Lesson 2.14 Tower of Hanoi**- Students use simpler cases of explore relationships in the number of moves needed for the general case of the Tower of Hanoi.

### Unit 3 – Data and Decision Making

**Lesson 3.1 Water Spots**- Students explore the relationship between the number of drops of water and the size of the water spot.

**Lesson 3.2 CSI Hawai‘i**- Students explore using the length of a person’s foot to infer who might be involved in a clean-up.

**Lesson 3.3 Open the Elevators**- Students use modeling to suggest when students should have access to elevators to get to first period on time.

**Lesson 3.4 Talk versus Text**- Students examine data for trends in the number of different types of phone usage.

**Lesson 3.5 Chances Are**- Students gather data to explore a winning strategy for a game and to devise a plan for obtaining free tickets.

**Lesson 3.6 Granting Licenses**- Students explore relationships to decide how many new licenses to allocate.

**Lesson 3.7 Sports Connection**- Students analyze given data to help answer questions related to sports performances.

**Unit 3 Project Leaky Faucets**- Students use modeling to understand the amount of water wasted by leaky faucets.

**Lesson 3.8 Bouncing Ball**- Students study the relationship between the height from which a ball is dropped and how high it bounces.

**Lesson 3.9 Will Women Run as Fast as Men?**- Students explore existing data to predict if women will ever run as fast as men.

**Lesson 3.10 Knotty Rope**- Students investigate the effect of tying knots in a length of rope.

**Lesson 3.11 Bungee Jumping**- Students use toy models to make recommendations for a bungee jump attraction.

### Unit 4 – Expressions and Equations

**Lesson 4.1 Unpacking the***Think-of-a-Number*Game- Students explore how mathematical expressions can be used to model operations in number tricks.

**Lesson 4.2 Quilting Patterns**- Students consider linear and quadratic models for the numbers of different pieces used in quilt patterns.

**Lesson 4.3 Exploring Exponential versus Power**- Students study relationships and make comparisons between exponential and power functions.

**Unit 4 Project How is Our Environment Changing?**- Students investigate environmental issues and use mathematical models to report their findings.

**Lesson 4.4 Hawaii Population Growth and Food Production**- Students determine whether data on population and food supply fit linear or exponential models.

**Lesson 4.5 Enlightening Exonentials**- Students find patterns for the quotient of powers having the same base.

**Lesson 4.6 Response Time**- Students examine how an exponential function can model data.

**Lesson 4.7 Rods and Spools Extended**- Students look for patterns from models based on pentagons and hexagons made with rods and spools.

**Lesson 4.8 The Shape of a Bottle**- Students model relationships between measurements of a bottle in graphical form.

**Lesson 4.9 Hawaiian Bloodline**- Students think about racial lineage through models of exponential decay.

**Lesson 4.10 Twelve Days of MOW Class**- Students look for patterns among the number of items distributed over 12 days of mathematics class.

**Lesson 4.11 Order from Chaos**- Students generate and examine fractal patterns to determine models for their lengths or areas.

**Lesson 4.12 Skelteton Tower Revisited**- Students find a model to determine the number of cubes in towers of varying heights.

### Unit 5 – Quadratic Functions and Modeling

**Lesson 5.1 Interpreting Graphs of a Rocket**- Students decide which graphs model the height of a rocket over time.

**Lesson 5.2 The Perfect Arch**- Students use quadratic formulas that model data related to the paths of objects.

**Lesson 5.3 Families of Parabolas**- Students look for characteristics of quadratic equations that effect features of the graphs (for example, x- and y-intercepts, directions in which the parabolas face).

**Lesson 5.4 Area Maximized**- Students design a plan for a maximum area using a specified length to form three sides of a rectangle.

**Unit 5 Project Modeling in Your World**- Students apply what they have learned from this course by conducting investigations based on their own interests and presenting their data using various models and representations.

**Lesson 5.5 Diagnals in a Polygon**- Students discover the relationship between the number of sides and number of diagonals in a polygon.

**Lesson 5.6 Things That ‘Go Round**- Students compare the circumference of a ball with that of a hoop through which it is thrown.

**Lesson 5.7 L-Shaped Patios**- Students find the area of a patio that is the difference of two square regions.

**Lesson 5.8 Pancake Palace**- Students look for patterns about the number of chords on a circle and the maximum number of regions into which it is divided.

**Lesson 5.9 The Changing Value of Money**- Students study the exponential effects of both growth and decay relative to money.

**Lesson 5.10 Toothpick Revisited**- Students consider quadratic models for patterns of toothpick arrangements.

**Lesson 5.11 BINGO Revisited**- Students determine how square numbers are used in different ways to model patterns.

**Lesson 5.12 Odd Square Patterns**- Students examine a food basket liner to decide on mathematical models for its geometric design.

**Lesson 5.13 Going Around Again**- Students explore how much fencing is needed to build a fence a certain distance from a building.

**Lesson 5.14 Rods and Spools Finale**- Students generalize patterns from polygons made with rods and spools.