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.
- 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.
