Course Outline

Overarching Enduring Understandings for the Course

• Mathematics takes on meaning when applied to problem solving situations
• Our number system describes quantities and operations on quantities in an orderly and predictable way.
• Measurement allow people to more accurately describe and interpret our world
• Spatial understandings are necessary for interpreting, describing, and appreciating our inherently geometric world.
• Probability is the tool used for anticipating what the distribution of data should look like under a given model.
• Problem situations can be represented, simplified, and solved with algebraic expressions and equations.

Unit 1 – Mathematical Models

Enduring Understandings

• Mathematics uses models to best represent information
• Mathematical models can be used to make predictions

Essential questions

• How do I build and analyze mathematical models
• How can I conduct experiments to gather data about how variables are related?
• How can I make predictions using a given model?

Knowledge and skills

• Interpret data on a graph and in a table
• Use a line of best fit to predict and explain data
• Explain the difference between linear and non-linear relationships.
• Represent variable quantities, through expressions, linear equations, inequalities, tables, and graphs of situations.
• Develop skill in collecting data from experiments and recording that data in tables
• Construct coordinate graphs to represent data
• Make predictions from data tables or graph models
• Use patterns in data to find equations that model relationships.
• Identify inverse relationships and describe their characteristics

Unit 2-The Pythagorean Theorem

Enduring Understandings

• There are different ways to describe and write numbers

Essential questions

• What are irrational numbers and how do I see them on a number line?
• How can I represent the same number in different ways?

Knowledge and skills

• Understand relationships between coordinates, slope, distance, and area
• Relate the area of a square to the length of a side
• Develop strategies for finding the distance between two points on a graph
• Discover and apply the Pythagorean theorem
• Extend understanding of number systems to include irrational numbers
• Locate irrational numbers on a number line
• Represent fractions as decimals and decimals as fractions
• Determine whether the decimal representation for a fraction terminates or repast
• Use slopes to solve interesting problems

Unit 3-Exponenital Relationships

Enduring Understanding

• Nature models exponential growth and decay in many ways
• Different data produces different shapes of graphs

Essential Questions

• What is the relationship between the data that is gathered and the shape of the graph it produces?
• Where does nature model exponential growth and decay?

Knowledge and skills

• Recognize and describe situations in which variables grow and decay exponentially
• Recognize and represent exponential patterns with tables, graphs, and equations
• Compare and contrast exponential relationships with linear relationships
• Determine growth factors and decay factors in exponential situations
• Use tables, graphs and equations to solve problems involving exponential growth and exponential decay
• Describe the effects of varying the values of a and b in the equation y=a(b^x) on the graph of that equation

Unit 4-Algebraic Reasoning

Enduring Understandings

• Equations represent real life situations
• Mathematics is systematic and done in a certain order

Essential Questions

• Why does it matter the order that I perform operations in an equation?
• How can an equation represent a real life situation and how can I change the equation to give different information?

Knowledge and skills

• Review and strengthen understanding of the conventional order of operation rules in the context of practice problems
• Evaluate expressions using order of operations
• Write symbolic sentences that communicate reasoning
• Recognize applications of the distributive and commutative properties
• Recognize and interpret equivalent expressions
• Explain the reasoning behind the solution of linear equations
• Understand and use symbolic expressions involving addition , subtraction, multiplication, division, and exponents
• Judge the equivalency of two of more expressions by examining the underlying reasoning and the related tables and graphs
• Apply the properties for mathematically manipulating expressions to solving linear equations
• Solve simple quadratic equations demonstrating and understanding of basic factoring techniques

Unit 5- Symmetry and Transformations-

Enduring Understandings

• Nature and art demonstrates symmetry and transformations
• We can use patterns to predict attributes of design

Essential Question

• Where do we see symmetry appear in nature?
• How do you use patterns to make predictions?

Knowledge and skills

• Understand important properties of symmetry
• Recognize and describe symmetries of figures
• Use tools to examine symmetries and transformations
• Create figures with specified symmetries
• Identify basic design elements that can be used to replicate a given design
• Perform symmetry transformations of figures, including reflections, translations, and rotations
• Give precise mathematical directions for performing reflections, rotations, and translations
• Write coordinate rules for specifying the image of a general point under particular transformations
• Combine transformations and find a single transformation that will produce the same result
• Find the symmetries of geometric figures and make tables showing the results of combining symmetry transformations
• Learn to appreciate the power of transformational geometry to describe motions, patterns, and designs in the real world

Unit 6-Data and Statistics

Enduring Understandings

• Graphical displays are created for the purpose of analysis and communication
• Careful planning is essential to obtaining valid data

Essential Questions

• How do we obtain data
• What does it mean to be a random sample and why is that important?

Knowledge and Skills

• Use statistical investigation to explore problems
• Analyze data using tables, stem-and-leaf plots, histograms, and box-and-whiskers plots
• Compare data using mean, median, range, percentiles, and data displays
• Explore relationships among data using scatter plots
• Distinguish between samples and populations, compare samples, and use information to make conclusions
• Apply the concepts of probability to understand the concept of randomness and to select random samples
• Explore the concepts of representativeness and sample size as they relate to using random and nonrandom samples to draw conclusions about the characteristics of populations
• Design a survey, focusing on how questions are asked

Unit 7-Probability

Enduring Understandings

• Probability is the tool used for anticipating what the distribution of data should look like under a given model
• Probability models are useful tools for making decisions and predictions

Essential Questions

• When is probability a sure thing?
• How can we base decisions on chance?

Knowledge and Skills

• Know when to use counting techniques
• Make lists of outcomes and find patterns
• Make and use counting trees
• Use estimation skills to make predictions
• Determine problem solving strategies that include counting
• Differentiate problems where order matters and where it doesn’t
• Analyze the number of paths in a network