Red Comet

## Course Details:

This course focuses on modeling with mathematics and problem-solving. The course emphasizes reasoning with math, statistics, probability theory and describing data using graphs and models. Students conduct and analyze research and study concepts in probability and modeling using these concepts.

## Syllabus:

Unit 1 - Mathematical Reasoning Objectives:
• Recognize different number forms
• Estimate the solutions of equations.
• Understand when to use scientific notation.
• Convert numbers in standard form to scientific notation and vice versa.
• Determine the reasonableness of solutions
• Recognize data patterns.
• Represent data graphically.
• Identify independent and dependent quantities.
• Gather and display data in tables, charts, and graphs.
• Write equations or inequalities to model data and predict future trends.
• Represent real-world problems involving data.
• Transform equations using the properties of addition and multiplication.
• Identify slope and intercepts.
• Use direct variation and proportions to solve problems
• Solve systems of equations.
Lessons:
• Real Numbers
• Numbers Forms For Solving Problems
• Scientific Notation
• Data Representation
• Relations and Functions
• Function Rules
• Properties of Addition and Multiplication
• Slope and Intercepts of Functions
• Direct Variation and proportional change
• Solving Systems of Equations
Unit 2 - Geometry, Probability and Statistics, and Problem Solving Objective:
• Plot points on the coordinate plane.
• Use dilations, reflections, and translations to create similar shapes.
• Apply right triangle properties to solve problems.
• Find the area and perimeter of two-dimensional figures.
• Find the volume and surface area of three-dimensional figures.
• Use proportions and formulas to solve real-world problems.
• Determine the probabilities of dependent and independent events.
• Compare theoretical and experimental probabilities.
• Define range, mean, median, and mode.
• Display data using various types of graphs.
• Analyze graphs and sampling methods.
• Use multiple mathematical processes to solve real-world problems.
• Identify and analyze given information in math problems.
• Apply proper formulas to real-world situations.
• Develop problem-solving strategies.
• Use appropriate properties and terminology to describe and communicate processes mathematically.
Lessons:
• Using the Coordinate Plane
• Right Triangle Properties and Problems
• Perimeter, Area, and Volume
• Proportions and Formulas in Problem Solving
• Probability
• Understanding Data
• Sampling Methods
• Applied Mathematics
• Using the Language of Mathematics to Communicate
Unit 3 - Describing Data Using Graphs and Models  Objectives:
• Understand and identify the slope and intercepts of linear equations.
• Develop and interpret circle and line graphs for real-world applications.
• Create scatter plots and write equations using technology.
• Create and understand the use of box and whisker plots to display central tendencies.
• Demonstrate correlations between mean, median, and mode.
• Analyze data for central tendencies.
• Understand and know how to calculate standard deviation.
• Determine appropriate models for data.
• Understand and calculate quadratic and exponential equations.
• Know how to graph quadratic and exponential equations using a calculator.
Lessons:
• The Slope and Intercepts of Linear Equations
• Circle Graphs and percentages
• Scatter Plots and Line of Best Fit
• Box and Whisker Plots
• Measures of Central tendencies
• Variability and Standard Deviation
• Exponential Functions and Equations
Unit 4 - Conducting and Analyzing Research Objectives:
• Understand the purpose of a research question.
• Define and understand what makes a good hypothesis.
• Learn how to collect and analyze data.
• Know how to draw conclusions given a set of data.
• Know the questions that must be answered when communicating research findings.
• Use appropriate terminology, such as randomand unbiased, to explain data and results.
• Validate hypotheses and conclusions using data.
• Understand how to choose an appropriate method to display results.
• Recognize linear, quadratic, and cubic models from a given set of data.
• Find the equations of linear, quadratic, and cubic models.
• Make predictions from a given set of data.
Lessons:
• Research Questions and Hypotheses
• Gathering Data
• Analyzing Data and Drawing conclucions
• Explaining data and Validating Conclusions
• Presentation Methods
• Linear Model Data
• Cubic Model Data
Unit 5 – Probability Objectives:
• Define theoretical probability.
• Determine the theoretical probability of dependent and independent events.
• Calculate factorials, permutations, and combinations.
• Define empirical probability.
• Determine outcomes for empirical probability.
• Understand the difference between theoretical and empirical probability.
• Calculate possible outcomes using theoretical or empirical models.
• Understand and calculate the mean, variance, and standard deviation in probabilities.
• Define, determine, and compare and contrast binomial probability using real-life examples and experiments.
Lessons:
• Dependent and Independent Events
• Factorials, Permutations, and Combinations
• Calculating Empirical Probability
• Applying Empirical Probability
• Comparing Theoretical and Empirical Probabilities
• Mean and Probability Distribution
• Variance and Standard Deviation
• Binomial Probability
• Comparing Binomial Models