Applied Mathematics and Modeling

Mathematics: Algebra

Courtesy · Pride · Perseverance · Cooperation

Chargers Promoting Positive Change

The mission of AHS is to prepare all students to reach their potential by teaching them the knowledge, skills and behaviors necessary for academic, civic, and social success. Students will be college and career ready in the ever-changing technological world of the 21st century by meeting high expectations, engaging in authentic problem solving, and utilizing critical thinking.

Academic Expectations

· Apply critical thinking skills to solve problems

· Access, evaluate, apply, and communicate information and ideas through writing, speaking, and effective use of technology

· Read effectively for a variety of purposes

· Work independently, reflectively, and/or collaboratively to accomplish goals

Civic Expectation

· Demonstrate service to the school and community

Social Expectation

· Demonstrate respect for self, others, and property within our school community

Ansonia's Vision of a Graduate

Content Area: Mathematics	Course: Applied Mathematics and Modeling
Vision of Graduate: Communication & Collaborator Critical Thinking Life Long Learner Responsible Citizen	Standards for Mathematical Practice Make Sense of Problems and Persevere in Solving Them Reason Abstractly and Quantitatively Construct Viable Arguments and Critique the Reasoning of Others Model w/ Mathematics Use Appropriate Tools Strategically Attend to Precision Look For and Make Use of Structure Look For and Express Regularity in Repeated Reasoning
Unit Titles
Unit 1: Solving Equations
Unit 2: Angle and Segment Addition
Unit 3: Similarity and Proportions
Unit 4: Properties of Triangles
Unit 5: Graphing Linear Equations
Unit 6: Data and Statistics
Unit 7: Polynomials

Course Overview:

This course combines the study of some algebra I & II topics, introductory geometry topics with an SAT component. This class will focus on topics included on the SAT and work to intertwine them. Topics include, but are not limited to solving equations, graphing linear and quadratic equations, functions, factoring and solving quadratics, systems, volume and surface area of geometric figures, angle relationships and right triangle geometry. Fulfills Math Requirement

Unit 1: Solving Equations

Priority Standards:	Supporting Standards:
CCSS.Math.Content.HSA.REI.B.3 CCSS.Math.Content.HSA.REI.B.4 CCSS.Math.Content.HSA.CED.A.1	CCSS.Math.Practice.MP1 CCSS.Math.Practice.MP7 CCSS.Math.Practice.MP8
Big Ideas	Essential Questions
Different types of equations require specific methods for finding solutions, including linear, quadratic, and polynomial equations. Mastering algebraic techniques for solving equations is essential for modeling and solving practical problems in various fields. Solving equations is a fundamental skill assessed on standardized tests like the SAT, impacting college readiness and opportunities.	What are the different types of equations, and how can they be solved? How do we apply algebraic techniques to solve linear, quadratic, and higher-order polynomial equations? How can solving equations help us understand and model real-world scenarios? How are solving equations skills critical for success on the SAT?
AHS Expectations
Apply critical thinking skills to solve problems Work independently, reflectively, and/or collaboratively to accomplish goals
Skills (I will be able to…)
I can solve linear equations and inequalities using algebraic methods. I can solve quadratic equations using factoring, completing the square, and the quadratic formula. I can solve higher-order polynomial equations using appropriate algebraic techniques. I can apply solving equations skills to real-world problems and SAT practice questions. I can analyze and interpret solutions to equations within practical contexts.

Unit 2: Angle and Segment Addition

Priority Standards:	Supporting Standards:
CCSS.Math.Content.HSG.CO.C.9 CCSS.Math.Content.HSG.CO.C.10 CCSS.Math.Content.HSG.CO.C.11	CCSS.Math.Practice.MP5 CCSS.Math.Practice.MP6 CCSS.Math.Practice.MP7
Big Ideas	Essential Questions
Angle and segment addition are fundamental concepts in geometry that help in measuring and calculating the properties of geometric figures. Understanding the relationships and properties of angles and segments is crucial for solving geometric problems and proofs. Angle and segment addition principles are applied in real-world scenarios and are important for standardized tests like the SAT.	How can we use the concepts of angle addition and segment addition to solve geometric problems? What are the relationships between angles and segments in geometric figures? How can understanding angle and segment addition help in solving real-world problems and in preparing for the SAT? How do properties of angles and segments influence the measurement and calculation in geometry?
AHS Expectations
Apply critical thinking skills to solve problems Work independently, reflectively, and/or collaboratively to accomplish goals
Skills (I will be able to…)
I can use the Angle Addition Postulate and the Segment Addition Postulate to solve geometric problems. I can identify and apply relationships between angles and segments in geometric figures. I can solve problems involving the measurement and calculation of angles and segments in practical contexts. I can apply geometric principles involving angles and segments to SAT practice questions and real-world scenarios. I can analyze geometric figures to determine missing angles and segment lengths using addition postulates.

Unit 3: Similarity and Proportions

Priority Standards:	Supporting Standards:
CCSS.Math.Content.HSG.SRT.A.1 CCSS.Math.Content.HSG.SRT.A.2 CCSS.Math.Content.HSG.SRT.A.3	CCSS.Math.Practice.MP4 CCSS.Math.Practice.MP5 CCSS.Math.Practice.MP7
Big Ideas	Essential Questions
Similar figures have the same shape but not necessarily the same size, and they follow specific criteria such as angle congruence and proportionality of sides. Proportions are equations that state two ratios are equivalent, and they are essential for solving problems involving similar figures. Understanding similarity and proportions is crucial for solving various geometric problems and has applications in real-world contexts and standardized tests like the SAT.	How do we determine if two figures are similar? What are the properties and criteria for similarity in geometric figures? How can proportions be used to solve problems involving similar figures? How can understanding similarity and proportions help in solving real-world problems and in preparing for the SAT?
AHS Expectations
Apply critical thinking skills to solve problems Work independently, reflectively, and/or collaboratively to accomplish goals
Skills (I will be able to…)
I can determine if two figures are similar by using angle congruence and side proportionality criteria. I can set up and solve proportions to find missing side lengths in similar figures. I can apply properties of similar figures to solve real-world problems, such as scaling and map reading. I can analyze and interpret similarity and proportion problems in SAT practice questions. I can use similarity and proportionality concepts to solve complex geometric problems.

Unit 4: Properties of Triangles

Priority Standards:	Supporting Standards:
CCSS.Math.Content.HSG.CO.C.10 CCSS.Math.Content.HSG.SRT.B.5 CCSS.Math.Content.HSG.SRT.C.8	CCSS.Math.Practice.MP4 CCSS.Math.Practice.MP5 CCSS.Math.Practice.MP7
Big Ideas	Essential Questions
Triangles can be classified by their side lengths (scalene, isosceles, equilateral) and angles (acute, right, obtuse), each with specific properties. Special triangles, such as 30-60-90 and 45-45-90 triangles, have unique properties that simplify solving geometric problems. Understanding triangle properties is essential for solving real-world problems and is a key component of standardized tests like the SAT.	What are the fundamental properties and classifications of triangles? How can we use triangle properties to solve geometric problems? What is the significance of special triangles (e.g., isosceles, equilateral, and right triangles) in geometry? How can understanding the properties of triangles help in solving real-world problems and in preparing for the SAT?
AHS Expectations
Apply critical thinking skills to solve problems Work independently, reflectively, and/or collaboratively to accomplish goals
Skills (I will be able to…)
I can classify triangles based on their side lengths and angles. I can use properties of triangles to find missing side lengths and angle measures. I can solve problems involving special triangles using their unique properties. I can apply triangle properties to solve real-world problems, such as construction and navigation. I can analyze and solve triangle problems in SAT practice questions using geometric principles.

Unit 5: Graphing Linear Equations

Priority Standards:	Supporting Standards:
CCSS.Math.Content.HSF.IF.B.4 CCSS.Math.Content.HSF.IF.C.7a CCSS.Math.Content.HSA.REI.D.10	CCSS.Math.Practice.MP1 CCSS.Math.Practice.MP4 CCSS.Math.Practice.MP5
Big Ideas	Essential Questions
Linear equations are used to model and solve a variety of real-world problems, including trends in data and relationships between variables. Graphing linear equations is crucial for visualizing and interpreting data, making predictions, and solving practical problems.	How do we graph linear equations on the coordinate plane? What is the significance of slope and y-intercept in the context of linear equations? How can we use linear equations to model and solve real-world problems? How does graphing linear equations help in understanding and interpreting data?
AHS Expectations
Apply critical thinking skills to solve problems Work independently, reflectively, and/or collaboratively to accomplish goals
Skills (I will be able to…)
I can graph linear equations using slope-intercept form, point-slope form, and standard form. I can interpret the slope and y-intercept of a linear equation in the context of real-world situations. I can use linear equations to model real-world problems and make predictions based on the graph. I can analyze and interpret graphs of linear equations in SAT practice questions. I can solve problems involving linear relationships by graphing and interpreting the results on the coordinate plane.

Unit 6: Data and Statistics

Priority Standards:	Supporting Standards:
CCSS.Math.Content.HSS.ID.A.1 CCSS.Math.Content.HSS.ID.A.2 CCSS.Math.Content.HSS.ID.A.3 CCSS.Math.Content.HSS.ID.B.5	CCSS.Math.Practice.MP2 CCSS.Math.Practice.MP4 CCSS.Math.Practice.MP5
Big Ideas	Essential Questions
Measures of central tendency (mean, median, mode) and variability (range, interquartile range, standard deviation) are essential for summarizing and interpreting data sets. Statistical methods help in making predictions, analyzing trends, and making informed decisions based on data. Probability and statistics are applied in various real-world contexts, such as business, healthcare, and social sciences, to analyze trends and solve problems.	How do we collect, organize, and display data effectively? What are the measures of central tendency and variability, and how do they describe data sets? How can statistical methods be used to interpret data and make informed decisions? How are probability and statistics used to solve real-world problems and analyze trends?
AHS Expectations
Apply critical thinking skills to solve problems Work independently, reflectively, and/or collaboratively to accomplish goals
Skills (I will be able to…)
I can collect, organize, and display data using tables, charts, and graphs. I can calculate and interpret measures of central tendency (mean, median, mode) and measures of variability (range, interquartile range, standard deviation). I can use statistical methods to analyze data sets and make informed decisions. I can apply concepts of probability to real-world scenarios and calculate probabilities of events. I can interpret and analyze statistical data in SAT practice questions and real-world problems.

Unit 7: Polynomials

Priority Standards:	Supporting Standards:
CCSS.Math.Content.HSA.APR.A.1 CCSS.Math.Content.HSA.APR.B.2 CCSS.Math.Content.HSA.SSE.B.3	CCSS.Math.Practice.MP1 CCSS.Math.Practice.MP3 CCSS.Math.Practice.MP7
Big Ideas	Essential Questions
Polynomials are algebraic expressions consisting of variables and coefficients, and they are classified by degree and number of terms. Performing operations with polynomials involves applying algebraic rules to add, subtract, multiply, and divide polynomial expressions. Polynomial functions model a variety of real-world situations, including physics, engineering, and economics.	What are the key characteristics and structures of polynomial expressions? How can we perform operations (addition, subtraction, multiplication, division) with polynomials? How are polynomial functions used to model and solve real-world problems? What methods are used to factor polynomial expressions, and how does factoring help in solving polynomial equations?
AHS Expectations
Apply critical thinking skills to solve problems Work independently, reflectively, and/or collaboratively to accomplish goals
Skills (I will be able to…)
I can identify and classify polynomial expressions by their degree and number of terms. I can perform addition, subtraction, multiplication, and division operations with polynomials. I can apply polynomial functions to model real-world problems and interpret their solutions. I can factor polynomial expressions using methods such as factoring by grouping, using the distributive property, and applying special product formulas. I can solve polynomial equations by factoring and using the Zero Product Property.