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Algebra 1 - Modeling Life With Functions

archives"Mathematics provides a powerful way of making sense of the world in which you live."

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Unit 1: Overview of Functions (4 weeks)

This first unit sets the stage for the year. The big idea is that many different functions can be used to model real life and these functions help us make predictions and solve problems. This unit introduces the idea of a function and exposes students to six types. Vocabulary and function language is introduced.  Students will grow in their understanding and mastery of vocabulary such as domain and range as well as use of function notation throughout the year.

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Unit 2: Linear Models (6 weeks)

This unit will focus on analyzing data that has a strong correlation. What linear model best fits? How do you write equations for such models? How do you use the model to answer questions? Explicit and recursive formulas will be used to describe linear relationships: (repeated addition)
Graphical, numerical, and algebraic techniques will be used to solve linear equations.

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Unit 3: Systems of Equations (4 weeks)

This unit will focus on solving systems of linear equations graphically, numerically, and analytically.

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Unit 4: Absolute Value Functions (3 weeks)

This unit will focus on analyzing data that is best modeled with an exponential function.  What model best fits?  How do you write equations for such models?  How do you use the model to answer questions?
Graphical and numerical techniques will be used to solve exponential equations.
Explicit and recursive formulas will be used to describe exponential relationships:  (repeated multiplication)

We will also work with the properties of exponents.

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Unit 5: Quadratic Models (6 weeks)

This unit will focus on analyzing data that is best modeled with a quadratic function. What quadratic model best fits? How do you write equations for such models? How do you use the model to answer questions? Graphical and numerical techniques will be used to solve quadratic equations. Various forms of quadratic functions as well as key features of quadratic graphs will be the focus.

Furthermore, the skills needed to understand quadratic expressions will be studied—expanding, factoring, completing the square, the quadratic formula, and solving quadratic equations algebraically.

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Unit 6: Radical Functions (3 weeks)

Launching from the idea of fractional exponents in exponential models, we will look at radical functions.  Simplified radical forms, domain and range, and function notation will be the focus.
Graphical and numerical techniques will be used to solve radical equations.

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Unit 7: Analyzing Data (3 weeks)

This unit will look at specifically at how data relates to life. In particular we will look at causality vs. association, making conclusions from data, and analyze effects of linear transformations on statistical measures.

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Unit 8: Exponential Models (4 weeks)

This unit will focus on analyzing data that is best modeled with an exponential function. What model best fits? How do you write equations for such models? How do you use the model to answer questions? Graphical and numerical techniques will be used to solve exponential equations. Explicit and recursive formulas will be used to describe exponential relationships: (repeated multiplication) We will also work with the properties of exponents.

 

 

 

 

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