Download Unit 4-Functions Algebra I Essential Questions Enduring

Unit 4-Functions
Algebra I
3 Weeks
Essential Questions
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How can you represent and describe functions?
How can functions describe real-world situations, model predictions and solve problems?
Enduring Understandings
1. Functions are a mathematical way to describe relationships between two quantities that
vary.
2. Functions can be represented in a variety of ways
3. Many real world functional relationships can be represented by equations. Equations can
be used to find the solution of given real-world problems.
Content
Students will know…
Topics (Pearson):
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(4-1) Using Graphs to Relate Two Quantities
(4-2) Patterns and Linear Functions
(4-3) Patterns and Non-Linear Functions
(4-4) Graphing a Function Rule
(4-5) Writing a Function Rule
(4-6) Formalizing Relations and Functions
(5-2) Direct Variation
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Real world data can be modeled with a
function.
Functions can be written in various
forms, including graphs, tables and
equations.
Graphs can be translated to describe a
variety of situations.
Data that varies directly, can be written
in the form y = kx.
21st Learning Expectations
Students will be able to…
 Employ mathematical problem solving skills effectively.
 Make decisions and solve problems in independent and collaborative settings.
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Unit 4-Functions
Algebra I
3 Weeks
21st Century Learning Skills
Students will be able to…
 ML #4 – Model with mathematics.
 ML # 5 – Use appropriate tools strategically.
Connecticut State Standards
CCSS
 A-CED 2. Create equations with two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
 A-REI 10. Understand that the graph of an equation in two variables is the set of all its
solutions plotted in the coordinate plane, often forming a curve (which could be a line).
 F-IF 1. Understand that a function from one set (domain) to another set (range) assigns to
each element of the domain exactly one element of the range. If f is a function and x is an
element of its domain, then f(x) denotes the output of f corresponding to the input x. The
graph of f is the graph of the equation y = f(x).
 F-IF 2. Use function notation, evaluate functions for inputs in their domains, and interpret
statements that use functions notation in terms of a context.
 F-IF 4. For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities and sketch graphs showing key
features given a verbal description of the relationship. Key features include: intercepts;
intervals where the function is increasing, decreasing, positive or negative.
 F-IF 5. Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes.
 F-IF 7. Graph square root, cube root, and piecewise-defined functions, including step
functions and absolute value functions.
 F-IF 9. Compare properties of two functions each represented in a different way.
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Unit 4-Functions
Algebra I
3 Weeks
Objectives
Students will be able to….
 Interpret, sketch, and analyze graphs from situations.
 Identify relations and functions.
 Use the vertical line test to determine if a relation is a function.
 Use a function rule and function notation to evaluate a function at a particular value.
 Model functions using rules, tables of value and graphs.
 Identify independent and dependent variables for a given situation.
Assessments
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Quiz – EU1 Graphing Functions
Quiz – EU2 Identifying Functions
Quiz – EU3 Writing Function Rules
Unit Test - Functions
Resources
Algebra I - Pearson
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