ALEX Classroom Resource

  

Algebra II Module 2, Topic A: The Story of Trigonometry and Its Context

  Classroom Resource Information  

Title:

 Algebra II Module 2, Topic A: The Story of Trigonometry and Its Context

URL:

 https://www.engageny.org/resource/algebra-ii-module-2-topic-a-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 2, Topic A, students develop an understanding of the six basic trigonometric functions as functions of the amount of rotation of a point on the unit circle (F-TF.A.1), and then translate that understanding to the trigonometric functions as functions on the real number line (F-TF.A.2). Students study graphs of the functions to discover properties of the trigonometric functions (F-IF.C.7e).

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

b. Graph piecewise-defined functions, including step functions and absolute value functions.

c. Graph exponential functions, showing intercepts and end behavior.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a symbolic representation of a function (including linear, quadratic, absolute value, piecewise-defined functions, and exponential,
  • Produce an accurate graph (by hand in simple cases and by technology in more complicated cases) and justify that the graph is an alternate representation of the symbolic function.
  • Identify key features of the graph and connect these graphical features to the symbolic function, specifically for special functions:
      quadratic or linear (intercepts, maxima, and minima) and piecewise-defined functions, including step functions and absolute value functions (descriptive features such as the values that are in the range of the function and those that are not).
    1. Exponential (intercepts and end behavior).
Teacher Vocabulary:
  • x-intercept
  • y-intercept
  • Maximum
  • Minimum
  • End behavior
  • Linear function
  • Factorization
  • Quadratic function
  • Intercepts
  • Piece-wise function
  • Step function
  • Absolute value function
  • Exponential function
  • Domain
  • Range
  • Period
  • Midline
  • Amplitude
  • Zeros
Knowledge:
Students know:
  • Techniques for graphing.
  • Key features of graphs of functions.
Skills:
Students are able to:
  • Identify the type of function from the symbolic representation.
  • Manipulate expressions to reveal important features for identification in the function.
  • Accurately graph any relationship.
Understanding:
Students understand that:
  • Key features are different depending on the function.
  • Identifying key features of functions aid in graphing and interpreting the function.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.30.1: Define piecewise-defined functions and step functions.
ALGI.30.2: Graph functions expressed symbolically by hand in simple cases.
ALGI.30.3: Graph functions expressed symbolically using technology for a more complicated case.

a.
ALGI.30.4: Graph quadratic functions showing maxima and minima.
ALGI.30.5: Graph quadratic functions showing intercepts.
ALGI.30.6: Graph linear functions showing intercepts.

b.
ALGI.30.7: Define square root, cube root, and absolute value function.
ALGI.30.8: Graph piecewise-defined functions.
ALGI.30.9: Graph step functions.
ALGI.30.10: Graph cube root functions.
ALGI.30.11: Graph square root functions.
ALGI.30.12: Graph absolute value functions.

c.
ALGI.30.13 Identify exponential numbers as repeated multiplication.
ALGI.30.14 Rewrite exponential numbers as repeated multiplication.

Prior Knowledge Skills:
  • Demonstrate how to plot points on a coordinate plane using ordered pairs from a table.
  • Graph a function given the slope-intercept form of an equation.
  • Recognize the absolute value of a rational number is its' distance from 0 on a vertical and horizontal number line.
  • Define absolute value and rational numbers.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.12.30 Given the graph of a linear function, identify the intercepts, the maxima, and minima.

Tags: functions, graph, number line, trigonometry, unit circle
License Type: Custom Permission Type
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Comments

There are ten lessons on this topic.

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  This resource provided by:  
Author: Hannah Bradley
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