ALEX Learning Activity

  

Radical Graphs Matter Prequel

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  This learning activity provided by:  
Author: Susan Honeycutt
System:Blount County
School:Locust Fork High School
  General Activity Information  
Activity ID: 2564
Title:
Radical Graphs Matter Prequel
Digital Tool/Resource:
Desmos.com Graphing Calculator
Web Address – URL:
Overview:

Students can graph the parent functions. They will use paper and pencil to graph the basic parent functions and list the key features of each function.  

This activity results from the ALEX Resource Development Summit.
  Associated Standards and Objectives  
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.

Learning Objectives:

The student will graph the parent function of various functions (square root, absolute value, quadratic, and trigonometric functions, to name a few) and list key features.
  Strategies, Preparations and Variations  
Phase:
Before/Engage
Activity:

1. The teacher will need a list of the parent functions and their graphs.

2. Students will need graph paper, rulers, pencil, and a list of the parent functions.  

3. The teacher will have the students graph the parent functions on graph paper. After they have completed this part of the task then the students can use graphing calculators to check their graphs. If the students do not have graphing calculators then they can use the graphing calculator online at www.desmos.com. Then the students need to record key features of the graph on their paper (such as zeros, intercepts, end behavior, etc.).

4. After students have checked their work they may turn it in for grading.

5. The teacher will monitor students' progress and assist students as needed. This activity can be done without modeling to see where the students are on their knowledge of graphing. After determining their level, modeling can be done to assist, or you may do before as you deem necessary.
Assessment Strategies:

The students will demonstrate their ability to graph the parent functions by drawing them on graph paper and turning them into the teacher. The student will also demonstrate their ability to label the key features of the graph. The teacher will determine if the students have successfully completed this task and return the graphs with a grade. If the teacher deems the graphs unsuccessful, then they will reteach using small group time.
Advanced Preparation:

The teacher will need to make a list of the parent functions from the website provided. Teachers will need a set of graphing calculators or access to an internet-capable device. Teachers who have a set of individual graphing boards can use them instead of the computer or calculators. The students will need graph paper, rulers, pencils, and a list of the parent functions.
Variation Tips (optional):

The parent functions can be used later to teach the transformations of functions. If the teacher has not taught that lesson yet, they can use the results from this activity to save time and not have to recreate the graphs.
Notes or Recommendations (optional):

ALCOS 2019

20. Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases. Extend to polynomial,
trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise
functions.
a. Graph polynomial functions expressed symbolically, identifying zeros when suitable
factorizations are available, and showing end behavior.
b. Graph sine and cosine functions expressed symbolically, showing period, midline, and
amplitude.
c. Graph logarithmic functions expressed symbolically, showing intercepts and end
behavior.
d. Graph reciprocal functions expressed symbolically, identifying horizontal and vertical
asymptotes.
e. Graph square root and cube root functions expressed symbolically.
f. Compare the graphs of inverse functions and the relationships between their key
features, including but not limited to quadratic, square root, exponential, and logarithmic
functions.
  Keywords and Search Tags  
Keywords and Search Tags: coordinate plane, domain, end behavior, graph, parent functions, radical functions, range