ALEX Learning Activity

  

Radical Graphs Matter Sequel

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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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: 2565
Title:
Radical Graphs Matter Sequel
Digital Tool/Resource:
Graphing Calculator/Desmos.com/Graph boards
Web Address – URL:
Overview:

Students will graph functions on a piece of large graph paper as a group. The teacher will display the finished product in the classroom or hallway.

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 students will demonstrate their ability to graph a variety of functions and label key features (zeros, intercepts, end behavior, period, amplitude, and others not listed) of the functions.  
  Strategies, Preparations and Variations  
Phase:
After/Explain/Elaborate
Activity:

1. The teacher will provide the students with a list of functions to pick from or assign specific functions. (The functions can include radical, quadratic, absolute value, reciprocal, and trigonometric functions.)

2.  The students will graph their functions and label key features.  

3.  Students can use www.desmos.com or a graphing calculator to check graphs before drawing them on the large graph paper. If the teacher does not have large graph paper then the students can use individual graph boards and will not need desmos.com.

 
Assessment Strategies:

Students will demonstrate their ability to graph functions and label key features on those graphs by graphing the given functions. The teacher will determine if the student has successfully displayed their ability to graph functions and reteach in small groups as needed.

 
Advanced Preparation:

The teacher will create a list of functions to have the students graph in a group. The teacher will need poster-sized graph paper. They will also need a set of graphing calculators or computers/Chromebooks if using the digital tool. The students will need yardsticks and markers for the poster-sized graph paper. (If the teacher does not have the poster-sized graph paper, individual graph boards can be used to assess understanding.)

The groups of two to four students would be appropriate for this activity. The teacher can use a deck of cards to randomly assign members to the groups or the members can be assigned to the groups by ability.
Variation Tips (optional):

If the teacher does not have the poster-sized graph paper, the students can do the graph on individual graph boards. If students need remediation the teacher can use small group instruction time to help the students. 
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, desmos, domain, end behavior, graph, parent functions, radical functions, range