ALEX Lesson Plan

     

It's All in the Family

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  This lesson provided by:  
Author:Michelle Russell
System: Florence City
School: Florence High School
The event this resource created for:CCRS
  General Lesson Information  
Lesson Plan ID: 33143

Title:

It's All in the Family

Overview/Annotation:

Students will be motivated to learn how to build new linear functions from existing linear functions.  Students will bring pictures of themselves and their parents from home to personally involve them in the lesson.  Students will learn to use the patterns inherent in functions to quickly and accurately graph linear functions.  This lesson will only deal with vertical shifts and the steepness of the line.  Horizontal shifts will be dealt with in future lessons. In addtion, in future lessons  students will transfer this knowledge to also graph exponential, quadratic, and absolute value functions.

This is a College- and Career-Ready Standards showcase lesson plan.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
17. Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions.

a. Use arithmetic operations to combine different types of standard functions to write and evaluate functions.

Example: Given two functions, one representing flow rate of water and the other representing evaporation of that water, combine the two functions to determine the amount of water in a container at a given time.

b. Use function composition to combine different types of standard functions to write and evaluate functions.

Example: Given the following relationships, determine what the expression S(T(t)) represents.

Function Input Output
G Amount of studying: s Grade in course: G(s)
S Grade in course: g Amount of screen time: S(g)
T Amount of screen time: t Number of follers: T(t)
Unpacked Content
Evidence Of Student Attainment:
Students:
Given different types of standard functions
  • Use arithmetic operations to combine functions in context.
  • Use function composition to combine functions in context.
  • Write, evaluate, and interpret combined functions in context.
Teacher Vocabulary:
  • Function composition
Knowledge:
Students know:
  • Techniques to combine functions using arithmetic operations.
  • Techniques for combining functions using function composition.
Skills:
Students are able to:
  • Accurately develop a model that shows the functional relationship between two quantities.
  • Accurately create a new function through arithmetic operations of other functions.
  • Present an argument to show how the function models the relationship between the quantities.
Understanding:
Students understand that:
  • Arithmetic combinations of functions may be used to improve the fit of a model.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.17.1: Define functions, relations (ordered pairs), input, output.
ALGI.17.2: Recall how to complete input/output tables.
ALGI.17.3: Recall how to read/interpret information from a table.
ALGI.17.4: Identify algebraic expressions.
ALGI.17.5: Recall how to name points from a graph (ordered pairs).
ALGI.17.6: Recall how to name points on a Cartesian plane using ordered pairs.

a.
ALGI.17.7: Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.
ALGI.17.8: Set up an equation to represent the given situation, using correct mathematical operations and variables.

b.
ALGI.17.9: Add, subtract, and multiply polynomials, showing that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtration, and multiplication.

Prior Knowledge Skills:
  • Explain the distributive property.
  • Give examples of the properties of operations including distributive.
  • Combine like terms of a given expression.
  • Recognize the correct order to solve expressions with more than one operation.
  • Calculate a numerical expression (Ex. V=(4x4x4).
  • Choose the correct value to replace each variable in the algebraic expression (Substitution).
  • Calculate an expression in the correct order (Ex. exponents, mult./div. from left to right, and add/sub. from left to right).

Local/National Standards:

Look for and make use of structure- Math Practice Standard #7

Primary Learning Objective(s):

The student will be able to build new functions from existing functions.

Additional Learning Objective(s):

 
 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

The PowerPoint presentation It's All in the Family will be printed and distributed to students so they can participate and make notes during the presentation.

The students will bring a picture from home that includes them and their parents (optional). 

Whiteboards with coordinate planes and dry erase markers (if not available provide graph paper to students)

 

Technology Resources Needed:

PowerPoint presentation "It's All in the Family"

PowerPoint presentation "Parents and Their Babies" (optional)

iPads (optional) for student web search.  If students do not have access to the Internet, the teacher can present the PowerPoint presentation "Parents and Their Babies"

Background/Preparation:

Major concepts to be taught: the effect on the graph of replacing f(x) by f(x) + k, f(kx), and f(x+k), specifically in relation to linear functions.  The teacher should emphasize that new functions can be built from the "parent functions".

Student background- students should be able to graph a line when written in slope intercept form.

Teacher- should be familar with the PowerPoint presentation and work through the examples. 

Teacher- prepare a designated place in the classroom for students to put their pictures from home. 

  Procedures/Activities: 

Before: 

1. To review and activate prior knowledge students will graph a line (given in slope-intercept form).  Students will use their whiteboards with the coordinate plane and graph y = 3x + 2.  The students will hold up their whiteboards as they finish and the teacher will assess their graphs.

2.  Students will post the pictures that they brought from home at the front of the room (optional).  Students will be given a few minutes to look at the pictures brought in by their classmates.  The teacher will compare the pictures of students and their parents to "parent functions and their babies".  The students can comment on how they are similar to their parents and how they are different from their parents.

During:

3.  Students will use their iPad to search for pictures of baby animals and their parents.  Students will be given five minutes for this activity.  The timer will be projected for students to see.  (See attached PowerPoint 5-down) At the end of the five minutes students will share their favorite pictures.  If students do not have access to an Ipad or computer the teacher may choose to show the PowerPoint "Parents and Their Babies" (attached).

4.  The teacher and students will work through the PowerPoint "It's All in the Family" which will require the student to describe the changes that the functions undergo compared to the parent function.   The PowerPoint concludes with a "one-minute paper" which will be completed and turned in at the end of the period.

5.  Cooperative learning activity- Students will work in pairs.  Students will use their whiteboards with the coordinate plane. (graph paper could also be used)  Each group will be given laminated cards of linear functions.  One student will graph the linear function on the whiteboard and one student will compare the new function to the parent function.  The students will then swap tasks.   The teacher will walk around the room and assess the students understanding. (for suggested problems see attached "Linear Functions")

After:

6.  The students will have one minute to summarize what they have learned about building new functions. (this is found at the end of the PowerPoint "It's All in the Family")



Attachments:
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  Assessment  

Assessment Strategies

The students will hold up their whiteboards after graphing the linear function for the teacher to assess their understanding.

The teacher will walk around the room and observe students as they participate in the group activity.

The students will summarize what they have learned with a "one minute paper" which they will turn in at the end of the lesson.

Acceleration:

The lesson could be modified so that students who were already familiar with linear functions could use the same principles and build new exponential, quadratic, and absolute value functions.

Intervention:

Students who need extra assistance will be purposefully paired with another student who can help them with the lesson.

Khan Academy video tutorial

 

 


View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.