Using BOPPPS in Mathematics

David Molina - ACP Lone Star Adjunct Certification Program Portfolio
-April 18, 2016-

Table of Contents
Syllabus Snapshot………………………………………………………………………………Section 1.0
Student Preparation Strategy…………………………………………………………….Section 2.0
BOPPPS Lesson Plan…………………………………………………………………………..Section 3.0
……………………………………………. Pre-Assessment……………………………………………….3.1
……………………………………………. Instructional Presentation……………………………….3.2
……………………………………………. Instructional Technology…………………………………3.3
……………………………………………. C.A.T……………………………………………………………….3.4
……………………………………………. Questions………………………………………………………..3.5
……………………………………………. Exit Tickets………………………………………………………3.6
……………………………………………. Rubric……………………………………………………………..3.7
ACP Showcase………………………………………………………………………………………..Section 4
Reflective Essay………………………………………………………………………………………Section 5

In order to receive the best grade possible: Be On-time
Here are your test dates! Be Prepared
Be Respectful
 Test 1: Saturday February 20, 2016 Be electronic-device FREE
15% of Class grade March 12, 2016 Be yourself!
April 16, 2016
 Test 2: Saturday May 7, 2016
15% of Class grade Assigned Weekly
May 14, 2016
 Test 3: Saturday
15% of Class grade

 Test 4: Saturday
15% of Class grade

 Homework
20% of Class grade

 Final: Saturday
20% of Class grade

Chair of this class: Mr. David Molina Disaster only follows if you forget the
following:
Course: Math 0310.1601(1748)
 NO make-up exams, and NO late homework
Location: Winship Building 106  IT IS YOUR RESPONSIBILITY TO DROP THE

Time: Saturday: 8:00 – 12:15 pm; 1/23 – 5/14, 2016 CLASS
 IP only received if you participate!
E-mail: [email protected]
This syllabus doesn't constitute the entirety of the
Book: McKeague, C. (2012). Intermediate algebra: official syllabus. Syllabus can be found online at
xyzhomework.com
concepts with applications. Boston: Pearson.

ISBN: 9781936368068

Web sites:

http://nhmath.lonestar.edu;http://www.

xyzhomework.com

Student Prep Strategy

Created by David Molina on Mar 7, 2016 11:40 PM

In order for the students to read BEFORE the class, I would do the following:

Make available online a 3-question handout for three problems associated with each of the objectives in
the reading. Each question would be a sample problem worked out by the book in a specific section.
Student would only need to look for the problem under the specific objective, copy down how the book
solved the problem and also list the objective that was being satisfied, the page number and the correct
solution as per the book.

BOPPPS LESSON PLAN-David Molina

COURSE: Math 0310 Intermediate Algebra
Lesson Title: Relations and Functions (90-minute class)
Bridge: Recall your last time at the gas station filling up with gasoline. If you were to pay $1.89 per gallon, then you would have a linear equation that would
describe how much money you spent after putting in x gallons. Think about the possible values for your “x” or gallons. What is the smallest number you can
pick? What about the largest? Can you pick fractions of a gallon? What about negative values? In this section, you will be introduced to considerations on
values you pick to use inside any equation. You will describe input and output values for any type of equations. This will help you determine what the graph of
any equation looks like in any mathematics class.
Estimated time: 3 minutes

Course Student Learning Outcome:
Outcome 5: Recognize functions defined as sets of ordered pairs, graphs, and equations and apply function notation to application

Learning Objectives (these should be the ones you wrote in Module 1): By the end of this lesson, students will be able to
 identify, list, and explain when a relation is a function when given a graph, table, concept mapping, and an equation with 100% accuracy. (Knowledge,
Comprehension, Application):
 describe the domain and range of a relation and function in any one of three forms with a 100% accuracy. (Knowledge, Comprehension)
 evaluate and solve functions for specific values and given intervals with a 100% accuracy. (Application)
 compare and contrast two relations: 1/2 circle and circle giving domain and range of each and justifying naming one a function with 100% accuracy.
(Analysis)
 construct a graph of a function such as f(x)=x, g(x)=|x|, and examine the interval of the domain and range, while defending why the function created is
named a function with 100% accuracy. (Analysis, Synthesis, Evaluation)
 apply functions to a given word problem using script f and g notation with a 100% accuracy. (Application )

Pre-Assessment: ½ Sheet: Functions-Pre-Assessment.pdf
Students will work collaborative in pods of 3-4 in search of any background knowledge they may have in relations versus
functions, and determining domain and range of a function.

Estimated time: 5 minutes

Participatory Learning:

Time Instructor Activities Learner Activities Lesson Materials
Bridge.
3 mins introduce objectives and bridge discuss table with partners the possible parameters for
the scenario in the bridge Functions: Pre-
5 mins Introduce Pre-Assessment and parameters Students will work collaboratively determine how much Assessment.pdf
do they know about domain, range, and functions.

30 Instruct using Functions Powerpoint slide Learners will be working problems on slide alongside PowerPoint:
minutes instructor as guided practice. Functions and Relations

15 Using a PowToon cartoon, students will have an Inst. Tech: Identifying Domain and
minutes animated cartoon they can play over and over again. Range
The objectives have been reiterated throughout the
carton on how to identify the domain by giving specific
examples and using common language like "weirdness"
for undefined or "nonsensical" for restrictions on the
domain.

12 Distribute ½ Sheet: Relations and Functions.pdf CAT:
minutes Students will demonstrate with 100% accuracy that they Relations and
can determine domain and range of a function in various Function
forms using teacher-created material while working
collaborative.

Post-assessment: Review steps involved in determining the domain and range, after which post the 4 questions on the board. Have students respond answer

the four questions while working with groups. Be ready to present (each pod!)

 4 questions with Bloom’s level identified

Q1: Given y=f(x), please give the function for y = 3x - 2. (Bloom's Comprehension)

a) y=f(x) - 2 --Distractor: Student plugs in f(x) for 3x

b) y = 3f(x) - 2 --Distractor: Student plugs in f(x) for just the x

c) f(x)=3y - 2 --Distractor: Student plugs in f(x) for y but puts the y in place of x since student feels an equation needs to have

both.

d) f(x) = 3x - 2 --Correct: Student understands that wherever student sees an "y" then an "f(x)" may replace it.

Q2: If g(x) = -4 - x, what is the value for g(-2) (Bloom's Application)

a) -6 --Distractor: Student plugs in -2 for x but assumes the "-" already there belongs to the x, so solves -4-2, which is an

incorrect substitution.

b) -8 --Distractor: Student plugs in -2 for x but assumes multiplication since the "f" and the "x" looks like two letters side by

side.

c) -2 --Correct: Student plugs in -2 for x and evaluates -4 - (-2), which gives a correct answer of -2

d) 8 --Distractor: Student plugs in -2 correctly, changes the signs, but assumes multiplication since he "f" and the "x" looks

like two letters side by side

Q3: As Karen was working on the linear relation y = 2x + 5, Brenda wanted her to rename it as a function, f(x) = 2x + 5 to which Karen replied,

"There is no difference, so it doesn't matter." If you were Brenda, what would you say to Karen to defend renaming it while explaining the

differences between relations and functions. (Bloom's Evaluation)

Q4: Pretend you have landed a part-time job at Starbucks as a barista to help you pay for college. Starbucks pays you $13 per hour and you do
not work more than 20 hours. Using appropriate variables and fuctional notation, create a function that depicts your total wages per
workweek listing both the domain and the range of your function. (Bloom's Synthesis)

Estimated time: 10 minutes.

Summary: Distribute Exit Tickets: Functions and Relations: Students must answer correctly the domain and range of the given figure
and determine if it is a function or a relation or pick another before they exit class. Answers must be shared with class
Estimated time: 5 minute.

Independent Practice: HOMEWORK: Students will work on independent project based on a rubric for technology. Students will create their
own equations, identifying each respective domain and range and will bring to class the next day to share with class.

ATTACH ANY LESSON MATERIALS (SLIDES, HANDOUTS, ETC.)

How Much Do I Know about Relations and Functions?

For the figure below, determine the following: For the figure below, determine the following:
~ all the values of x that are associated with the ~ all the values of x that are associated with the

graph graph
~ all the values of y that are associated with the ~ all the values of y that are associated with the

graph. graph.
~ identify any x values that have more than one y ~ identify any x values that have more than one

value associated with it. y value associated with it.

x-values: ___________ x-values: ___________
y-values: ___________ y-values: ___________
repeating x-values: ___________ repeating x-values: ___________

Compare the two graphs and answers to the values. What do you see? Turn to your partner and share
your findings for 2 minutes. Allow your partner to respond as well.

How Much Do I Know about Relations and Functions?

For the figure below, determine the following: For the figure below, determine the following:
~ all the values of x that are associated with the ~ all the values of x that are associated with the

graph graph
~ all the values of y that are associated with the ~ all the values of y that are associated with the

graph. graph.
~ identify any x values that have more than one y ~ identify any x values that have more than one

value associated with it. y value associated with it.

x-values: ___________ x-values: ___________
y-values: ___________ y-values: ___________
repeating x-values: ___________ repeating x-values: ___________

Compare the two graphs and answers to the values. What do you see? Turn to your partner and share
your findings for 2 minutes. Allow your partner to respond as well.













































EXIT ONE RELATION OR FUNCTION EXIT ONE EXIT ONE RELATION OR FUNCTION EXIT ONE
RELATION OR FUNCTION RELATION OR FUNCTION
EXIT ONE RELATION OR FUNCTION EXIT ONE EXIT ONE RELATION OR FUNCTION EXIT ONE
RELATION OR FUNCTION RELATION OR FUNCTION
EXIT ONE EXIT ONE EXIT ONE EXIT ONE

EXIT ONE EXIT ONE EXIT ONE EXIT ONE

Math 0310 Molina
Relations and Functions
For each figure, determine the domain and the range. Explain if it is a function.

Math 0310 Molina
Relations and Functions
For each figure, determine the domain and the range. Explain if it is a function.

Making Relations Function

A one-to-one correspondence

Warm-Up

Instruct: Comparing Functions and Relations

GP: Comparing Functions and Relations

Instruct: Domain, Range, 1-1, Function

GP:

Instruct: Evaluate Function for Given Values

GP: Evaluate Function for Given Values

Instruct: Explain Domain, Range, Is it a Function or Relation

GP: Determine Domain, Range, Is it a Function or Relation

Instruct: Determine Domain, Range, Is it a Function or Relation

GP: Determine Domain, Range, Is it a Function or Relation

Instruct: Apply Functions to Word Problems

Instruct: Apply Functions to Word Problems

GP: Apply Functions to Word Problems

GP: Apply Functions to Word Problems

Closure: Exit Tickets

Name: David Molina

Department: Math 0310

Creating Questinos with Bloom’s Level Identified.

Directions: Review steps involved in determining the domain and range, after which post the 4 questions
on the flip board. Have students respond answer the four questions while working with groups. Be
ready to present (each pod!)

 4 questions with Bloom’s level identified

Q1: Given y=f(x), please give the function for y = 3x - 2. (Bloom's Comprehension)

a) y=f(x) - 2 --Distractor: Student plugs in f(x) for 3x

b) y = 3f(x) - 2 --Distractor: Student plugs in f(x) for just the x

c) f(x)=3y - 2 --Distractor: Student plugs in f(x) for y but puts the y in

place of x since student feels an equation needs to have both.

d) f(x) = 3x - 2 --Correct: Student understands that wherever student
sees an "y" then an "f(x)" may replace it.

Q2: If g(x) = -4 - x, what is the value for g(-2) (Bloom's Application)

a) -6 --Distractor: Student plugs in -2 for x but assumes the "-"

already there belongs to the x, so solves -4-2, which is an incorrect

substitution.

b) -8 --Distractor: Student plugs in -2 for x but assumes multiplication

since the "f" and the "x" looks like two letters side by side.

c) -2 --Correct: Student plugs in -2 for x and evaluates -4 - (-2), which

gives a correct answer of -2

d) 8 --Distractor: Student plugs in -2 correctly, changes the signs,
but assumes multiplication since he "f" and the "x" looks like two letters
side by side

Q3: As Karen was working on the linear relation y = 2x + 5, Brenda wanted her to
rename it as a function, f(x) = 2x + 5 to which Karen replied, "There is no difference, so it
doesn't matter." If you were Brenda, what would you say to Karen to defend renaming
it while explaining the differences between relations and functions. (Bloom's
Evaluation)

Q4: Pretend you have landed a part-time job at Starbucks as a barista to help you pay
for college. Starbucks pays you $13 per hour and you do not work more than 20 hours.
Using appropriate variables and fuctional notation, create a function that depicts your