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Standards-Aligned Lesson Plan Template

Subject(s): Enhanced Mathematics 1 Grade: 8

Teacher(s):Miss Morgan Haner Date: N/A


1. Common Core Learning Standard(s) Addressed:
F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship,

2. State Content Standard Addressed (History/Social Science, Science, Physical Education, Visual and Performing Arts):


3. ELD Standard Addressed: (include Part I, II; Communicative Modes – A. Collaborative, B. Interpretive, C. Productive; and Proficiency
Level addressing – Emerging, Expanding, Bridging)
ELD.PI.8.1 Exchanging information and ideas with others through oral collaborative discussions on a range of social and academic topics.
ELD. PI.8.3. Offering and justifying opinions, negotiating with and persuading others in communicative exchanges.
ELD.PII.8.6. Connecting ideas

4. Learning Objective: (What will students know & be able to do as a result of this lesson?) STUDENT-FRIENDLY TRANSLATION
I can identify and define arithmetic and
Students will be able to identify and define arithmetic and geometric sequences by connecting these geometric sequences by participating in
new concepts to their prior knowledge of linear and exponential functions. the inside-outside-circle activity and
completing the worksheet.

5. Relevance/Rationale:(Why are the outcomes of this lesson important in the real world? Why STUDENT-FRIENDLY TRANSLATION
are these outcomes essential for future learning?)(TPE1.3) I can solve problems using what I
Students will work together and develop 21st century skills to solve problems using their prior already know.
knowledge as a resource.

6. Essential Questions (TPE1.5):

 What do the patterns discussed in the activity “Inside-Outside Circle” remind us of?
 Is an arithmetic sequence linear or exponential?
 Is a geometric sequence linear or exponential?
 What mathematical vocabulary words that we used for linear and exponential functions can we use to describe arithmetic and geometric
 What is significant about common difference and common ratio and how do we find them in our sequences?
 When looking at our graph on Demos, what can we conclude about these sequences?

Part II – STUDENTS’ INFORMATION (TPE1.1,3.2,4.1,4.2, 4.5 SSP-DAP)

7. Class Information:

a. Total number -
30 Students
b. English Learners/Standard English Learners –
1 English Learner (First Language: Mandarin)
c. Students with Special Needs –
d. Academic language abilities, content knowledge and skills in content area (TPE5.2) -
Students will know vocabulary words for linear and exponential functions. The vocabulary words that they know are: linear,
exponential, additive change, multiplicative change, constant rate of change, growth, and decay. Students use complete sentences
when talking to each other, and in their written responses.

e. Linguistic background–

87% of students in the classroom are English Only. There are two R-FEP students who speak Spanish. There is one I-FEP students
who speaks Armenian. There is one English Learner who speaks Mandarin Chinese.

f. Cultural background (home/family) –

75% of the school’s population is Hispanic. This is found true in the classroom as well.
g. Health considerations (if any) –
3 Environmental Allergies. 3 Nut Allergies. 1 Autoimmune disorder.
h. Physical development factors that may influence instruction in this academic content area–
Typical development:
 Mental development: Students are flexible with their thinking and are able to check their work. Useful in inquiry/discovery

i. Social development factors that may influence instruction in this academic content area –
The majority of my students come from low socioeconomic Hispanic families. Therefore, before the semester, most of the students
lacked communication or collaboration skills. Their interactions between their peers were minimal and not effective. Because of the
type of lessons planed and the environment that was created, students now are capable of effectively communicating and participating
in 21st century skills such as collaboration, communication, creativity, and critical thinking. They socially are able to cooperate with
peers and adults. They formulate their thoughts and sophisticatedly present them. Because of their background, it is important to
constantly practice cooperation and the other 21st century skills necessary for their future high school, college and career experiences.

j. Emotional development factors that may influence instruction in this academic content area –
1 student is self-identified as gay.
k. Interests/Aspirations (relevant to this academic area)–
This class is Enhanced Mathematics 1. This means that these are eighth grades in a high school level math class. They have high
expectation as students, and have high expectations for themselves. They all plan to go to Estancia High school, and will further their
education after high school by attending various colleges. Because this is an enhanced honors course, all of these students love and
or are good at math. It is obvious in their participation effort in and outside of the classroom.

8. Anticipated Difficulties(Based on the information above, what difficulties do you think students may have with the content? Please
specify anticipated difficulties for English Learners, Standard English Learners, and/or students with special needs. )):
 English Learner: My English Learner is on level 4 of the CELDT. Her scores describe her as being “Early Advanced.” Even though they
are close to proficiency, there are still difficulties that they face. Their lowest score on the CELDT was speaking. Before looking at their
scores, it was obvious that speaking was their weakest skill. Because this student is still an English Learner, the academic vocabulary may
serve as a challenge. Mathematics, being a language of its own, is hard for all students to learn, especially English Learners. This lesson
has many new mathematical terms.
 504 Student: The student has a 504 for handwriting. This disability does not harm their academic performance, but could hinder them if
the teacher is unable to read it. This student will have trouble writing their answers within the given lines for their responses for the activity.
In this activity, the students will be asked to write out several components in their own words such as reasoning for grouping; definitions
for words such as arithmetic, geometric, common difference, and common ratio; and finally what they noticed about the graphs that they
drew. Students will also have to fill in T-Charts and graph their own graph. Because of the student’s condition, they will have difficulties
writing the responses needed.
 All Students: Because this lesson is an outside cooperative activity, classroom management will need to be utilized and kept. Students
will want to talk and mess around because this outside activity is out of the norm. The hook of the lesson (cooperative activity) will be
strictly auditory. This could serve as an issue for visual learners. Students will get off track and overwhelmed if they are to do the packet all
at once. Also for this lesson, there is a lot of critical thinking and creativity that will be taking place. Students always have a hard time
getting to the critical thinking stage. Students will be asked to create definitions or write in their own words what they believe something to
be. This could be difficult for students without proper preparation. The students could get board and noisy if the lesson is not moved at a
proper rate.

Part III - LESSON ADAPTATIONS (TPE1.4,3.5,3.6,4.4,4.5,5.7,5.8 SSP-ELD)

9. Modifications/Accommodations(What specific modifications/accommodations are you going to make based on the anticipated
difficulties? Ex:) Please specify modifications/accommodations for English Learners, Standard English Learners, and/or students with
special needs.)
 English Learner: In this lesson, I want them practice their speaking and listening through the Kagan Cooperative-based learning strategy,
“Inside-Outside-Circle.” This also is a SDAIE strategy. This lesson requires a lot of speaking and cooperative listening. Because speaking
is difficult for this student, I will provide them with sentence starters. These sentence starters will help my student begin to formulate their
thoughts. It is important to have a classroom where RTI can be possible and functional; high quality teaching must be in place. Therefore,
this cooperative strategy will help to ensure that there is a higher level of teaching, communication, and skill building being implemented.
This strategy will be highly beneficial for all of my students, especially my English Learner, because it highlights the importance of the 21 st
century skill - communication. Another SDAIE strategy that I will use is Think-Pair-Share. My EL student is a table partner with a willing
and able student. Thought they are not bilingual, they are friends with my EL student outside of the classroom. This relationship between
them allows them to freely respond, discuss, and leaves room for correction. My EL student’s partner is also a high achieving student.
With their abilities, they are able to give correct guidance and feedback. Think-Pair-Share will be beneficial for my English Learner
because they will be able to think independently, turn to their strategically placed partner, and speak using mathematical vocabulary in a
safe and judgment free environment. Think-Pair-Share will also create a great confidence in my English Learner and the rest of my
students for when we bring the discussion class-wide. This strategy creates a safe environment for my students to feel comfortable in
sharing with their partner and then the whole class. It allows for more engaged and deep conversations.

 504 Student: Because of this student’s handwriting difficulty, acceptable accommodations for them is speech-to-text, raised paper, and
extended time. Unfortunately, the student refuses to use speech-to-text. They do not like having to do things differently from their
classmates. Therefore, the appropriate accommodation to make is having him use raised paper. It is a mechanism that the student uses
as “bumpers” to keep his writing between the lines. Their disability forces the student to struggle to keep their handwriting within the lines.
This is a great and discrete accommodation that they could use to help them complete the assignment. An accommodation that I
personally had in mind when I was creating my worksheet was to make sure that there was a lot of space between the lines given for the
responses. These large amounts of spaces gave them more room to write their answers instead of feeling the pressure of writing smaller.
Another accommodation that they could receive for this activity is an extended amount of time. If this student does not finish the activity
because of their disability they are allowed more time outside of class to finish. This allows the student to be present in the classroom and
thought the lesson without the pressure of time.
 All the students: Due to the outside conditions of the hook activity, I will make sure to give clear expectations of how I want their behavior
to be. Prior to class I will have the number cards that circle B will need already placed on the desk. This will save time and reduce noise at
the beginning of class. When the students walk in, I will greet them and explain that we will be doing partner work, but a little bit differently.
Before giving any instructions I will tell them that I will expect conversation level 2 when we are outside in order to be respectful to the
classes around us, and also to ensure that we can hear other classmates’ responses. I will tell them to listen to their peers when they are
talking to be respectful, and also because the information that they are saying will be informative and help with their own answers. I will tell
them to speak loud enough so that the rest of the class can hear their answer. Next, before I give instructions for the activity I will ask table
partner A to raise their hand (this is the student on the right side of the table). I will tell them to go make a circle outside in the courtyard.
Next I will tell the tale partner B’s to take the number card found on their desk and to make a circle around the A’s in numerical order. I
planned my instruction out this way to make sure that I was able to give my expectations to my class before losing them to their own
curiosity of who they will partner up with, and to the excitement about going outside. This way my circles will be formed quietly and
correctly. I will give the instructions for the activity outside while the students are in the circle so I can physically show them how they will
move and answer the questions. I will walk them through one round, and then verbally give them the rule for the rest of the rounds. This
way the students will be focused and will get a visual example of how the cooperative activity is expected to go. Once back inside, I will
pass out the packet, Arithmetic and Geometric Sequences. I created this worksheet myself, so I made sure to give the students T-Charts
of the information that was discussed in the outside activity. The students will fill in the T-Charts with the information that was discussed
outside. This way the visual learners will be able to benefit from the information that was discussed outside. I want my visual and auditory
students to have the same opportunities to learn in the classroom and have equal access to information. In order to keep the lesson
moving along at an appropriate pace, I will chunk my lesson. I will make sure to give the students segments to Think-Pair-Share. The
chunks will not be too much information and will make sure to cover one concept at a time. Then, after the students have thought about
and shared their answers with their partner, we will discuss it as a class to ensure correct answers and serve as an assessment for
myself. I anticipate students to get stuck on defining arithmetic, geometric, common difference, and common ratio. I will use probing
questions to help guide them to the desired outcome. I have great content knowledge of sequences so I will know what questions to ask
them in order to get their thinking back on track. I personally completed the packet to make sure it ran smoothly and to get an idea of
where students could struggle or get stuck.

10. 21st Century Skills – Circle all that are applicable

Communication Collaboration Creativity Critical Thinking

Describe how the 21st century skill(s) you have circled will be observed during the lesson (TPE1.5,3.3,4.7):
 Communication: Since this lesson has cooperative components, my students will be working on their communication skills. Before I give
my lesson and have my students participate in the activity, I will go over necessary communication components. Students will have
expectations to be respectful when someone is speaking, to give relevant and focused answers, and to be respectful of the other classes
and students around them. My students will be given specific questions to help guide their conversations with their partners to allow for
effective communicate. My goal with this lesson will be to help my students practice the important skill of communication. My job is to
prepare them for their future, and establishing communication will be very beneficial in the workforce.
 Collaboration: Students will work as a class to complete the outside activity. They will have to collaborate and cooperate to get the
desired outcome. Inside of the classroom, students will participate in the SDAIE strategy, Think-Pair-Share.” They will individually think
about the concept and then collaborate with their partner to combine their answers. Collaboration is a key 21st century skill. It is important
to incorporate this into every lesson to help refine and teach it to students to help prepare them for their future.
 Critical Thinking: Students will have to critically think about the data that they collected to create their own definition of mathematical
terms. Having students create these definitions and put them into their own words moves them into the upper levels of Bloom’s Taxonomy.
The highest level of Bloom’s Taxonomy is creating. Having students create and critically think about ideas is the highest level of thinking.
Introducing students to this skill at a young age is detrimental to their development as a 21st century thinker. In order to create, students
will tap into the third highest level of Bloom’s Taxonomy, which is analyze. Students will analyze their data that they collected and
discussed, and will have to thus infer and create concepts. Students will also be reaching depth of knowledge level 3. They will have to
develop arguments and will justify their answers during Think-Pair-Share. They will individually come up with an answer, and then have to
justify their reasoning to their partner. This enhances a students’ understanding and thinking greatly.

11. Technology - How will you incorporate technology into your lesson? (TPE3.6,3.7,4.4, 4.8)
 Overhead Projector: I will use the overhead projector to visually work through the packet with my students. It is important to visually
represent what is being discussed as a class in order to give all students equal access to learning. This will also allow students to visually
see what other answers were given, and will give them a chance to write them down these answers on their own worksheet.
 Desmos: Desmos is an interactive graphing website that allows students to discover concepts and make connections through the use of
graphs. Students have the option to use Demos to help graph their sequences. Demos has a feature to where students can input values
into a T-Chart, much like the one found on their worksheet. This will show them that much like functions, sequences can be graphed as
well. It will help them connect linear functions to arithmetic sequences, and exponential functions to geometric sequences. Using
technology engages students because students are so familiar with technology and it is a 21st century tool for learning.
12. Visual and Performing Arts – How will you provide the students with opportunities to access the curriculum by incorporating the visual
and performing arts? (TPE1.7)


13. Assessment Criteria for Success: (How will you & your students know if they have successfully met the outcomes? What specific

a. Formative:
 Exit Ticket: The exit ticket will help me gauge if my students understood the lesson. I will ask them to write about what helped them learn
arithmetic and geometric sequences during the lesson. The students will then discuss a part of the lesson that helped them understand
the concept the most. This exit ticket will help students self-assess themselves and reflect upon what was learned. The students will have
to first identify if they know the terms arithmetic and geometric sequences are, and then they will have to identify how they best learned it.
This is key in their own self-assessment, and will help them determine if they understand the material, what kind of techniques they learn
best from, and if they have any uncertainties about the content. This assessment will also help me assess my students and my own
teaching. I will get a clear representation of my students grasp the material. Their answer and language used within the answer will help
me determine if they truly understood the material and if they were engaged during the lesson. If there are notecards that do not give
specifics or say that they do not understand arithmetic or geometric sequences I will be able to use that information to assess if I need to
reteach or clear up a misconception that they experienced from the lesson in the next lesson given.
 Observational: During the lesson, I will be circulating around the room to listen to conversations being had, viewing students’ work, and
making sure all students are on task. This circulation will serve as an assessment. While I am listening to the students’ conversations and
looking at students work, I will look and listen for correct use of language and correct answers. If I hear that something is not right, I will
address it in that moment, or bring it up to the whole class, depending on the relevance to the class. I will be able to assess what my
probing questions need to address in order to help the students further understand arithmetic and geometric sequences. I will keep track
of common trends or wrong answers to use as examples for the class to discuss. The students that I select will serve as examples for the
class. This is where students will have to justify their reasoning. Another informal assessment that I plan to incorporate into my classroom
is our class discussion. I will have students create their own definitions for arithmetic, geometric, common ration, and common difference. I
will have them “Think-Pair-Share” these portions of the lesson. After they have shared with their partner, we will go over it as a class. In
order to properly check for understanding, I will use name cards that were created at the beginning of the semester. This will give me a
variety of students’ answers. This strategy will also keep all of the students aware and engaged because they will be anticipating their
name being called. When I am going through the name cards to answer the questions, I will be able to determine if all of my students
understand these rigorous mathematical terms and concepts. I want all of my students to be engaged, and I want to give all of them a
chance to participate and feel like they are part of the class. If there is a wrong answer, I will address it with the class, and ask them to
determine if there is a wrong answer in the list of definitions. This will not only get them thinking, but also involved in self-assessment. With
this strategy, they will be analyzing their own thoughts and ideas about what the content and definitions are about. With my assessments, I
will be assessing if the students are able to define arithmetic and geometric sequences by connecting their prior knowledge of linear and
exponential functions to these new sequence definitions.
b. Summative (if applicable):


c. Attach Rubric here (and copy and paste your objective above your rubric):
Learning objective: Students will be able to identify and define arithmetic and geometric sequences by connecting these new concepts to their
prior knowledge of linear and exponential functions.

“Arithmetic and Geometric

Rubric 3 2 1
Student was fully involved Student was partially Student was not engaged at
during the Inside-Outside- involved during the Inside- all during the Inside-Outside-
Circle and the Arithmetic and Outside-Circle and the Circle and the Arithmetic and
Participation Geometric worksheet. They Arithmetic and Geometric Geometric worksheet.
collaborated and engaged worksheet.. They partially Student did not collaborate
with their partner, and collaborated with their or discuss with their partner
participated in class partner, and participated in and their participation in
discussion. Student was class discussion adequately. class discussion was
actively listening. Student was listening. minimal. Student was not
Students worked together Student had worked with Students’ participation was
with their partner to finish the their partner adequately to minimal; therefore their
in-class work. If it was not finish in class assignment. classwork was below
Completion completed with a partner, There was discussion, but satisfactory.
they asked questions and moments of silence.
participated in class to finish
Student responded well to Student showed an Student showed minimal
the inquiry-based lesson. adequate understanding of understanding of arithmetic
Their participation led to arithmetic and geometric and geometric sequences.
Grasp of Concept their understanding of sequences. They were unable to discuss
arithmetic and geometric They were able to answer or answer questions.
sequences. They accurately questions, but unable to Because they let their
answered questions and explain reasoning. Student partner do the talking in the
were able to explain their identified that sequences are collaboration. Student was
reasoning to me. Student like functions. unable to identify that
was able to identify that arithmetic sequences are
arithmetic sequences are linear functions and
linear functions and geometric sequences are
geometric sequences are exponential functions.
exponential functions.

d. How do you plan to involve all students in self-assessment and reflection on their learning goals and progress? (TPE5.3)
I plan to incorporate my students in self-assessment through the exit ticket. The students will be asked to identify and explain on a 3x5 notecard
the learning activity that helped them understand arithmetic and geometric sequences. The students will have to first, reflect upon what they
personally learned during the lesson, and then, what helped them learn it best. The students will have to assess how much they truly know about
arithmetic and geometric sequences. They will be assessing their own degree of understanding. This will help them decide if they need further
explanation of any aspect of arithmetic and geometric sequences. This exit ticket addressed the learning objective, and gave the students an
opportunity to reflect upon the lesson to determine if they were able to reach the objective. Another way that I plan to include my students in self-
assessment is during our in-class discussions. In order to effectively check for all students’ understanding, I have notecards with every students’
name that I use to ensure that I call on every student. My goal is to go through my stack of notecards every lesson. This method gives all of my
students a chance to give an answer. This lesson requires multiple answers for each question. The answers that the students will be giving during
these in-class discussions will be comprised of previously learned vocabulary words. These vocabulary words will be sued to describe the new
vocabulary words: arithmetic, geometric, common difference, and common ratio. If there is a word or definition that does not quite fit the criteria, I
will ask my students to determine if there is something in this list that is not exactly right. This will make students reflect upon their own
understanding of these definitions, and if they need more clarification. It is very important to include students in self-assessment and reflection
because it not only is beneficial to their understanding of the content, but also an important life skill.


14. Instructional Method: Circle one – Direct Instruction Inquiry Cooperative Learning

Cooperative: Opening activity (Inside-Outside-Circle)

Inquiry: In-class worksheet

15. Resources/Materials: (What texts, digital resources, & materials will be used in this lesson?)
 Sentence Starters (EL Student)
 Number cards
 Chrome books -Desomos
 “Arithmetic and Geometric Sequences” worksheet
16. Procedure (Include estimated times. Please write a detailed procedure, including questions that you are planning to ask.):
OPEN: (15 minutes)
 Welcome students.
 Discuss instructions and expectations for the activity, “Inside-Outside Circle”
 Students must be at a conversation level 2. This is because this activity is an outside activity. Students must be respectful of the classes
going on around them.
 Students must also listen during this activity. It is important for students to listen because other students’ answers will be very important
information for their own answers during this activity. Also, it is respectful to listen to someone when they are speaking.
 Students must talk loud enough for all students to hear. While still being respectful of the classrooms around us, it is important for students
to talk loud enough for the class to hear.
 Table partner A (right side of the desk) forms a circle outside in the courtyard first. This classroom management strategy will eliminate a
massive crowd at the door, and will eliminate noise. They will be told to wait quietly outside until further instructions.
 Table partner B (left side of desk) will be instructed to take the number cards found on their desk (which were placed there before class
began) and form a circle around A’s in numerical order. They then will wait for further instruction.
Kagan Strategy Inside-Outside Circle
 Say to the class: “Circle B, line up directly behind a member of circle A. This is your partner for this round.”
 Say to the class: “Today we will be counting. Each round we will be counting by different numbers each time.”
 Find number one. Tell them to raise their card. Tell circle A that when their partner raises their card, they must say out loud the number that
is next in the pattern.
 Say to the class: “The first round we will be counting by 2 starting at 2. Student with number card 1 hold up your number card. Partner in
circle A say aloud the number that we are starting at….Number 2, raise your number card.” Now say to partner in circle A, “Since we are
counting by 2’s, What is your number?... How about 3?...When I point to you B’s raise your card and A’s say the next number.” Students
now have enough information to count. Have them count all the way until we get back to 1.
 Have Circle A shift 3 people to the left. Now, B’s will hand their number cards to students in circle A. Roles are now changing. Circle A will
hold up the number card while circle B counts. The new pattern for this round is multiplying by 2 starting at 1/2. Find number one and have
them hold up their number card. Explain to them that we are going to be using the same instructions to complete this round. Have them
multiply by 2 starting at ½ until they get back to number one.
 Explain that now the counting will be harder. Have circle A shift 2 people to the left. Now circle A hands their number cards to circle B to
switch roles.
 Students will be counting by ½ starting at 100. Start this round of counting with the student with number card one. Stop students once they
get to 3.125 (number card 6). Tell them to turn to their face partner and discuss what the next term will be. Explain that they can get help
from other classmates too. Once there is an answer, move on to next round.
 Students will now be counting by 4 starting at -6. Have circle A shift 3 steps to the left. Circle B hands their number cards to circle A to
switch roles. Now, locate number card one and explain to the class that you are only going to tell the first three number cards the starting
point and number we are counting by. They will have to try to continue the pattern. Whisper to students with number cards one, two, and
three the instructions (counting by 4 starting at -6). Tell them to begin. Let the rest of the class try to continue the pattern until it gets back
to number 1. Instruct them to turn to their face partner and discuss what they thought the rule was. Have a student share and ask numbers
one, two, and three to tell them if they are right or wrong.
 Thank them for their cooperation and instruct circle B to go back inside and sit at their seat. Once they are inside instruct circle A to do the

BODY: (33 minutes)

I do:
 Distribute the packet, Arithmetic and Geometric Sequences
 Tell students that these tables on page 1 are the different rounds that we did in the activity outside. Explain that they were only able to
audibly hear it, so now it is time to visually see it.
They do:
 Tell them to work with a partner to recall and fill out the information in the data tales.
 Once students are finished, ask them if this information reminds them of anything that they have done or seen before. They should say
linear or exponential.
 Ask a student to read aloud the instructions at the top of page 2. Once they are finished reading, tell them to individually think of ways to
group the data tables on page 2. Then, when they and their partner are done, discuss it with their partner and prove to them why they
grouped them the way that they did.
We do:
 Then discuss this as a class. Call on two students and ask them what they wrote. Then, ask the class if someone has anything to add to
the reasoning. This should serve as an assessment for you to determine if the students are beginning to reach the learning objective, or if
there are any probing questions to be asked to ensure any further explanation that is needed.
 Call on a student to read the sentences following the Group 1 and 2 explanations.
They do:
 Have the students individually think about and come up with a definition for arithmetic and geometric sequences. Once they and their
partner are done, instruct them to discuss and justify their definition to their partner. This is also known as the SDAIE strategy, “Think-Pair-
We do:
 Once students look done, pull their attention to the front of the class and discuss the different definitions that they created as you write
down definitions that they give you. Call on two students to give their definitions, and then ask the whole class if anyone can add any
 Once answers are satisfactory and you have assessed that they understand these definitions, ask a student to read the sentence about
common difference and common ratio.
They do:
 Have students “Think-Pair-Share” these definitions like you did for arithmetic and geometric. Follow those same steps.
I do/We do:
 With common difference and common ratio, make sure to tell them that, “In linear and exponential functions, we used additive change and
multiplicative change as vocabulary words to describe how the functions were changing from one point to the next. In sequences, we use
common difference and common ratio to describe that same change. The only difference between the functions definition and the
sequences is that common difference and common ratio are the act of doing something.” Probe them to connect common ratio to when
they did next term over previous term during the linear and exponential functions unit to find their ratio and change. For sequences, they
will be describing the act of finding the change of the sequence using the mathematical terms, common difference and common ratio.

They do:
 With a partner, have the students turn the page, to page 3 and complete part C of the packet. They will have to determine if the question is
arithmetic or geometric, and then what their common difference or common ratio is.
We do:
 Go over this as a class to ensure that their answers are correct and that they understand this new concept.
They do:
 Next, move on to part D which is graphing. Instruct students to get out their chromes and go to Desmos. With their partner, they will be
graphing the sequences that we have discussed throughout this activity. There are 4 graphs to complete. Have them discuss with their
partner the two questions at the end of the activity.
We do:
 As a class, when they are done graphing, discuss the last two questions and have them connect arithmetic sequences to linear functions,
and geometric sequences to exponential functions.

CLOSE: (5 minutes)
 Exit Ticket: Post the Exit Ticket question up on the projector and hand out note cards. Tell the students to write down what helped them
during the lesson to understand arithmetic and geometric sequences.
 This should take them to the end of the period. Collect the note cards and tell them to have a great Thanksgiving.

Part VI –REFLECTION (TPE3.4,6.1)

1. Were the students successful at achieving the lesson objective?

a) If so, explain which a reason which students were successful, according to your data analysis.

Students were very successful at achieving the learning objective. During the lesson, the students connected the data and patterns
discussed during the Inside-Outside-Circle activity to linear and exponential functions. They then used their knowledge of linear and
exponential functions to define arithmetic and geometric sequences, along with common difference and common ratio. I really wanted
to develop academic language in this lesson because it was an introduction lesson. It is important to give students definitions and
concepts before giving them formulas. The students displayed their success through their conversations with their peers, written
definitions of arithmetic, geometric, common ratio, and common difference, their in-class discussions, and also their Exit Ticket.

b) If not, explain which a reason which students were not successful, according to your data analysis. Why do you think they were not
able to achieve the lesson objective in these areas?

2. What instructional strategies did you use to help students achieve the lesson objective? Which subject-specific pedagogical skills did you
employ to help students be successful? (Reference TPE Part 2: Subject-Specific Pedagogy) (TPE SSP1-7)

The strategies that I used to help my students be successful in learning the lesson objective were the Inside-Outside-Circle, the
worksheet, the SDAIE strategy Think-Pair-Share, and the Exit Ticket. The Inside-Outside-Circle was a great hook lesson that engaged all
students. Students were collaborating with each other, thinking critically, and having fun. This really helped set the learning environment.
What helped make this a functional activity were the behavioral expectation that I discussed before the lesson. Explaining the
expectations for the activity before giving them instructions on how to complete the activity enabled me to get the students focused, and
established classroom management for an activity that could easily turn into mayhem. I explained the instructions outside when students
were already in circles to help give them physical examples for instruction that would otherwise be very verbal. Combining the two aspects
helped reach my kinesthetic, verbal, and auditory students. This enabled all of my students to participate in the activity in a meaningful
way. They were able to contribute to the conversations and the atmosphere. I then linked the information discussed in the Inside-Outside-
Circle with T-Charts that I created on a worksheet. These T-charts were given so students could visualize what was being discussed
outside. They already did the critical thinking for the information, now, I just wanted them to write it down to use for the rest of the lesson.
Connecting the hook activity to the actual lesson was very helpful for me when trying to engage my students. Reminding them of the fun
activity got them re-engaged. These T-charts were also used to help my students connect linear and exponential functions to this new
information. They saw the trends within the T-Charts. The students then grouped these T-charts into two unspecified groups. I wanted
them to group them and label the groups on their own so that they could make the connection to their prior knowledge. They were
extremely successful with this portion of the lesson. Every single one of the students described two groups that represented linear and
exponential functions. Through this process of grouping, students used the SDAIE strategy, Think-Pair-Share. The students first thought
about the grouped data on their own, then turned to their partner and justified their answer. The conversations that I saw were full of
academic language. This strategy was very helpful for my FS1. She used sentence starters to discuss her answers with her partner.
Because she is strong in writing, having her write her answers first, and then read them to her partner, gave her confidence to speak and
share during class. She also was able to understand the content better by practicing all four domains of language. FS2 also was
accommodated through this strategy. He has a 504 for handwriting, so the writing portion of this lesson is more frustrating for him than
helpful. Because I gave him opportunities to speak, he thrived during the lesson. The environment that it created helped make a judgment
free space for FS3. This strategy set up the premise for the introduction of sequences. To introduce arithmetic and geometric sequences,
the students were to define these terms using their prior knowledge of linear and exponential functions. They used incredible
mathematical vocabulary and academic language. I witnessed all of the vocab words that were used during the functions unit to describe
sequences. Students also used Think-Pair-Share to complete this portion of the lesson. After terms were defined, students used Desmos
to graph the data. Desmos is an interactive graphing website that students can utilize on their chromes. This helped students discover that
physically, arithmetic and geometric sequences are identical to linear and exponential. They saw that linear functions are arithmetic
sequences, and exponential functions are geometric sequences. This was a good activity to end the lesson on because students were
able to prove their hypothesis that arithmetic and geometric sequences are identical to linear and exponential functions. They saw
graphically that they are exactly the same. Technology was good to use here because students love this website and always enjoy
learning while using it. Students also have an incredible interest in technology, so incorporating technology into the lesson addresses
students’ assets and needs. The Exit Ticket that I used asked students what part of the lesson helped them learned arithmetic and
geometric sequences.

3. What would you change about the lesson and why (according to your data analysis)?
According to my students’ work and answers to the Exit Ticket, I would have put more emphasis on the Think-Pair-Share portions of the
lesson to ensure that all students were collaborating. I would have organized the Think-Pair-Share differently. Instead of instructing the
students to think about the information on their own and share their thoughts when both them and their partner are done, I should have
given the students a specific amount of time to think about the information individually. After I observe that every student has had enough
time to develop their own answer, I would give a certain amount of time for them to share their thoughts with their partner. Organizing my
Think-Pair-Share this way would give students actual time to create their own opinions, rather than allowing them to use their partner’s.
Their answers ranged across the whole lesson. A lot of students put the Inside-Outside-Circle. I noticed that it was all of my kinesthetic
leaners. My linguistically intelligent students put that the conversations that they had with their peers helped them learn the most. I also
saw some students specify that creating the definitions for arithmetic and geometric sequences helped them learn the most. The
responses were a great tool or me to see what activities to incorporate in my next lessons, if the students truly understood the content,
which students need further explaining, and where I was lacking in my teaching. All of these activities helped me teach my students and
create an environment conducive to learning.