lesson plan with reflection

7/21/2019 Lesson Plan with Reflection

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Karly Sachs

November 7, 2014

Professor Huey

Lesson Plan Assignment

Polar Graphs

Secondary Lesson Plan Template: Polar Graphs (Doing Math Lesson)

Name of class: Pre Calculus Length of class: 90 minutes

LEARNING GOALS to be addressed in this lesson (What standards or umbrella

learning goals will I address?):

Represent complex numbers on the complex plane in rectangular and polarform (including real and imaginary numbers), [and explain why the rectangular

and polar forms of a given complex number represent the same number]. (N-

CN.4.)

**The part in brackets is not addressed in this lesson but will be addressed in the

lesson the day before.

LEARNING OBJECTIVES (in ABCD format using verbs from Blooms Taxonomy):

Students will identify the different types of polar curves and parametric curves.

Students will compare and contrast the difference between polar curves and

parametric curves.

Students will analyze the different polar graphs by finding maximum and

minimum R-values as well as the line of symmetry.

By using the equation given, students will predict the graph of the polar

function or vise versa.

I can statements for the students:

1. I can identify the different types of polar curves and parametric curves.

2. I can compare and contrast the difference between polar curves and

parametric curves.


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3. I can analyze the different polar graphs by finding maximum and minimum

R-values as well as the line of symmetry.

4. By using the equation given, I can predict the graph of the polar function or

vise versa.

CONTENT (What specific

concepts, facts, or vocabulary

words will I be teaching in this

lesson?):

Polar Curve

Parametric Curve

Rose Curve

Limacon Curveo Limacon with an

inner loop

o Cardioid

o Dimpled Limacon

o Convex Limacon

Lemniscate Curve

R-Value

Theta

SKILLS: (What skills will students acquire or

practice?)

Prerequisites:

Students will be taught the section on Polar

Coordinates the day prior to this lesson.

Students will know how to graph equationsin the rectangular plain.

Students should be able to list important

characteristics of graphs.

Skills acquired in this lesson:

Define polar curve (x,y plane) and

parametric curve

Identification of polar graph types given an

equation (rose, limacon, lemniscate)

Identification of polar graph types given a

graph

Determine r values given an equation or

graph (maximum)

Determine symmetry types (if any)

Determine other characteristics of polar

curves

o Domain

o Range

o Bounded or Unbounded

o Continuous


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RESOURCES/MATERIALS NEEDED (What materials and resources will I need?):

Launch:

Yellow Post-it Notes

Pink Post-it Notes

Lesson:

Instructions handout

Timer

Mini Guided Instruction handouts for each person in the discovery group

Rose Curve Guided Discovery

Limacon Guided Discovery Lemniscate Guided Discovery

Colored Cards (to form groups)

Graphing Utility

Graph paper

Colored Pencils

Notes Outline handouts for each person in the home group

Assessment:

Ticket Out handout

LEARNING PLAN (How will you organize student learning in this lesson?

ACTIVATE (How will I pre-assess my students understanding, activate their prior

knowledge, or get them excited about my lesson?)

The teacher will activate the lesson with a Think, Pair, Share. He/she will have

their students

Think, Pair, Shareto the question What are the important characteristics to

look for while graphing an equation? Make a list of these characteristics. First

think to yourself and write down some ideas on the yellow post it note in front ofyou. After two minutes or so, turn to your shoulder partner and discuss your

ideas. Together, write down some ideas on the pink post it note in front of you.

After three minutes or so, face front and be ready to share your pink post it

note to the class. (This activity in general should take about 10 minutes)

ACQUIRE& APPLY (What instructional strategies will I choose to help my

students acquire and apply the knowledge, skills, attitudes, and behaviors


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outlined above?

The activity the teacher will use to teach the lesson will be a JIGSAW Activity.

First we will divide the class into six different groups (there will be two groups

working on each topic). Each group will be given one of three different topics

to discover. They will become the experts on this topic. The three topicsinclude:

Rose Curve

Limacon

Lemniscate

Each group will be assigned a topic strategically. Once the topics are assigned

and the groups are formed, students will use the Important Characteristics of a

Graph list from the launch to investigate their equation. They will be asked to

come up with a general form of the equation as well as diagrams and different

rules. We will guide them to come up with the following facts:

General form of the equationo How did you come up with this?

o What does each part of the general form tell you?

Sketch(s) of the graph

Line(s) of symmetry (if any)

o How do you know this?

o Are there different formulas you can use to check?

Continuous?

o Why?

Bounded or unbounded?

o Why?

Is there a max?

o Why?

Is there a min?

o Why?

What is the domain?

o How did you find this?

What is the range?

o How did you find this?

Compare the graph using polar coordinates and rectangular

coordinates. Sketch them both. How are they the same? How are they

different?o Domain?

o Range?

o Max?

o Min?

o Bounded?

o Continuous?


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**Depending on the ability level of each group, they will be guided with

different questions. This is where the differentiation aspect of the lesson comes

into play.

While each group collaborates and learns about their topic, the teacher willput colored cards on each student desk. These cards will determine what

home group students are in. The teacher will determine this strategically.

After thirty minutes or so, students will move groups. They will change from their

discovery group to their home group. In each home group, there should be

4 to 6 members (depending on the classroom size); each member should be

an expert on a different topic. For the next thirty minutes or so, students will

teach their group members about their topics.

After the thirty minutes, students will be asked to compare and contrast each

type of graph. We will do this as a class. How do the general forms of the equations differ?

How do the graphs differ?

o How do the three graphs differ? (Limacon, Rose, Lemniscate)

o How does the graph of the rose curve in the polar plane differ

from the graph of the rose curve in the rectangular plane?

o How does the graph of the limacon curve in the polar plane differ

from the graph of the limacon curve in the rectangular plane?

o How does the graph of the lemniscate curve in the polar plane

differ from the graph of the lemniscate curve in the rectangular

plane?

Students will address what they think is important to address at this time.

ASSESSMENT (How will asses student understanding?):

To assess student understanding, a ticket out will be given at the end of class.

The ticket out will ask students to match different formulas with the different

graphs. They will then be asked to sketch out their favorite graph of the day

and write three facts about it.

LESSON PLAN SEQUENCE & PACING (How will I organize this lesson? How much

time will each part of the lesson take?)

1. Launch:Think, Pair, Share (10 minutes)

2. Discovery Group: Part One of the JIGSAW (30 minutes)


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3. Home Group: Part Two of the JIGSAW (30 minutes)

4. Come together as a class andcompare and contrast the polar graphs. We

will discuss general findings during this time as well. (15 minutes)

5. Ticket Out (5 minutes)


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Instructions for the Day

1. In your discovery groups, complete the guided activity

on either the

a) Rose Curve

b) Limacon Curve

c) Lemniscate Curve

You will be assigned a group. Everyone must write. If you

have any questions raise your hand. (30 minutes)

2. If you finish before the timer goes off, raise you hand.

3. When the timer goes off, you will be asked to get in your

home groups. Get into these groups as quickly and as

efficiently as possible. They will be assigned as well. In these

groups (30 minutes)

a) Each member of the group with teach the rest of thegroup their topic.

b) Take notes while classmates are talking

c) Do NOT just copy each others packets and call it a

day

4. When the timer goes off again, it is time to discuss as a

class. Face forward and be ready to listen !(15 minutes)


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2. The following functions are also Rose Curves. By looking at the functions and

graphing the equations, can you come up with a general form for a rose curve?

Write the general form of the function below. How did you come up with this?

(Hint: the general form of a function is an equation with variables)

a. r = 5 sin (2!)b. r = 7 sin (5!)

c. r = 8 sin (6!)

The general form of the function is: ___________________________________________

Because:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

3. Number of Petals:

How can one tell how many petals a rose curve contains by just looking at an

equation?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Can one tell if the graph has an odd or even number of petals just by looking at

the equation? If so, how?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

How can one tell how long a petal is by just looking at the equation?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________


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a. The y-axis? If so, when?

______________________________________________________________________________

______________________________________________________________________________

b. The x-axis? If so, when?______________________________________________________________________________

______________________________________________________________________________

c. The origin? If so, when?

______________________________________________________________________________

______________________________________________________________________________

6. Compare and Contrast the Graphs in DIFFERENT planes

Come up with an example of an equation of a Rose Curve. Graph it in the polar

plane.

My equation is _____________________________________________________________

In the polar plane is looks like

Now graph this equation in the rectangular plane. Sketch the graph in the

space below.


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Analyze the graph in the rectangular plane. Find the

a. Maximum and Minimum: __________________________________________________

b. Domain: __________________________________________________________________

c. Range: ____________________________________________________________________

d. Altitude: __________________________________________________________________

e. Period: ____________________________________________________________________

Do these characteristics relate to any of the characteristics of the graph in the

polar plane? If so, which ones? How do they relate? Explain your answer.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________


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Name: ___________________________

Date: ____________________________

Polar Graph Exploration

What are some important characteristics of graphs? List as many as

you can.

The Lemniscate Curve:

Use the following website to explore the different properties of a Lemniscate

Curve.The website is https://www.desmos.com/calculator

Type in the following functions:

a. !!= !!sin(2!)

b. !!= !! sin (2!)

c. !!= 4sin (2!)

1. What are some characteristics of a Lemniscate curve? Sketch it below.


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2. The following functions are also Lemniscate Curves. By looking at the functions

and graphing the equations, can you come up with a general form for a

Lemniscate curve? Write the general form of the function below. How did you

come up with this? (Hint: the general form of a function is an equation with

variables)

a. r = 2!!"#!"

b. r = 6!!"#!"

c. r = 4!!"#!"


Because:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

3. Sin(!) and Cos(!) and Tan(!) oh my!

If one replaces Sin(!) with Cos(!), how does the graph change? Pick one of the

graphs from number two. Sketch the graph as well as the Cos(!) version of

that graph. How does the graph change?

Sine Graph Cosine Graph


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Describe the transformation occurring between the sine graph to the cosine

graph.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

4. Symmetry

Is the Lemniscate Curve Symmetrical about the x-axis, y-axis, and origin? Use the

space below to show your work algebraically as well as graphically. (Hint: Pay

attention to when the function contains sin or cos.)


______________________________________________________________________________

______________________________________________________________________________

b. The x-axis? If so, when?

______________________________________________________________________________

______________________________________________________________________________


______________________________________________________________________________

______________________________________________________________________________


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Come up with an example of an equation of a Lemniscate Curve. Graph it in

the polar plane.

My equation is _____________________________________________________________



space below.



b. Domain: __________________________________________________________________

c. Range: ____________________________________________________________________

d. Altitude: __________________________________________________________________

e. Period: ____________________________________________________________________


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______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________


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Name: ___________________________

Date: ____________________________

Polar Graph Exploration


you can.

The Limacon Curve:

Use the following website to explore the different properties of a Limacon Curve.

The website is https://www.desmos.com/calculator


a. r = 3+2sin(!)

b. r = 6+4sin(!)

c. r = 4+4sin(!)

1. What are some general characteristics of a Limacon Curve? Sketch it below.


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2. The Limacon Curve can be divided up into four different graph types.

a. Limacon with an inner loop-- When (!

!)< 1

b. Cardioid-- When (!

!

)= 1

c. Dimpled Limacon-- When 1 < (!

!)< 2

d. Convex Limacon-- When (!

!)! 2

Sketch the graphs below and label them with the proper term above. (Hint: in

the first example, a=5 and b=4)

a. r = 5 + 4 sin (!)

b. r = 7 + 7 sin (!)

c. r = 8 + 2 sin (!)

d. r = 2 + 3 sin (!)


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Because:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________







graph.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________


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4. Symmetry

Is the Limacon Curve Symmetrical about the x-axis, y-axis, and origin? Use the




______________________________________________________________________________

______________________________________________________________________________

b. The x-axis? If so, when?

______________________________________________________________________________

______________________________________________________________________________


______________________________________________________________________________

______________________________________________________________________________


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Come up with an example of an equation of a Limacon Curve. Graph it in the

Polar Plane.

My equation is _____________________________________________________________

In the Polar plane is looks like

Now graph this equation in the rectangular plane. Sketch the graph in thespace below.



b. Domain: __________________________________________________________________

c. Range: ____________________________________________________________________

d. Altitude: __________________________________________________________________

e. Period: ____________________________________________________________________


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2. The following functions are also Rose Curves. By looking at the functions and

graphing the equations, can you come up with a general form for a rose curve?

Write the general form of the function below. How did you come up with this?

(Hint: the general form of a function is an equation with variables)

a. r = 5 sin (2!)

b. r = 7 sin (5!)

c. r = 8 sin (6!)

The general form of the function is:

1. r = a sin (n !)

2. r = a cos (n !)

Because: I came to this general conclusion by looking at the patterns of the

equations above.

3. Number of Petals:

How can one tell how many petals a rose curve contains by just looking at an

equation? If n is an odd number, the number of petals is n. If n is an even

number, the number of petals is 2n.

Can one tell if the graph has an odd or even number of petals just by looking at

the equation? If so, how? Yes. Look at the value of n.

How can one tell how long a petal is by just looking at the equation? Look at the

value of a.


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r = 5 sin (2 !) r = 5 cos (2 !)


graph. The cosine graph is the sine graph rotated 90 degrees clockwise.

5. Symmetry

Is the Rose Curve symmetrical about the x-axis, y-axis, and origin? Use the space

below to show your work algebraically as well as graphically. (Hint: When

answering these questions pay attention to when the number of petals is even or

odd. Also pay attention to when the function contains sine or cosine).


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a. The y-axis? If so, when? 1) When n is even and 2) When n is odd and r = a cos

(n !)

b. The x-axis? If so, when? 1) When n is even and 2) when n is odd and r = a sin

(n !)

c. The origin? If so, when? When n is even


Come up with an example of an equation of a Rose Curve. Graph it in the polar

plane.

My equation isr = 4 cos (3!)



space below.


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a. Maximum and Minimum: absolute value of a

b. Domain: All real numbers

c. Range: [- |a|, |a|]

d. Altitude: a

e. Period: Not pertinent information



The Maximum R Value and AltitudeRelate

The are both continuous

They are both bounded

There are no asymptotes


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Name: ___________________________

Date: ____________________________

Polar Graph Exploration (Answer Key)


you can.

Zeroes/Solutions/Intercepts

Y-intercept

Maximum (absolute/local)

Minimum (absolute/local)Domain

Range

Symmetry

Altitude

Period

The Lemniscate Curve:

Use the following website to explore the different properties of a LemniscateCurve.

The website is https://www.desmos.com/calculator


a. !!= !!sin(2!)

b. !!= !! sin (2!)

c. !!= 4sin (2!)

1. What are some characteristics of a Lemniscate curve? Sketch it below. Some

characteristics are 1) looks like an infinity sign, 2) symmetric about the origin, and

3) seems like the general form contains (2!)


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2. The following functions are also Lemniscate Curves. By looking at the functions

and graphing the equations, can you come up with a general form for a

Lemniscate curve? Write the general form of the function below. How did you

come up with this? (Hint: the general form of a function is an equation with

variables)

a. r = 2!!"#!"

b. r = 6!!"#!"

c. r = 4!!"#!"


!!= !!sin(2!)

!!= !!cos(2!)

Because: It contains both sine and cosine






!!= !!sin(2!) !!= !!cos(2!)


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graph.

The graph seems to rotate 90 degrees clockwise

4. Symmetry

Is the Lemniscate Curve Symmetrical about the x-axis, y-axis, and origin? Use the



a. The y-axis? If so, when? The Cosine graph is

b. The x-axis? If so, when? The Cosine graph is

c. The origin? If so, when? The Sine and Cosine graph are


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Come up with an example of an equation of a Lemniscate Curve. Graph it in

the polar plane.

My equation is:!!= 4 sin (2!)



space below.


a. Maximum and Minimum: (!

!, 4)is one of the maximum and (!

!

!, -4) is one of

the minimumsThe value of a determines the Range

b. Domain: All real numbers

c. Range: [-4, 4]


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d. Altitude: 4

e. Period: Pi



Both graphs go through the origin

The length of a petal is half the Altitude


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Name: ___________________________

Date: ____________________________

Polar Graph Exploration (Answer Key)


you can.

Zeroes/Solutions/Intercepts

Y-intercept

Maximum (absolute/local)

Minimum (absolute/local)Domain

Range

Symmetry

Altitude

Period

The Limacon Curve:

Use the following website to explore the different properties of a Limacon Curve.The website is https://www.desmos.com/calculator


a. r = 3+2sin(!)

b. r = 6+4sin(!)

c. r = 4+4sin(!)


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b. r = 7 + 7 sin (!)

Cardioid

c. r = 8 + 2 sin (!)

Convex

d. r = 2 + 3 sin (!)

Inner Loop


r = a !b sin (!)

r = a !b cos (!)

Because: I came to this general conclusion by looking at the general patterns of

the equations above.


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r = 3+2 sin (!) r = 3+2 cos (!)


graph.

The graph seems to rotate 90 degrees clockwise.

4. Symmetry

Is the Limacon Curve Symmetrical about the x-axis, y-axis, and origin? Use the




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c. Range: [a-b, a+b]

d. Altitude: 5 or a+b

e. Period: Irrelevant to the problem



The Maximum R Value and

Altitude Relate

The are both continuous

They are both bounded

There are no asymptotes


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Ticket Out

Two-way match up:Match the graph to its general form. Write the name of the

curve near the graph.

r = a cos (n!)

r = a sin (n!)

Where n > 1

r = a !b sin(!)

r = a !b cos (!)

Where a > 0 and b > 0

!!= asin (2!)

!!= acos (2!)

What is your favorite graph of the day? Sketch it. Write three facts about it.

My favorite graph is _______________________________________________

1.

2.

3.


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Karly Sachs

November 16, 2014

Professor Huey

Mathematics Methods

Reflection on Pre Calculus Lesson

Launch:

For the launch of our lesson, TJ and I decided to really emphasize the aspect of

activating students prior knowledge to increase student engagement. Our launch

activity was having students do a Think, Pair, Share to the question, What are the

important characteristics to look for while graphing an equation? Make a list of these

characteristics. We felt that by asking this question students would really have to think

back about what they knew/learned about graphs prior to this lesson. After students

came up with a list, our goal was to relate the characteristics they came up with to

characteristics of graphs in the polar plane.

We wrote the question on the bored, passed out the sticky notes ahead of time,

and were ready to start the launch when the bell rang. When the bell rang, we quickly

started the lesson because we knew we had a lot to do in a short amount of time. The

only problem was that students walked into class late. This made us have to repeat the

activity quite a few times. I do not think this was too concerning of a problem, however.

The problem arose when we asked students to share what they wrote to the entire

class. The room was silent. We provided wait time but the room was still pretty quiet. We

then proceeded to call on tables that we thought had good ideas when we walked

around the classroom and observed during the launch. I thought this was a pretty good

idea, but we should have made each table share at least one idea. This would have

kept everyone engaged during share time instead of just the tables we called on. I


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will be sure to make every table share an idea the text time I do a Think, Pair, Share

activity.

Explore:

The explore aspect of our lesson was a heavily guided Doing Mathematics

activity. We thought the lesson fell into the definition of Stein and Smiths Doing

Mathematics because our lesson 1) required complex and nonalgorithmic thinking, 2)

required students to explore and understand the nature of mathematical concepts,

processes, and relationships, 3) demanded self-monitoring and self-regulation of ones

own cognitive processes, and 4) required students to access relevant knowledge and

experiences to make appropriate use of them in working through the task. We made

our task into a Jigsaw Activity so that the students could practice teaching their

classmates about the topic they discovered. After the launch, the next thirty minutes of

class time was designated to becoming an expert of the rose curve, limacon curve, or

lemniscate curve. After students got into their groups, we soon found out that this part

of the activity was going to take longer than anticipated. Instead of taking the

anticipated thirty minutes, we gave the students fifty minutes to become an expert on

their type of curve. After fifty minutes students were still not finished with their first packet

and we still had more than half of the lesson to go. Even though the students were not

finished, TJ and I made the decision to move on and have the students get into their

home groups. We had a perfect transition planned out, but it did not happen. With all

of the hype in the classroom, we forgot about our colored card idea and just

numbered the students off. This was a bad idea on our part because students did not

feel like moving to go to another spot in the classroom. It was also very unorganized.

What made this transition especially poor was the fact that after students got into their


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home groups, we had them get up once again to grab two more packets. Most

students did what they were told, but there were a handful that did not feel like getting

up yet another time. Because of this, they did not have the other packets until we

noticed a good ten minutes later. One way we could have avoided this unorganized

mess is if we were to pass out the packets while students were still in their expert

groups. This way, before the students were even grouped off they would have already

had the materials they needed. We could of then used our colored card system to

group the students off.

While the students were in their home groups they literally just copied down

what their classmates wrote, which is the last thing I wanted to occur. TJ and I had

planned to express our expectations of what students should be doing during this time

but we ended up forgetting. We even had an instruction sheet to put on the Elmo of

our expectations during the lesson but we forgot to put it up. I think this would have

benefitted our lesson quite substantially because maybe then students would not have

just copied their classmates packets. I was pretty surprised to see everyone explaining

his or her curves though!

Summarize:

The summarizing of our lesson was pretty sparse, which is something I do regret. In

my opinion, the close of the lesson is just as important as the launch and task of the

lesson, maybe even more important. Originally we had planned fifteen minutes to close

our lesson. We thought of doing a whole class discussion on each of the curves. We

thought of going over each curve expressing the most important aspects of each

graph, and then comparing and contrasting the curves as a class. We came up with

general guiding questions that we would ask during this time.


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When it came to the end of the class period, though, we were short for time so

our close lasted all of three minutes. During the close, we asked very low cognitive

ability questions, which is the complete opposite of what we wanted to do. We also did

not think to write down what the students were saying during this time. We should have

written down each point the students were saying on the white bored to reemphasize

what they learned. I also wish we took the time to discuss higher level thinking questions

during the close. We kind of dropped the ball on this aspect of the lesson.

What went according to plan? What did not?

Overall, I do think our lesson on Polar Graphs went pretty well. Here is what I think

went according to plan and what did not.

Components of the

Lesson:

Positives: Negatives:

Launch I think our launch really

activated students prior

knowledge

I think the think, pair,

share went according

to plan. Students

thought to themselvesand worked in groups

like they were supposed

to do.

Students contributed to

the large group

discussion, which is what

we wanted.

During the large

group discussion, not

all groups had a

chance to share

their ideasthis

could have been

avoided. Students did not

come up with some

of the key aspects of

graphs we intended

for them to come up

with. This made it

hard to make all the

connections we

intended to make at

the end of the

lesson.Explore

Expert Groups Most students worked

together as a team to

discover the

information.

The guiding questions TJ

and I came up with

Some students

worked ahead of

their group.

Some students were

off task in general.

Some of the


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came in handy when

students were confused.

questions on the task

were confusing to

students. One

question that really

tripped up students

was the questionabout writing an

equation in general

form. I did not

anticipate this

happening.

This component of

the lesson took

longer than

anticipated

Transition Most students actually

moved.

Passing out the

second and third

packets was a

disaster. We should

have actually

passed them out

versus having

students come get

them.

Home Groups Students actually shared

what they came up

with.

The timing of this

component of thelesson went according

to plan.

Students copied

down their

classmates packets.

Summarize A close component of

the lesson occurred

Our types of

questions we

wanted to ask

during this part of

the lesson did not go

according to plan

The time allotted for

this component of

the lesson did not goaccording to plan

The main purpose of

the close did not go

according to plan.

The main purpose of

the close was to

really get at the


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higher ordered

thinking of the

lesson. We did not

have time for it

though.

Assessment

Students worked on theticket out and turned it

in.

Students did notwork on it

individually

Students did not

answer the questions

on how we were

expecting them to

answer them. For

instance, we asked

the students to write

three facts about

their favorite type of

graph. Some facts

that were written

included it is

pretty, it is

beautiful, and it

looks like a butt. This

is not quite what we

wanted the facts to

be.

What surprises or challenges occurred during teaching?

One surprise that occurred during teaching was the fact that the timing of our

lesson was all off. Every aspect of our lesson took longer than anticipated, which meant

we really had to be on our toes and plan accordingly. I am really shocked that the

exploring component of the lesson took so long and the students did not even finish it. If

I were to use this lesson again I now know to give the students more time to complete

the task.

Another aspect of the lesson that surprised me was the confusion students had

during the completion of the task. The questions were very confusing for some, which is


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not what TJ and I had anticipated at all. One question of the task that seemed to

cause the most confusion was the question asking the students to write their curve in its

general form. Students did not really know what this was. After TJ and I explained it to

them, they seemed to only write down the sine version of the equation. No student

thought to write the cosine version of the graph. TJ and I did not anticipate this at all

and it was hard to guide them to write the cosine version without actually saying,

There is a cosine version of this graph as well. This was a big challenge.

The biggest challenge TJ and I came across would probably have to be the

handful of students who decided to not participate in the activity. Everyone knows

there are a handful of students in every classroom that are like this, but how can one

motivate these students to do their work? TJ and I constantly found ourselves making

sure these boys were on task, and in most cases, they were not. The main aspect of this

challenge to remember here is that this will happen in every classroom and in order to

motivate these students, you have to get to know them on a personal level. As a

teacher, I will do this.

What did you learn through this process?

Through this process, I learned a lot! I learned that when one is student teaching

they really need to communicate with their cooperative teachers because they really

do give helpful advice. Mr. Seeley gave TJ and I a lot of input that really helped us get

through our lesson. As student teachers, this input is crucial in order to teach the

students properly. Another thing I learned through this process is how one needs to be

on their toes and be ready to adapt their lesson plan to fit the needs of the students. TJ

and I had to change our lesson plan timing quite a few times to meet the needs of the


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students. A lesson plan is really just that, a plan! One cannot stick to it the entire time.

This is what I am most worried about.

lesson plan with reflection

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