EDTE 314 Math Mini-PACT
Prompt #1: What is the central focus of the learning segment? Apart from being present in the school
curriculum, student academic content standards, or ELD standards, why is the content of the learning
segment important for your particular students to learn?
The central focus of the learning segment is for students to be able to identify a radius and diameter of a
circle and be able to determine the distance of one in relation to the other. Apart from the school
curriculum and academic standards, the content of this learning segment is important to my students
because being able to identify radius and diameter are important in real world situations as well as
contributes to problem solving strategies. The words radius and diameter are commonly used in tools,
measurements, cooking, and trade jobs. The contents of this lesson help provide an underlying
knowledge of measurement skills for their future.
Context for Learning
1. How much time is devoted each day to mathematics instruction in your classroom?
a. Each day our morning begins with what we call “Math for Today” which is a series of
math problems incorporating skills learning from first grade to fourth grade. Math for
Today takes about ten minutes a day to complete and is done daily.
b. In addition to “Math for Today” the children have one hour per day to do mathematics.
This includes no more than twenty minutes instruction and note taking, fifteen minutes
of practice and informal assessment using white boards and then thirty-five minutes of
differentiated instruction and independent work.
2. How many students are in the class you are documenting?
a. There are currently thirty-three students in the class I am documenting.
3. How many students in the class are: English learners __5__ Proficient English Speakers __5__
4. How many students have Individualized Education Plans (IEPs) or 504 plans? __10__
5. How many students participate in a Gifted and Talented Education (GATE) program? __0__
6. Describe any specialized features of your classroom setting, e.g., bilingual, structured English
immersion, team taught with a special education teacher.
a. The classroom does have five EL students but they are all proficient English speakers and
there are not any children that require extra services thus there are not bilingual
instructors or special education teachers. I do have two students that leave to go to
speech once a week and four students that leave to go to learning center every day
after lunch.
7. If there is a particular textbook or instructional program you primarily use for mathematics
instruction, what is it? (If a textbook, please provide the name, publisher, and date of
publication.)
a. The students use the Houghton Mifflin text book with its corresponding workbook.
8. What other major resources do you use for mathematics instruction in this class?
a. The text book is the main major resource I use in the classroom. I rely on manipulatives
to help support the information in the text and I provide worksheets that can be filled in
for notes to shorten the time duration the students must sit in their desks for direct
instruction. Occasionally I will use the internet for suggestions for uses of manipulatives.
I have recently implemented the use of the activities and teaching strategies stated in
my course textbook and suggested use of activities from the videos shown in EDTE 314.
9. How many computers are available to support your instruction?
a. There are two computers for the children in the classroom and there are 40 computers
in the computer lab; all of which can be used to log onto math websites for children.
Although I am aware of the benefits of the use of computer software for digital
manipulatives, I do not heavily rely on the computers for my instruction. The classroom
is not equipped to show the computer screen onto the projector screen.
Context
Other than what is stated in the lesson plan(s), what occurred immediately prior to and after
the video clip(s) that is important to know in order to understand and interpret the
interactions between and among you and your students? Please provide any other
information needed to interpret the events and interactions in the video clips(s).
Just prior to the video clip, I had asked the students to get out their math journals, put them on
their desk and then come to the carpet to share with me and their fellow students what they
knew and wanted to know about circles. During the video I am writing on a T chart what they
know on the left and what they want to know on the right. The students are actively engaged
raising their hands to share. Also, prior to filling in the chart, I had selected two students to be
my “scouts” and they spend the time looking for positive behaviors among their classmates.
During the video there is an activity where the students made a circle and I had selected at
random a student to be the “center” and to reinforce the concept, she wore a sign around her
neck that said, “center”. Then I used yarn to represent the radius and the diameter and had my
“center” hold the string to show that the radius and diameter must pass through the center.
Once the students understood that the radius was half way across the circle compared to the
diameter which goes all the way across, I added values to the radius and diameter. I took an
index card and folded it in half and wrote 4 on both sides then set it on the radius of our circle. I
explained to the students that 4 represented the length of the radius. Then I asked, “if the
radius is half way across the circle and it is a length of 4 then how long is the diameter?” The
students quickly answered, “8”. I supported their answer by running the yarn all the way across
the circle and to the other side where another student held onto it and then I placed another
index card on the string labeled, “8”. I gave a series of example problems for the students to
solve using the distance of the diameter to determine the radius and the distance of the radius
to determine the diameter. After we were done the students returned to their seats, opened
their notebooks and wrote down what they learned. I modeled the note taking on the overhead
to ensure that the students would get everything they needed to be able to do their homework
and study for the quiz. The students then kept out their notebook and did independent work
out of their math book. I pulled a small group for re-teach and had a challenge group at the
front of the room.
Describe any routines or working structures of the class (e.g., group work roles, class discussion
norms) that were operating in the learning task(s) seen on the video clips(s). If specific routines or
working structures are new to the students, how did you prepare students for them? (TPE 10)
A routine of the class is to get out their math notebooks to take notes right away then they usually put
their notebooks away and get out their white boards for five to ten minutes of drills. Then the
students usually divide into three groups for differentiated instruction and independent work for
about twenty minutes.
I felt that the radius and the diameter are two terms that the students would get easily mixed up and
a concept that would be fun and educational at the same time if taught through physical models and
interactions. The students are use to coming to the carpet for group discussions so expectations had
already been set at the beginning of the year. The students, however, are not use to moving around
the room for math activities so when I had the students at the carped, we discussed the expectations
during the upcoming activity. The students were able to follow instructions well and even came up
with the terms, “center, radius, and diameter” on their own without me introducing it.
This kind of instruction worked well because the students only had about three to five minutes of
direct instruction and note taking before they moved on to independent work. I was able to see during
the activity and the note taking as well as knowing who my normal strugglers are to determine the
four students that went with me to the back table for intervention time (re-teach). The great thing I
can conclude from instructing this concept the way I did is that when the students took the quiz two
days later, every single student passed with a B or better.
In the instruction seen in the clip(s), how did you further the students’ knowledge and skills and
engage them intellectually in understanding mathematical concepts and participating in mathematical
discourse? Provide examples of both general strategies to address the needs of all of your students
and strategies to address specific individual needs. (TPEs 1,2,4,5,7,11)
The previous day’s lesson was on lines, line segments, points and rays. The lesson that is recorded is on
circles, radius and diameter. I was able to include the academic terminology from the previous day’s
lesson by referring to the radius and diameter as line segments and the students identified the center as
a point. At this point, the students started using the academic language and terminology to answer
questions showing me that they were making connections. I also noticed in the clip that the students
were able to use their prior knowledge to form new knowledge in the interactive activity. This activation
of prior knowledge allowed for a more interesting time learning as well as less time taking notes and less
time spend re-teaching the subject.
Given the language abilities of your students as described in Task 1, Context for Learning, provide
examples of language supports seen in the clips that help your students understand the content
and/or academic language central to the lesson. (TPE’s 4,7)
The students showed while at the carpet constructing the list of what they knew that they had some
prior knowledge of a circle, radius, diameter and center. They had even suggested the day before that
they had prior knowledge of a ray, line segment, and line and were able to make those connections on
the video clip. When I asked them the question, “what do we call the line segment that goes from the
center to the edge of the circle?” many students were able to respond using the word “radius” before I
had introduced the term. This quickly made me realize that I didn’t have to start from scratch when
teaching the topic thus the students were engaged more and I didn’t have to spend as much time
reviewing the topic in the weeks to follow. This isn’t to say that every single student knew the terms but
through large group interaction and differentiated instruction, each student not only said they felt
comfortable doing the math and using the terminology but they also succeeded on the assessment
portion with proficient grades.
My EL students have tested out and are considered proficient in English. Based on their writing and
comprehension skills, I still feel that it is necessary to provide visual aids alongside the introduction of
new vocabulary. This tool is not solely useful for EL students; it is also useful for my visual and
kinesthetic learners.
Describe the strategies you used to monitor student learning during the learning task shown on the
video clip(s). Cite one or two examples of what students said and/or did in the video clip(s) or in
assessments related to the lesson that indicated their progress toward accomplishing the lesson’s
learning objectives. (TPEs 2,3)
I began monitoring the students learning by activating their prior knowledge. I pulled them to the carpet
to not only increase participation from the students but to also help with classroom management. I was
able to ask them what they already knew and then what they wanted to know about the circle, radius,
diameter and center. By doing this, the students proved to have made connections to the previous day’s
lesson on line segments and points as well as right angles as we moved about the circle with the radius
making right angles using the center as the vertex.
After activating their prior knowledge, the students became involved in kinesthetic learning as we
modeled a circle, center, radius, and diameter all the while, the students provided the information that
made up their objective; students will be able to identify parts of a circle and turns about the center of a
circle. There was very little direct instruction even needed after the modeled lesson. All the students
needed to do was to copy down what we had just done/learned into their note books.
Throughout the entire lesson, I was watching the reaction of the students and there were a couple that
had a blank face at times and didn’t participate in much of the verbal part of the lesson. During note
taking they took the longest and relied heaviest on what I wrote on the overhead thus those were the
students that were pulled into the re-teach group. Those that had an answer for everything and seemed
above proficient over the past two lessons were chosen to join the challenge group at the front of the
room where they used the current knowledge to challenge their skills and enhance their understanding.
During independent work, I had more closely evaluated my four students in the re-teach group and
within a few minutes of differentiated instruction they were competent in the objective and returned to
their seats to finish their math book page. Meanwhile, I circulated the room and checked the answers of
the independent group and gave stars to those who got the hang of everything. Usually, anyone who
appears to be struggling with the concept(s) are pulled back to the re-teach group (rotate the students
in and out of the group), but in this case all the students met the objective and some exceeded.
Reflection: If you could go back and teach this learning segment again to the same group of students,
what would you do differently in relation to planning, instruction, and assessment? How would the
changes improve the learning of students with different needs and characteristics?
If I could go back and teach this learning segment again to the same students, I would probably move
some tables out of the way. If it were my classroom, my tables wouldn’t even be in rows, they would be
in groups thus I would have more room at the front of the room to be able to make a circle. In the video
I had asked the students to make a circle around the room but looks can be deceiving; the students only
needed about one sixth of the space. In the video, I had asked the students if they knew what kind of
line a radius was and one said, “ray” and so, not paying closer attention, I was referring to the line
segment as a ray instead of a segment.
I do have one student with ADHD and is not medicated. While I was watching the video, I noticed he
moved around a lot, but was still actively participating in discussion and received an A on his quiz. He
doesn’t distract me or the students when he moves around. This is an adjustment I had to make because
at the beginning of the year, it was more distracting to try to keep him sitting still and he was getting
frustrated and shut down easily and not passing his exams. I don’t think I would change how I planned it
only because it worked so well. The students loved sharing what they knew and felt comfortable asking
questions about what they wanted to know. Then the kinesthetic model helped the students distinguish
the difference between radius and diameter. Notes were short and simple, independent work was
successful and the average of the scores for the assessment was 10 out of 11 (91%). Very little review
was necessary.
Math Lesson: Circles
Lesson Title/Subject: Chapter 10 Lesson 5 - Circles
Standards: Algebra and Functions 1.4
Measurement and Geometry: 3.0, 3.2, 3.5
Mathematical Reasoning: 2.3
Instructional Objectives
Learning/Content Objectives
Assessment (formal/informal) – HOW you
will assess: WHAT you will be looking for
SWBAT identify parts of a circle and turns
about the center of a circle.
Students will do drills on their whiteboards
for quick informal assessments.
Students will work independently while I
walk around and check the students work for
another informal assessment.
Language Objectives
Assessment (formal/informal) – HOW you
will assess: WHAT you will be looking for
SWBAT identify and use the terms circle,
center, radius (radii) and diameter.
Students will give answers using these terms
in their statements.
Students will give answers based on
questions that use these terms.
Assessment: I will be able to quickly assess the students using whiteboards. I will ask the students to identify
several parts of a circle by writing the answer on their white boards and holding them up. I can quickly glance at
the whiteboards to see who needs to be in my re-teach group and my challenge group.
Evidence: The students’ answers on their whiteboards during drills will determine what group they need
to be in during independent work; re-teach, independent, or challenge. I will be looking for the proper
and consistent use of the vocabulary terms circle, center, radius and diameter when stating their answers
or explanations. I will also be looking for solutions to problems given using these terms.
Materials and Safety Precautions (if applicable) White boards, markers, erasers, clean overhead, wet erase
marker, math books, math notebooks, pencils, yarn, and index cards (labeled center, radius, diameter).
Procedures
Into (hook/anticipatory set): Bring students to the carpet and find out what they know and what they
want to know about circles, including the vocabulary.
Through (main learning activities)
1. Have students line up, go outside and form a circle in the grass with me in the middle wearing a
sign called the center.
2. Hold one end of string and hand the other end to a student. Ask, “who knows what this line
segment is called?”
a. Explain that it is called a radius and that it is the distance half way across the circle from
the center to the edge.
b. Place index card on in that says “Radius”.
3. Then hand the other end of the string to someone directly across from the student holding the
string and ask how many diameters are there?
a. Answer: 2
b. Then ask, “What is this entire line called?” A: Diameter.
c. Explain that a diameter is a line segment that goes from one side of the circle to the
other while passing through the center.
4. Ask students to return to the room and have a seat with their notebooks open to a fresh page.
5. Draw a circle and label the parts on the overhead and have students copy this into their
notebooks.
6. Have students keep out their note books and get out their white boards and markers.
7. Give sample problems:
a. Draw a circle with a radius, diameter, center and none of these and have students
identify which ones they are on their white boards.
b. When done with the drills, have students put white boards away and follow instructions
below.
c. If anyone is struggling they will join me at the re-tech group at the back table. If this
appears too easy for a few students, they will join the challenge group, and rest of class
will get out their math books, open to page 471 and do problems 1-15 all.
Beyond (closure): When it is time to wrap up, everyone returns to their seat, and then we will look at
the clock. Ask students to tell me to name the parts and as a review from yesterday, tell me what kind of
the angle the two hands are making on the clock.
Accommodations for special needs, advanced and English language learners: Michael, my ADHD non
medicated student will sit with me at the back table so I can keep him on track. My EL students have tested out, but
just in case, I will have demonstrations using visuals and labeling throughout the entire class. Usually my low
achievers are with me at the back table forming the re-teach groups and my high achievers are at the front of the
room forming the challenge group.
Reflection (What worked? Did not work? Why? What did the students learn? How do you know? What would
you do differently next time? How will this inform the next lesson?
Math Chapter 10 Lesson 2
Lesson Title/Subject: Math 10-2 Rays and Angles
Standards: Measurement and Geometry: 3.0, 3.5
Mathematical Reasoning: 1.1, 2.4
Instructional Objectives
Learning/Content Objectives
Assessment (formal/informal) – HOW you
will assess: WHAT you will be looking for
SWBAT name and describe the characteristics
of rays and angles.
Students will form the angle requested using
their arms and also white boards at times.
Language Objectives
Assessment (formal/informal) – HOW you
will assess: WHAT you will be looking for
Ray, Angle, Sides, Vertex, Right Angle, Obtuse
Angle, Acute Angle.
Students will model these terms using their
bodies.
Assessment: Informal assessments will be done through various activities on whiteboards and bodily kinesthetic.
Evidence: I will give several chances for the students to model what an acute, obtuse and right angle is
using their bodies. Then I will put an angle on the overhead and have the students write what kind of
angle it is on their white boards then hold them up for quick informal assessment. I will then have them
draw examples of the three angles on their whiteboards, prior to independent work.
Materials and Safety Precautions (if applicable) White boards, markers, bodies, overhead and pens, math
book and notebook.
Procedures
Into (hook/anticipatory set): have students think, pair, share what they already know about angles.
Through (main learning activities)
1. Have students get out their notebooks to take notes on angles. (building on their previous
knowledge).
2. Have students draw and label a ray.
3. Have students draw example of and label all three angles.
a. Explain labeling/identifying using letters <ABC etc.
4. Have students stand up and model each angle with their arms.
a. Mix up the angles while modeling with their arms.
b. Have students put away their notebooks and get out their white boards.
c. Have students draw examples of the angles
d. Have students label the angles given.
5. Put whiteboards away, get out math books and do pg. 465 #1-15 all
6. Beyond (closure) Using the clock, tell me what angle the hands are making then release to
computers.
Accommodations for special needs, advanced and English language learners For my EL students we will
do kinesthetic movements and labeling pictures to help understand concept. For ADHD students, the
kinesthetic movements will help break up the monotony of sitting in the desks for a long time.
Reflection (What worked? Did not work? Why? What did the students learn? How do you know? What would
you do differently next time? How will this inform the next lesson?