Tag Archives: Mathematics

Week 13 – Mathematics – Finishing 2D Shapes

The end of the year is fast approaching and I am just so thankful for all of the opportunities that I have had in the Residency (UTRPP) Program. I am so glad that my collaborating teacher has provided me with the opportunity to continue to take the lead on teaching and planning in all subject areas so I can continue to gain more experience in front of the classroom.

I have many chances to experience guiding students through multiple units and on Monday we finished our 2D Shapes unit. The students took the assessment and based on what I observed, many of the students understood the content. There are still many students (about 6) who were unable to take the test because they were absent but I am eager to see their scores because I think they will show a good understanding of the content. One of the great things about teaching and planning math for the entire unit was that I am able to see the growth of my students and help address misconceptions and alter lesson plans to meet their needs.

For example, when teaching about equal parts, my students were confusing about whether or not certain squares were split into fourths. The students were able to recognize that four small squares or four rectangles that all looked the same are fourths but they were unable to make the connection when looking at a square split in half where the two halves are split in different ways.


In the top squares, each piece is the same size. (I apologize that the rectangular pieces are not perfect on the second square but I wanted to show a pictorial representation of a misconception that my students had.) The third square, however, looks as if the four parts are no equal. But each side of the square (shown below using colors) is half of the square. Since these two pieces are cut in half each of the four parts are equal.


This was a difficult concept for my students to grasp so I used actual paper that I cut up in front of the students along with drawings on the white board to help them understand. By providing this realia, I was able to bridge the gap in my students’ knowledge and allow many of them to grasp the idea. I felt like this was an important part to teach to help build their conceptual knowledge of splitting shapes into equal and unequal parts because my students made the assumption (which is a misconception) that when a 2D shape is split into parts of different shapes, that the parts are unequal.


For example the fourth shape is split into rectangles and squares as taken from the other shapes on top. The parts are all equal even though they are different shapes because they are all half of half of the original shape. Although this terminology seems confusing, this conceptual knowledge can be helpful in the future, especially when students have to discuss fractions using ½ and ¼ and multiplying fractions to find half of a half or ½ x ½ = ¼.

I am approaching the final days of my internship, which is exciting because of the new opportunities that await me in the future but also a bit sad because I will really miss my classroom and my students. I have made so much growth and progress over the course of this year and I just cannot believe everything that has happened to me throughout my experience in the Residency Program. I can definitely say I would not trade this for anything.


Week 12 – Mathematics – 2D Shapes

Lesson Plan for Observation on 4.9.15

I have continued to take the lead on teaching all subject areas in my classroom, which has been such a wonderful experience. I can clearly tell that I am making growth with my teaching. My collaborating teacher commented that my flow has definitely improved. I am just so excited to be able to practice. In the previous week, I had used a timer to help me stay on track and once I got a feel for the time, I was able to stop using it because I was more familiar with the timing of my lessons.

I planned a special mathematics lesson about decomposing 2D shapes in which I designed all but one of the worksheets. I was really proud of this lesson because it was a real observation to evaluate my teaching and I believe I did a good job. I introduced the lesson by engaging the students with a mathematics game. Then I did some explicit modeling for the students.


Once I collected enough anecdotal data through a quick check and observations, I made groups based on ability levels and gave the students worksheets that I created. I pulled a small group to provide extra support. Then I called the students back together to complete an exit ticket and for the closure of the lesson I had the students answer the essential question. I really liked the lesson because I gave the students the opportunity to explore the 2D shapes with lots of hands on experiences and movement. One aspect of the lesson that I would have liked to work on would be to give the students a bit more time for the exit ticket but I wanted to make sure that there was enough time for the closure.

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One thing that I really like about creating my own worksheets is that I can make them to meet the needs of my students. For example, on the worksheets there are four small shapes: a triangle, a rhombus, a trapezoid, and a hexagon. The original worksheets that I found (see the first worksheet) had the students simply draw lines to show how they decomposed the shapes but after watching my students during other lessons, I noticed that my students had a lot of trouble with this. I think this may be related to difficulties with fine and gross motor skills but also because it is difficult to record the information even though students can explain it verbally. So I provided my students with the opportunity to circle the shapes they used in order to show me what they did so I could gain a better understanding of whether or not my students grasped the concept. On the actual worksheets, I colored in each of these shapes so the students can choose what shapes they used because they resemble the pattern blocks that they used just in case the students could not tell what the shapes were since I hand drew them. All in all, I really liked my lesson and I am glad that I was able to teach all of the previous lessons so I had enough anecdotal data and observations to make these key decisions to help my students be successful.

Another aspect of my classroom that I am extremely excited about is the amount of exploration elements in the room related to our science content. We have multiple plants growing inside and outside of the classroom. For our Long Term Investigation (LTI) the students are analyzing the changes and growth of catnip grass plants inside and outside, then we are also trying to grow lima beans and two potatoes. We are also raising meal worm beetles and we just received a shipment of pill bugs that we will be introducing shortly. The final, most exciting, element in my classroom right now is monarch butterfly caterpillars.

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The students are extremely excited about the caterpillars. They check them every day in the morning to see their growth and to see how much of the plant has been eaten. I was very happy to see one student doing research on caterpillars when she was in the classroom library so we put the book (as seen in the above picture) next to the caterpillars so they students can learn about the caterpillars as well. One of the best parts about this is that the students are so engaged that they want to share the butterfly garden with everyone that enters the room, including the principal.

I have had so many wonderful experiences in my classroom which I am extremely thankful for. I am so happy that my collaborating teacher has provided me with a lot of support so I can do things such as providing students with all of these exciting parts of the classroom to explore.

Week 11 – Mathematics Content Coaching – Observation 2D Shapes

Lesson Plan: Mathematics – Week 1 – 2D Shapes 

I taught a mathematics lesson about the defining attributes of 2D shapes on Wednesday of the previous week. For this lesson, I met FEAP 1A by aligning my lesson with the standard: “MAFS.1.G.1.1 – Distinguish between defining attributes (e.g., triangles are closed and three-sides) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.” By the end of the lesson, my students had to be able to answer thee essential question: “What attributes can you use to define 2D shapes?”

When I was younger, I built 2D and 3D shapes using toothpicks and marshmallows and I wanted to incorporate that fun and engaging activity into my lesson to keep the students interested. I made sure to discuss the importance of using the items as math manipulatives. My collaborating teacher and the math content coach both agreed that the students were able to use the tools well and there were few, if any, distractions or students who misused (or ate) the tools. I first asked the students to make a rectangle and then I had a few students build rectangles under the document camera. My content coach offered a great suggestion to decrease the amount of time spent waiting for students to build these shapes; she said I should have the students build the shapes on dry erase boards and then have them lift the board and bring it to the front to share.

I had the students build a few other 2D shapes and then I challenged them to build a circle using the toothpicks and marshmallows. Immediately the students were very vocal, telling me that they could not make a circle. I challenged them and told them to try, which unfortunately actually brought one student to tears when we became frustrated. I wanted my students to fully understand that a circle is made up of curved lines, no straight lines, which is why it has no flat sides or vertices and cannot be considered a polygon. I then gave the students a pipe cleaner, which they were able to easily form into a circle. I was a bit shocked that a student actually started to cry from frustrated but I definitely wanted to challenge my students and have them think critically about the shape. One student actually made a circle with marshmallows, which was great thinking but technically not aligned with the question. But I had her share what she did because I think it is so important for students to think outside of the box.

The students then completed differentiated worksheets independently and then they completed an exit ticket, which they helped design the rubric for. They had to answer the essential question, “What attributes can you use to define a 2D shape?”


I really love this rubric system and have used it many times in the classroom. Purple is the “highest” score one can receive, next green, then orange, and yellow is the bottom color. The students aim to get a purple score, but a green is still a good score. The students led the creation of this rubric.

In mathematics, we have our students explain their thinking using a “5 Star Sentence.” Which is a sentence with a capital letter at the beginning, correct punctuation, correctly spelled sight words, and if a student does not know how to spell a word, he or she underlines the word. The students also needed to make a drawing/model of a 2D shape and label the shape with the attributes. The students decided not to put a specific number for the amount of labels for purple, which I liked because it gave them the opportunity to talk about all different kinds of defining attributes, instead of just sides and vertices.

One interesting part that the students wanted to add was the phrase “Don’t try” to the yellow part of the rubric. I have noticed that sometimes the students want to add this to the rubric. I think that on almost all occasions, students want to try and be successful in the classroom; however, my collaborating teacher and I have made it very clear to the students that they can receive assistance if necessary and that it is better to ask for help instead of not trying. I feel like this word choice was very interesting and it shows that they really want to show what they know and believe it is important to always try their best.

After the students turned in their exit tickets, the math content coach had them discussed what they learned in relation to the essential question. She recorded their responses on the board to see if my class had a good understanding of the content and were able to answer the essential question.


After the recorded their answers she asked them to tell her what the attributes are of a 2D shape, which she labeled with a box (which one student pointed out is the shape of a rectangle). I was very, very pleased with their answers and I really felt like this discussion showed that my students clearly understood the content from my lesson.

I was really excited that my math lesson turned out well. I will continue to be a part of mathematics content coaching, although I may not receive another full observation cycle but the content coach may come in to observe me. I am excited for the end of the year but I still have a lot to do during these last few weeks. I have been granted the wonderful opportunity to take the lead on teaching all content areas for over two weeks (excluding testing week), which I hope will continue so I can gain more and more experience to help me improve my teaching.

End of Semester – Weekly Reflection

The semester is winding down and the first part of my final internship is coming to a close. I am so excited to be a part of a classroom as a virtually full-time teacher. I have gained so much knowledge and experience by being a member of the Urban Teacher Residency Partnership Program (UTRPP). I am excited to continue my journey to becoming a future educator by co-teaching and co-planning and taking the lead on various subject areas in the classroom. For this semester, I have taken the lead in both Social Studies and Science. I co-plan most subject areas with my collaborating teacher and we co-teach the ELA block as well as Mathematics. I am still absorbing lots of information for my collaborating teacher by observing her lessons and teaching methods.

Although there was no content coaching this week, I still participated in the classroom as much as possible. In Social Studies, I taught the students based on the standard “SS.1.A.2.2 – Compare life now with life in the past.” For this current week and the following week, we will focus on “SS.1.A.2.1 – Understand history tells the story of people and events of other times and places.” I have introduced the topic of biographies to my students and will teach them about famous individuals such as Susan B. Anthony, Jane Goodall and George Washington Carver. In order to make this lesson more meaningful to the students, for the last week of December, my students will write biographies about their classmates. This culturally responsive teaching allows the students to explore facts about each other and make each individual feel important and special.

In Mathematics, we have been working on place value and reading numbers on a Hundred Chart.



This aligns with the standards “MAFS.1.NBT.1.1 – Count to 120, starting at any number less than one 120. In this range, read and write numerals and represent a number of objects with a written numeral” and “MAFS.1.NBT.2.2 – Understand that the two digits of a two-digit number represent the amounts of tens and ones.”

One of my favorite activities for these standards is Hundred Chart Puzzles. The students are give a “piece” of a hundreds chart and must use their knowledge of counting by ones and tens to fill it out.



These standards are important to help students understand concepts in the later grades, for example, a student needs to understand the basic concepts of place value before learning about hundreds and thousands as well as decimals. Teaching students to count by tens also helps create a basic understanding of multiplication by tens.

In Science, the students have participated in multiple design challenges not only through the Inquiry Monday lessons but through my science lessons. The science content that we are learning about aligns with the standard “SC.1.E.5.1 – Observe and discuss that there are more stars in the sky than anyone can easily count and that they are not scattered evenly in the sky.” This is an important concept to teach because it introduces the idea of the vastness of space and types of stars in the sky. It is important that students notice that even though there are constellations in the sky, the stars are not arranged in specific patterns that match these constellations.

I am excited to continue working with my collaborating teacher as we finish up the final weeks of the semester. I cannot wait to go on my first field trip to a farm during the last week of school (December 15th through December 19th). I will continue to work in my internship during the final week of school. My college courses ended last week and this week is considered “finals week” although technically speaking I do not have any finals. I am happy that I can put all of my efforts into focusing on my internship and making the most out of my experience. There is so much to come and I cannot wait!

Mathematics Lesson Plan – Basic Facts to Twenty Reflection

Math – Week 1 – Lesson Plan – Adding And Subtracting Within Twenty

Nicole L Pre Observation Coaching Lesson Document (PPQT) 11.17.14

Math – Week 1 – Lesson Plan Draft 2 – Adding And Subtracting Within Twenty

Math – Week 1 – Pose Purposeful Questions Reflection Tool

The mathematics content coaching cycle was a bit different than the previous content coaching cycles. For this cycle, the mathematics coach will focus on three or four residents each week. I designed and implemented my lesson plan for mathematics in the first week. The mathematics coach wants to make sure that she gives everyone ample time to perform a pre-conference, observation, and post-conference so it was decided that each resident would receive specific coaching for one week. I will continue to work with my collaborating teacher to co-plan and co-teach mathematics during the semester but at this point in time, I will not participate in the content coaching observation cycle for the remainder of the semester.

Before my mathematics lesson, I met with the mathematics content coach to discuss my five page lesson plan and how I would pose purposeful questions. We talked through some of the elements of the five page lesson plan such as the goals, possible misconceptions, and prior knowledge but the main focus was on question types. It is important for me to not only use and create higher order thinking (HOT) questions but to pose questions of various types to elicit student thinking. There are four types of questions that we analyzed: gathering information, probing thinking, making mathematics visible, and encouraging reflection and justification. I believe that it is important to focus on these questions so that I do not only ask questions on the lower levels of Bloom’s taxonomy. By working with the mathematics coach on my questioning, I met FEAP 3F – “Employ higher-order questioning techniques.” We worked together to create questions for each framework and I determined how I would use them in my lesson.

After our discussion, I revised my lesson plan to change some of the questions, add new questions, and charge the order of some questions in my lesson. The majority of my lesson plan was the same. I aligned my lesson with the standards MAFS.1.OA.1.1
“Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem” and MAFS.1.OA.3.6 – “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten,; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums by creating the known equation.” This allowed me to meet FEAP 1A –  “Aligns instruction with state-adopted standards at the appropriate level of rigor.”

For this lesson, I designed my own groups based on previous data that I collected through anecdotal notes and observations. This allowed me to meet FEAP 3H – “Differentiate instruction based on an assessment of student learning needs and recognition of individual differences in students.” There were a few students that I believed would need additional support for the lesson. I collected data through observations and used this to inform my instruction by pulling a small group as the other students worked in pairs. I designed the assessments based on the abilities of my students to match their learning needs. This allowed me to meet FEAP 4B – Designs and aligns formative and summative assessments that match learning objectives and lead to mastery as well as FEAP 4D – “Modifies assessments and testing conditions to accommodate learning styles and varying levels of knowledge.”

When I implemented the lesson, I modified it in order to meet the needs of my students and address their misconceptions, which allowed me to meet FEAP 3D – “Modify instruction to respond to preconceptions or misconceptions.” I asked the students to show me two ways to make ten. We listed these methods on the board and I asked them if there were other ways to make ten. After we had about five methods (all addition) on the board, I asked how many ways we can make ten. Not surprisingly, my students counted the methods on the board. I decided to take the time to show my students there are many ways to make ten using addition of two and three addends as well as subtraction. I tried to grant the students the opportunity to list ways to make ten without explicitly mentioning using three addends or subtraction. After some gentle pushes, the students grasped the concept and realized that there are a lot of ways to make ten.

I wanted to highlight this point because I want my students to become familiar with the various basic facts within twenty. My students have been working on balancing equations on each sides of the number line and finding equations that are equal. This lesson connected to these previous lessons by showing students there are multiple number sentences that equal ten or any other number. By doing this, I met FEAP 1B – “Sequences lessons and concepts to ensure coherence and required prior knowledge.”

After my lesson, I watched the recording and took notes about my questioning strategies and the types of questions that I asked. One important aspect of my teaching that I noticed is that the majority of my questions were unplanned. This is important to know so I can focus on planning more questions ahead of time. This could also show how I respond to my students. I noticed that I repeated some questions a lot such as “are there more ways to make ten?” I did this because I wanted to probe my students’ thinking without explicitly telling them to use subtraction or three addends to find a number. In the end, they needed some guidance to understand this concept but I assumed this would occur. My students typically have more success with addition as compared to subtraction. I assumed that my students would easily see the addition facts and need some help finding subtraction facts, which is what occurred. This shows me that my collaborating teacher and I should provide extra support in the area of subtraction and provide our students with many opportunities to practice subtraction. This allows me to meet FEAP 4A – “Analyzes and applies data from multiple assessments and measures to diagnose students’ learning needs, informs instruction based on those needs, and drives the learning process.”

As always, I am excited to continue taking the lead on planning and teaching various subjects in the classroom. I hope to continue co-teaching mathematics with my collaborating teacher and taking the lead on lessons to increase my comfort level with mathematics and gain more experience. I am excited to continue focusing on mathematics in the upcoming weeks even if I do not participate in formal observations and conferences.

Story of My Professional Learning

For the end of the semester, I created a video entitled the “Story of My Professional Learning” to document my growth over the past semester. I cannot post the video online; however, I wanted to post the script to my video to show my journey.


This semester I was placed in a co-teach kindergarten classroom with thirty six students. I was nervous at first because I had no experience in this type of setting but over time I became comfortable and took over many responsibilities in the classroom. Internship has been challenging at times but I would not trade this experience for anything.

Instructional Planning/Exceptional Students:

In the beginning of the year, I collected data about the learning styles of my students. I used this information with observations and anecdotal notes to inform my instructional planning. When I created lessons, I did my best to meet the needs of my students, which was a part of my FEAPS 2H goal: “Adapts the learning environment to accommodate the differing needs and diversity of students.” I designed a variety of differentiated lesson plans for mathematics, social studies, and literacy to meet the needs of the exceptional students in my classroom.

Social Studies:

In my classroom, social studies is typically integrated into the curriculum through literacy. My students have learned a lot about other cultures through celebrations of Black History month and the Chinese New Year.

I created my own lesson plan in which students learned to use and create timelines. I taught a small group of advanced learners to manipulated timelines and then they created their own timeline of the events in a typical school day. The students used post-it notes to write down the events of the day, which allowed them to rearrange the events easily if necessary. Providing students with these supports allowed them to be successful in this lesson.

I incorporated technology like Prezi and Mimio into this lesson plan. I used Mimio for the first time this semester and I think it is a great tool for the students to use. My students enjoy using the Mimio so much that we created a play center for piece of technology so the students have constant access with this technology to build knowledge.

Intermediate Literacy:

Before coming into the residency program, I had almost no experience with literacy education. In the previous semester I performed multiple read alouds and took on a literature circle. This semester I challenged myself to get out of my comfort zone and participate in more areas of literacy in the classroom: shared reading, guided reading, and writing lessons. I also made a goal for myself to perform more read alouds in the classroom. I still get nervous when I am in the front of the classroom, but I was able to overcome my nervous and focus on the lesson.

For my read aloud of Armadillo Rodeo, I created questions to ask before and after the read aloud that aligned with the standards, which helps me meet my FEAP 1A goal to “align instruction with state-adopted standards at the appropriate level or rigor.”

This semester, I also pulled guided reading groups in my classroom. The groups are named based on the areas of need. My groups were “Letter Leopards” and “Sound Seals.” It was a bit difficult to keep the students on task, but I was able to help them understand the text through open ended questions.

I also took over writing in my classroom over the past few weeks. During writing instruction, the students write sentences and I walk around the room to provide support. During the first few lessons, I struggled to remember what my students had written since their words did not always match up with their thoughts. To fix this, I began taking notes so I could record the information and pass it along to my collaborating teacher so we could determine if the students were meeting their goals for writing.


In mathematics, I worked with many small groups of students to provide them with extra support. When I worked with the students, I included questions based on the Common Core Standards for Mathematical practice to help students think critically about the lessons.

For one lesson, my teacher did a read aloud of Pete the Cat and His Four Groovy Buttons for subtraction. I worked with a small group of students at a slower pace to provide additional support. One of my English Language Learners excelled in this small group because he was able to verbally convey his knowledge because he struggled with writing his ideas down.


This semester, I used data-informed research, as part of my FEAP 5B goal, in order to perform inquiry in my classroom. My inquiry question is: “How do I accommodate for the visual, kinesthetic, and auditory learning styles of my students in social studies, mathematics, and English to increase student engagement?” I chose this question because I want all of my students to have their needs met so they can learn in the best way possible.

For my inquiry, I surveyed the class to determine their learning styles and formed a group of six learners with visual, kinesthetic, and auditory learning styles. I taught and helped with multiple lesson plans, some of which were differentiated and others that were not, and interviewed the students to determine which lesson engaged them the most. The three lessons were Word Wizard, a sight words lesson, Land and Water on the Globe, a lesson about discovering if there is more water or land on the earth, and Letter Sorting with Whiteboards, in which the students spell out words and determined if they began with a chosen letter.

I discovered that a visual, a kinesthetic, and an auditory learner all found that Word Wizard was the most engaging and interesting lesson. I believe this is because Word Wizard is one of the most differentiated and accommodated lessons plans in my classroom. It is also one of my favorite lessons to teach.

I took over Word Wizard in the beginning of the semester. For these lessons, the students say, spell, and use sight words in a sentence. The students stand up and perform Total Physical Response as they do fun movements while they spell out the words. I noticed that the verbal responses and movements accommodated auditory and kinesthetic learners but I wanted something for visual learners so I created posters for these students. The students really loved these posters and told me so on many occasions. I am very glad that the students enjoy this lesson and I will continue to evolve it and improve it to meet the needs of my class.


The residency program has provided me with amazing experiences inside and outside of the classroom that has helped me grow as a future educator. I am so thankful for this program and everything that I have learned so far.


I would like to thank my collaborating teachers, UTRPP professors, my students, my elementary school, and my peers for their continual support in making me a better educator.