# Spring 2019 Internship – Unit Plan w/ Math Focus

Below is a link to an entire unit, seven days worth of material, that planned for use within my second placement during my internship at Salem Church Elementary School.  It encompasses seven days worth of lessons, a summative assessment that is not a test, and fifteen additional resources that can be used to further support student learning in the area of second grade fractions.

Second Grade – Fractions Unit Plan

# TEDU 522 – Diagnostic Student Interviews

Here is a piece pertaining to and reflecting upon the student interviews that I conducted with third grade students in my previous field placement classroom pertaining to math.

Mathematics Student Interviews

After having the chance to interview several students from my third grade practicum placement class, I have learned quite a lot about not only how children learn and what they understand in terms of mathematics, but also about how complex the process of learning math really can be. It is something that takes time and a lot of work in order to grasp a solid understanding and the capability to then take that understanding and apply it in new, multiple different ways in learning and in our world.

First and foremost, I have learned that one on one interviews are a fantastic way to understand an individual student’s thinking when it comes to different topics in math. They also help to gain a larger picture about where the student stands over all with math and what concepts they truly understand and which they still need work with. But, in order to gain a good picture of what a child understands in terms of math, one must be willing to listen as well as prompt and urge the child to explain more with questioning. A lot of times, children are often not used to explaining what they have done or why. And as such, a teacher must be able to prompt them with questioning and comments to get the student to open up and really share their thought processes and methods. Then it is simply a matter of allowing the student the chance to speak, without interruption no matter if they are wrong or right, and bring to words their thinking. It may sound simple, but this process of interviewing, asking, and listening can be challenging and requires that a teacher be prepared with questions and ideas before the interview, and that these questions be meaningful in sparking critical thinking in a student’s mind.

The most important thing comes from student interviews for a teacher, at least as I believe, is the knowledge of where next to focus their teaching to help better improve and solidify their student’s mathematical thinking. Interviews like these really allow a teacher to see if the student has procedural understanding and can follow the steps to a method, and if they have conceptual understanding, which is desired, and can then explain and expand upon the method in different ways. They let teachers gain a personal, individual understanding of so many different aspects of a child’s mathematical learning and help to guide future direction towards improvement and better understanding. I can personally use the information that I have attained to help the two students I interviewed to practice working on areas where they seemed confused. For example, one student had issues with multiple representations, and so I could work on having her try and use different methods, visuals, words, numbers, etc, to express an answer to a problem. That is only one of many things that can be done to help. The bottom line is, student interviews help educators to help their students.

This experience connects to the reading the class has done through the idea that the interviews help us to move our students to a more engaged and deeper way of thinking about math. Not only can they help us to know where to focus on so that students have multiple ways to solve or interpret a problem, but also how we can they better help them to make connections, explain concepts, or indulge in any number of the other process skills. The interviews help us to see what needs work, and the readings from the book help us to know what to do to better facilitate learning for the desired outcome while still keeping math interesting and relevant in student lives.

I learned a few different things about being a teacher from this experience. For one, I learned that even for one on one tasks, a teacher needs to have patience. They must be willing to sit down and allow a student to work through their own thinking and to make their own mistakes. I have also learned that they also have to be willing to let their students struggle and flail at times in order to gain a true understanding of where the class or a student is. We cannot always be there, holding their hands, through everything. For myself, I learned that I have a knack for making sure that students feel comfortable around me. During both my interviews, neither of my students were shy or displayed any feelings of discomfort even as I questioned them. I can only assume this because of my experience with working with very young children and learning how to speak and interactive with them to keep them comfortable. I have also learned that I need to slow down with me talking. I have a tendency to talk very quickly. There were even a few times my students had to ask what I had just asked because I spoke too fast. This I feel can be remedied through practice speaking slower and timing myself to see just how fast I talk and how ridiculous it is. I feel like I learned a lot about myself and teaching, as well as what I would do differently given the chance.

There are a few aspects I would like to change given the chance to do the interviews over again. I would like to have questioned my students even further, with a wider range of questions, just so I could be sure about what their thinking looked like. I would also like to try and make sure to do the interviews in the morning and not the afternoon, as it seems the students tend to lose focus as they day wears on. I want them to think about their answers in depth and not just blurt out answers because they are burnt out for the day. Aside from that, all I would really say is I would like to make sure that I had all supplies I needed for the interview, like having two pencils so that both the student and I could write at the same time. They may not sound like very big changes, but I feel like they could really help my interviews to better reach their full potential and yield the most enlightening results as possible.

# TEDU 522 – Math Lesson Sequence, Plan, and Reflection

Below is both the lesson sequence that I created for a second grade class, focusing on math, and the lesson plan that I conducted with a second grade, field placement class. Additionally, my reflection for the lesson is also included and helps to offer insight not only into what I had planned to do, but then what actually happened and what I was able to take away from the experience.

Lesson Sequence Assignment:

Strategies for Subtraction – 2nd Grade

Big Idea:

Different strategies that can be used to solve subtraction problems, such as:

• Use a Ten
• Subtract the Parts
• Open Number Lines

Related SOL:

2.6 – The student will

1. a) estimate sums and differences;
2. b) determine sums and differences, using various methods; and
3. c) create and solve single-step and two-step practical problems involving addition and subtraction.

Lesson Plan:

Open Number Line for Subtraction & Addition

Purpose

• Students will gain an understanding of what an open number line is, as well as, how to use one to solve both subtraction and addition problems with numbers containing up to two digits.
• SOL: 2.6 – The student will
1. a) estimate sums and differences;
2. b) determine sums and differences, using various methods; and
3. c) create and solve single-step and two-step practical problems involving addition                                   and subtraction.
• NCTM Process Skills and Mathematical Practices:
• Communication, Reasoning and Proof, Representation
• Model with Math, Looking for and expressing regularity in repeated reasoning

Objectives

• The second-grade students will be able to correctly model using an open number line to solve a subtraction and an addition problem given a subtraction and addition problem, a strip of receipt paper, and a prior review of open numbers lines and operations without error.
• The second-grade students will be able to correctly demonstrate an understanding of different strategies for solving subtraction problems, as they have learned in class, in a number talk given the number talk problem and prompting from the teacher without error.

Procedure

• Introduction:
• Begin the lesson by telling the class that you need their help. Tell them that you want to create a number line but cannot remember what one looks like. Ask them to think about what a number line is and then raise their hands to tell you. Scribe what they say on the board.
• Afterwards, go over the parts of a number line and revise what is on the board if needed.
• A number line is a straight line with two arrows or endpoints, one at each end of the line. It has lines on the actual number line that indicate how much each ‘jump’ is worth.
• Next, tell students that you will be learning how to use a number line to subtract and add. Explain and model that they will use an open number line, which is a number line just without the ‘jumps’/integers. Draw an example on the board.
• Then solve the problems 43 + 36 and 80 – 53 on an open number line, walking the class through the different steps you do to solve it (Model with Math).
• For 43 + 36, start at 43 the make a jump forward of 30 to 73 then another jump of 2 to 75 and a final jump of 4 to 79.
• For 80 – 53, start at 80 then jump backwards 30 to get to 50 then jump back 20 to get to 30 and finally jump back 3 to get to 27.
• Take any questions about using an open number line.
• Development:
• Next, tell students that they will be working on their own open number lines to solve a problem.
• Pass out the receipt paper, one strip to each student, and the index cards with the subtraction and the addition problems on them, one card per table.
• See attached index cards for problems and answer key
• Tell students that everyone will be making their own open number line, but that each person at a table will be working on the same problem. Ask them to do this individually and to start on the subtraction problem. When they finish, they should flip their number line over and try the addition problem on the back.
• Allow students time to work and walk around observing and answering any questions that the students might have.
• Summary:
• When everyone has finished, ask the different tables, one at a time, to stand up in front of their desks and share with the class their original problem and the number lines that they created (Communication and Looking for and expressing regularity in repeated reasoning).
• Be sure to prompt the students to what they did for their number line and why.
• Once each table has gone, thank the class and collect the number lines.
• Then tell them that you have one last thing for them to do and that you would like for them to join you at the front carpet, calling each table to join you at a time.
• Write the problem 47 – 12 on the board and tell students that you will be doing a number talk.
• Go over the rules of a number talk and ask students to think about how they would solve the problem. Tell them that they can use any subtraction strategy they want to.
• Allow them time to think and then ask for some answers. Scribe them on the board and then have students raise their hands and tell you their various methods for solving the problem, scribe these as well (Reasoning and proof and Representation).
• The answer to the problem is 35
• Once students have shared, ask the class for their conclusion and answer and then thank them again for taking part in your lesson.
• Differentiation
• Visual and Auditory learners will have support through the explanation of using an open number line and the number talk.
• Kinesthetic learners will have support through the actual activity of creating their own open number lines
• Students who finish early can be prompted to share with other students, Kagan strategies, about what they think about open number lines.
• Students who finish early can try and create their own problem and solve it on another number line.
• Students who are struggling can have teacher support during their work on the number lines.
• Students who are struggling can have peer support while taking part in the number talk.

Materials

• Teacher
• White board/ Smart board
• Dry erase marker/ Smart board marker
• Index cards w/ each table’s problems
• Students
• Pencils
• Receipt paper strip

Evaluation A

• Student learning will be evaluated by whether or not they have successfully solved their given subtraction and addition problem using the open number line strategy individually and without error.
• Student learning will be evaluated as a class and by whether or not students were able to successfully use, talk about, and explain the different subtraction strategies during the number talk without error.

Lesson Reflection

The math lesson I taught with my second-grade, practicum class went over rather well. My students were very engaged and had a lot of fun making their own open numbers lines, so much so that they were begging their teacher to display them around the room afterwards. But aside from all of the fun, my students were also able to learn from my lesson as well. They not only learned about how to use open number lines to solve both addition and subtraction problems, they also gained more of an understanding that you can use whatever method you want to solve math problems, thanks to the number talk we had. I know they learned how to use open number lines based on the results that I got from each of my students’ open number lines on their receipt paper. My students, of all levels, were able to complete both subtraction and addition problems. Not only that, but they also seemed to realize that they were not limited to just one method for the number talk, though it did take some prompting and a suggestion of my own favorite method while we talked about the problem. Over all, I do feel like my students learned from my lesson and I would love the chance to go back and review subtraction strategies with them to see if it stuck.

I learned a few things from this lesson. For one, I learned that when teaching, a great way to get students excited or interested is to get them to work on things that they can show off or take home. They love being able to show what they can do to those around them. Another thing is that it is super important to see where your students are before you teach a lesson. You do not want to try and teach students a new idea building on a concept if they do not know what the concept you are building on is. It would just lead to a lot of confusion. For myself, I learned that I am actually quite a bit better at direct instruction than I thought. I was able to properly convey my ideas and the concept to my students as they were able to take it and apply it afterwards. Not only that, but I also learned that I enjoy seeing the students make things that they are proud of just as much as they do. I loved seeing them complete their number lines and then have them share them with me.

If I had the chance to teach this lesson again in my own class, I would change a few things. I would be sure to try and make my warm up activity more appealing to everyone so that all students stayed focused, perhaps by incorporating a roleplay aspect into it or having them work in partners or groups to think of something. I would also see if I could do something similar with my direct instruction, having students help me with examples or finishing ideas. I would still, of course, make sure they were right though. And finally, I would definitely try and collect my students’ number lines once they finished, just so I could gain a real feel for whether or not everyone not only got the concept but could then correctly apply it. We would hopefully still have a lot of fun, but I could tweak the lesson to make sure that it was as effective as it could be.

This plan is a like to best practice in a few ways. One way is that it got students to not only communicate with me and each other about what they did to solve problems, but they also had to consider why and how they worked, which would be implementing reasoning and proof, for both the number line activity and the number talk. Not only that, but students also had a hand in using representations during the lesson with the number talk in which they were able to use any method or model they wanted to solve a problem. The number talk also helped to promote more conceptual understanding than just procedural. Students looked at a problem and then decided how they would work with it. There was no set method or prompt for them to follow. Students also worked through productive struggle when I would ask them about a method they used and to explain it for everyone. It really did take some thought for them to be able to do so. I feel that while my lesson could of course include more to fit with best practice, it also did have a lot of the ideas from best practice incorporated into it to help make student learning as focal as it could be.

# TEDU 414 – Multicultural Lesson Plan (Math Centered)

This is a lesson plan created for TEDU 414 that focuses on incorporating a diversity based element into a lesson for a class. This particular lesson is focused on math, bar graphs, with an incorporation of diversity within it.

Diversity Incorporated Lesson Plan

Purpose

Students will gain an understanding of what a bar graph is, its parts, and how to create one. This will allow them to better understand and use information, in the form of graphs, in both school and real life applications. The graphing will be facilitated with the theme of diversity, in which the graph’s content will reflect the various foods of the world and how the students have or have not experienced them.

SOL: 3.17

The student will
a) collect and organize data, using observations, measurements, surveys, or experiments;
b) construct a line plot, a picture graph, or a bar graph to represent the data; and
c) read and interpret the data represented in line plots, bar graphs, and picture graphs and
write a sentence analyzing the data.

Objective

The student will be able to correctly construct a bar graph and interpret the data of one through questions given a blank, graphing worksheet, a diversity based theme, and an example graph without error.

Procedure

Introduction:

o   The lesson will begin with the teacher introducing the learning target(s) for the day and have the students read along, out loud.

• 1. I can collect and organize data.
• 2. I can construct a bar graph and include all necessary parts (title, axis, interval, labels, spaces).
• 3. I can analyze bar graphs and pictographs and write at least one sentence about the data.

o   Students should be asked what they know about both bar graphs and diversity, sharing their prior knowledge with the class.

Development:

o   Have the class convene in a group near the white board or e chart paper.

o   Introduce the book Whoever You Are and read it aloud to the class.

o   Afterwards, relate the concept, that everyone is different, but we all enjoy the same things, to the lesson by telling the class that everyone has tried some sort of food from a different place in their lifetime.

o   Tell them that the class is going to prove it by creating a bar graph and explain what a bar graph is. Be sure to talk about the different parts of a bar graph as well (TAILS) (aural learning).

• A bar graph is a type of graph using big bars to represent an amount of something in a category. They are used to compare data of different categories.
• T – Title, A – Axises (they do not need to know the specific names, just that there are two axises), I – Intervals (rate of increase), L – Labels, S – Spaces (bars are not on top of each other)

o   Using the whiteboard or chart paper, model creating a bar graph for the class. Be sure to go over each of the parts as you create it, telling the class and writing down what the title, axises, labels, spaces, and the intervals are (visual learning).

o   Then write in four different categories at the bottom related to foods around the world, such as:

• Spaghetti, Sushi, Tacos, and Fish & Chips (any combination will work)

o   Ask the class to raise their hands if they have ever had the different foods, and then record the information on the graph (interpersonal learning).

o   Allow the students to see the data and then ask them the following questions (at least two);

• Which food have the most students in our class eaten?
• Together, which two foods have the most students tried?
• How many more people have tried (insert food) than (insert second food)?
• Why do you think we eat so many different foods from different places? (diversity link)

o  Next have students return to their seats and ask them to construct a bar graph of their own based on the following question about these different foods and consequent data (on tally chart linked below):

• “Have you ever tried Chinese food, Hamburgers, Frog legs, or Pizza?”

o   Pass out the blank graphing worksheet, one per student.

o   Allow them to set up a bar graph, using the one you did as a class as an example. Be sure to give them the interval to use.

o   Once that is done, allow time for students to construct their bar graphs based off of the info. Remind them that this is individual work (intrapersonal learning).

o   When finished students should turn over their papers.

Summary:

o   End the lesson by having each student answer a question about a bar graph as an exit ticket (logical learning).

O Write the following question:

• Which two foods have people tried a total of thirty times together?

o Have students answer the questions on the back of their graphing worksheet and turn them in when they are finished. Be sure to review the exit ticket question as a class.

Differentiation

o   Students who finish early can work on coming up with their own questions that might be able to use a bar graph to answer.

O Students who finish early can practice constructing bar graphs and labeling the different parts.

o   Students who struggling could have teacher assistance

o   Students who are struggling could have assistance from students who have already finished help

Materials

Teacher

o   The book; Whoever You Are by Mem Fox

o   Writing tool; expo maker, pen, pencil, etc.

Students

o   Blank graphing worksheet (see below)

o   Pencil

Evaluation

(Part A)

–          Students will be assessed by the bar graph and the exit ticket that they turn in. Student work will be evaluated and learning progress will be considered based on whether or not they have correctly created and organized their bar graph, and whether or not they have correctly answered the question to the exit ticket.

(Part B)
Did the students meet your objectives?

How do you know?

What were the strengths of the lesson?

What were the weaknesses?

How would you change the lesson if you could teach it again?

Bar graph worksheet courtesy of Education.com

Tally Chart with Food Data

# MATH 362 – Student Work Discussion and Analysis

The experience of working with students in a classroom environment has been very enlightening to me. I have learned quite a bit about how math students have been learning material. For one, I have noticed that there are quite an extensive number of different ways that students have been learning to solve problems for the same concepts. While one student may draw pictures, another might use the standard algorithm. This is important because it helps me to see and be ready to teach math in various ways. I have to be able to pay attention to the students and understand that every one learns things differently, and then tailor my teaching to the methods that work best for my students at the time. On top of that, I should also try to challenge students, not so much with more difficult numbers or operations, but rather with having them do more critical thinking. Instead of just having them solve a problem, I should work towards having them explain it as well. That way they gain a better and fuller understanding of the mathematical concepts and why we do the things we do with them. I would also help to try me to better see where my students still need extra help with and then I can, again, adjust my teaching to hopefully make sure that everyone has a better understanding of the material being presented to them. Though it will most definitely be a challenge, especially with limited time in a day to teach, I will do my best to make sure that I try to incorporate these ideas into my teaching and work to make sure that students get the fullest out of their education, not only with math but with in all the subjects that they have to learn.

# Math 303 – Geometer’s SketchPad in the Classroom

Creating Carnival Tickets with the Geometer’s Sketchpad

Instructions:

1. First construct a line segment, we’ll call it AB. Make sure to label the points, A and B.

2. Create a point somewhere above AB and label it C.

3. Mark AB as a vector, by selecting it, clicking on the  transform tool, and selecting mark as vector, then select point C.

4. With point C selected, use the transform option to translate AB with point C.

5. With the translation in place, close off the rest of the polygon for a parallelogram like figure.

6. Use the line segment tool to create multiple little segments from point A to C, much like a torn section of paper.

7. Making sure that AB is still the marked vector, select all the little line segments from the previous step and translate them.

8. Select all the vertices of the shape and use the construct tool to fill in the interior. Use any color you’d like.

9. Keep AB as your vector and then select the interior of the shape.

10. Translate the shape. And repeat this, by selecting the newly created shape each time, until they disappear off of the page.

11. Then make BA your new vector and repeat the translating with the colored interior.

12. Make sure that each alternating shape is a different color.

13. Using the Polygon Edge tool, create another parallelogram within the first one. This does not have to be perfect. Do this for each of the shapes your created while tessellating.

14. Make sure that the new shapes are not the same color as the first ones and then use your text tool to make up any kind of ticket information you’d like. (Optional, hide any unwanted lines and vertices from the original shape)

And voila, there is your finished line of carnival tickets.

Reflection:

A. How has the program allowed you to explore geometry in the classroom this semester?

With the use of Geometer’s Sketchpad, I have been able to understand the concepts that we have covered in class on a more in depth level. I have been able to not only review ideas that we have gone over in class, but also gotten hands on experience with working with these various concepts thanks to the assignments we have been given for the program. Aside from what was covered in class, simply being able to work on my own and look at all the different tools in the program has introduced me to more geometric concepts. I have been able to look more at what makes a polygon and how they can vary in shape and size, not just be regular. And working with polygons more is just one of the things I have had the chance to explore with GSP. I hope to continue using it to learn and understand more about geometry as a whole.

B. What are the uses of the program in your future classroom?

The uses of this program in my own future classroom will be many and varied. I can use it as a way to introduce basic shapes, teach about angles and measurements, how to work with rigid motions, and a number of different things. Most of which will probably be in class demonstrations followed by students replicating their own versions of the assignments. I hope that it will be a hands on tool that will not only help to teach students further about geometry, in all different grade levels, but also help to keep them interested in the subject as a whole.

C. What are the strengths and/or weaknesses of the program?

The strengths of this program definitely lie within how it offers more hands on experience for students to be able to work with concepts that, at times, can be very confusing. They are able to try an assignment and work with a geometric concept at their own pace with their own thought processes and hands. Its weaknesses, however, are that it can be rather confusing, especially to start with. Students need to have very clear instructions to be able to properly use the tools that the program offers and work with the concepts, at least until they have become more accustomed to it. A different format for the program with more clearly labelled tools would definitely not hurt it, particularly for younger students who may be using it. But with both its goods and bads, I would definitely suggest it for anyone learning or teaching geometry to use GSP.