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Teacher Work Sample – Electronic Submission Document

Introduction Student Teacher Michala Maurer Cooperating Teacher Brad Vancura School Seward Middle School

Context of Teaching

My Student Teaching I experience took place at the Seward Middle School in the 6th grade classroom. I slowly took over Mr. Vancura’s math classes during the time I was at the middle school. Mr. Vancura teaches math during five periods of his day and here is the breakup: 2nd hour includes his middle level students, 3rd hour includes his lower level students-many have an IEP, 4th hour includes his upper level students, 6th hour includes his second group of middle level students, and finally his 8th hour includes his math intervention students. I then did my teacher work sample with the 4th hour students (28 students-14 girls and 14 boys). This particular period moves through material fairly quickly and picks up on the concepts more easily than the other periods. Mr. Vancura and I decided that I should focus more on this period for my teacher work sample because he knew we would be able to make it through my unit and that they would enjoy the performance task at the end. Whereas, the other hours take longer to pick up on concepts and need more repetition with material so we weren’t 100% sure we would through my lesson by the time I was done at the middle school. Mr. Vancura let me pick up 4th hour the second week that I was with him and before that I taught bell ringers and went over homework the second day I was there. Mr. Vancura told me what unit I would be teaching during the time I was with him and then beyond that I would tell him my ideas and give him my lesson plans and he would give me advice and suggestions from there. So my TWS material involves graphs, mean, median, mode, and range from Unit 6 in the schools Math Connects Series. Students do bell ringer problems that will appear on their state test in April, which is a good form of reviewing old material as we move through new units.

Brief overlay of what we will be covering: Day 1-Bar Graphs, Day 2-Line Graphs, Day 3-Mean & Median, Day 4-Mode & Range, Day-5-Work on surveys and graphs, Day 6-Work on surveys and graphs, and Day 7-Work on surveys and turn in graphs.

Understanding by Design Stage One

Stage 1 – Identify Desired Results Established Goals:

MA 6.4.1 Display and Analysis: Students will organize, display, compare, and interpret

data.

MA 6.4.1.c Find the mean, median, mode and range for a set of data.

http://nde.ne.gov/math/index.html

What understandings are desired? Students will understand that.

Overarching: Mathematicians use graphs and data to find patterns and relationships.

Topical: Bar graphs and line graphs can be used to organize data.

We can determine patterns in data by finding the mean, median, mode, and range.

What essential questions will be considered?

Overarching: Why do we study graphs and data?

Topical: How can we easily organize our data?

How can we determine patterns in our data?

What key knowledge and skills will students acquire as a result of this unit? Students will know. . .

Bar graphs

Line graphs

Mean

Median

Mode

Range Students will be able to. . .

Read and analyze bar graphs and their data

Read and analyze line graphs and their data

Explain the differences between mean, median, mode, and range

Compute the mean, median, mode, and range for a set of data

Pre-Assessment

Name____________________________ Period_______________

Label the name of each graph:

___________________________________ _______________________________

1. Find the mean of the following values: 20, 33, 46, 22, 34

2. Find the median of the following values: 2, 6, 1, 9, 10, 32, 15

3. Find the range of the following values: 110, 120, 135, 145, 176

4. Find the mode in the set of values: 66, 45, 33, 43, 20, 21, 33, 40, 50

Student Name_____________________________

Category 3 2 1

Able to determine

the names of

graphs

Students has a clear

understanding of

the difference

between a bar and

line graphs.

Student appears to

have an idea of the

difference between

a bar and line

graph.

Student appears to

not have a grasp on

the idea of the

difference between

bar and line graphs.

Recognize the

definition of mean

and use the correct

steps to find it

Student knows what

mean means and

used the correct

steps to find it.

Student appears to

have an idea of

what mean means

but shows the

incorrect steps to

find it.

Student is unable to

complete the

problem or solves it

incorrectly.

Recognize the

definition of

median and be able

to find it

Student knows what

median means and

was able to show

how they found it

Student appears to

have an idea of

what median means

but doesn’t show

work.


complete the


incorrectly.

Recognize the

definition of mode

and be able to find

it

Student knows what

mode means and

was able to show

how they found it.

Student appears to

have an idea of

what mode means

but doesn’t show

work.


complete the


incorrectly.

Recognize the

definition of range

and be able to find

it

Student knows what

range means and

was able to show

how they found it.

Student apears to

have an idea of

what range means

but doesn’t show

work.


complete the


incorrectly.

In the above chart we see that the majority of students knew the difference between bar graphs and line graphs. All students were able to correctly label bar graphs, but eight students labeled line graphs incorrectly labeling them as dot graphs, line plots, chart graphs, number graphs, or a grid graph. The two items students seemed to struggle with the most was mean and range based on these results.

This information gives me a great base to build upon. The students seem to have a solid understanding of what the important vocabulary means. But looking at students’ papers it was easy to tell that students were confusing the terms and mixing up the definitions of mean, median, mode, and range. Even though students were clearly mixing up definitions which were affecting their answers, it was clear that most students had background knowledge in this chapter.

In light of the pre-assessment results, I realized that we were going to have to give a vast majority of our attention to learning and understanding the differences between mean, median, mode, and range. A large chunk of this time would be spent on mean and range since those are the most troublesome areas, but I knew that if we spent a good chunk of time on each it will help explain the differences and steps needed to solve for each. So I had students make vocabulary foldables that had the terms, their definitions, steps to follow, and an example of each. Almost all students had a clear understanding of bar and line graphs so I knew that a great deal of that information would be review and reestablishing prior knowledge.

Understanding by Design Stage Two

Stage 2 – Determine Acceptable Evidence What evidence will show that students understand? Performance Tasks* (summary in GRASPS form):

0

5

10

15

20

25

30

LabelingGraph Types

(Blue-BarGraph,

Orange-LineGraph)

Mean Median Mode Range

Number of Problems Students

got

Correct/Incorrect

Section of Pre-Test

Pre-Test Results

Correct

Incorrect

G=The students will be able to apply the concepts of bar graphs and line graphs to their own graphs and sets of data. R=The students will be able to collect real world data and find relationships and patterns by analyzing their graphs. A=The target audience is their classmates and I. S=Students will be divided into groups, each group will decided on a different survey question to ask the other 6th grade study hall periods. Student will then either be making a bar graph or line graph of their data and then find the mean, median, mode, and range. P=The students will need to collect data from the other 6th grade study hall periods and then make either a bar graph or line graph of their data. Then students will need to find the mean, median, mode, and range of their data. S=The standards are included in the rubric that can be found under post-assessment.

Other Evidence (quizzes, tests, prompts, observations, dialogues, work samples):

Set of worksheets-one contains data and a bar graph to fill in the bars along with a couple questions to analyze the graph and the other one contains a completely empty bar graph that needs labels and the data filled in

Two worksheets-working with a partner students will make and interpret line graphs

Worksheet Pg. 41 to practice finding the mean of a set of data

Worksheet Pg. 49 to practice finding the median, mode, and range o All worksheets are shown along with the lesson plans.

Two work days on graphs in lab with their gathered data

Student Self-Assessment and Reflection:

What challenges did you encounter?

Which part was particularly helpful or enjoyable?

How may I improve the unit to assist your learning?

How would you describe your comfort level with the material that we covered in Unit 6?

Did you enjoy the graphs and data unit?

Post-Assessment Post-Assessment examples and the activity are posted at the end of this document. The post-assessment consisted of taking surveys of the other 6th grade Zap (Study Hall) periods. Then students created graphs on the computers from the information from the surveys. Students were then asked to print off their graphs and calculate the mean, median, mode, and range of their information.

I also had students take the pre-assessment again to see how we improved in each section again to see the growth in each area:

From the post-assessment it is easy to see that all students now understand bar and

line graphs completely because all 28 students answered those graph questions correctly.

It is also clear to see that students understand mean, medina, mode, and range

dramatically better than they did the first time around. Some students still struggled in

the areas of mean, median, and range but it was clear from their work that they

understood and just made minor mistakes in their calculations or still mixed up one or

two terms. It was also clear that the students who were still messing up and mixing up

terms were sick a couple days, so I tried my best to have those students come in during

their study hall period to review more and hit on those trouble spots.

Lesson Plans Day 1: Bar Graphs

State Standard: MA 6.4.1 Display and Analysis: Students will organize, display,

compare, and interpret data. Subject: Math

Name of Lesson: Bar Graphs Period / Time: 42 minutes

I. Goal: Students will compare and interpret data sets and their graphical representations.

Required Adaptations/Modifications:

II. Objectives: When given a set of data students will be able to form


and interpret bar graphs, along with labeling the important parts of the graphs.

III: Faith / Values Integration: Students will be respectful of the teacher as they present directions and material, be respectful of other students as they ask questions, and work cooperatively on their homework as directed to.


IV. Integrated Technology: Laptop and overhead projector used for bell ringer.


V. Materials: Laptop, worksheets, white board marker, sticky notes


VI: Procedure: A. Set / Hook: I will have one to two short bell ringer problems pulled up onto the board for students to start working on as they come into the classroom. These problems will be problems they will see on their state test (5-8 min). B. Transition: Go over the bell ringer and answer any questions that may have come up (5 min). C. Main Lesson: As we begin our main lesson I will start by asking the students if they know what graphs are used for. Possible answers: record information, organize information, visual representation of data, etc. Key Vocabulary (which is recorded in student math journals): This vocabulary is information that is needed for any graphs. -scale -data -intervals -statistics -vertical axis -horizontal axis Then we will go over the different parts to setting up a bar graph and practice making a bar graph on the board by taking a survey of the class with either: -favorite ice cream flavor -student’s eye color But I will have students place their vote on the board by using sticky notes to make the bars on the graph. I will ask questions about the bar graph we make to make sure students know how to interpret the graph as well: -Which is most popular/occurs the most? -Which is least popular/occurs the least? -To have the same number of votes for soccer and

Required Adaptations/Modifications: Have these notes pulled up on projector for students to copy. How to make a bar graph: 1. Use the data from the table to choose the right scale. All scales start at 0. 2. Draw and label the scale on the vertical axis. (Vertical means "up and down.") 3. Draw and label the horizontal axis. (Horizontal means "across.") 4. List the name of each item. 5. Draw vertical bars to represent each number. 6. Title the graph.

football, how many more votes will soccer/football need? -If 20 more readers vote for soccer, would it be the new topper on the chart? D. Transition: Ask students if they have any questions or for anything to be explained more and then give the class their homework assignment (2-3 min).

E. Conclusion: Let students work on their assignment as time permits and walk around monitoring students’ work and assisting with work as needed.

VII. Assessment: Formative assessment-questions students have, observing how well students answer my interpretation questions, and observing work as students work on their worksheets


VIII. Assignment: Worksheets-one will contain data and a bar graph to fill in along with a couple questions, and the last one will consist of making their own graph


IX. Self-Evaluation: Did I pace my lesson well? Did I speak at an appropriate level? Did I have students engaged throughout the lesson? Did having students form the bar graph with sticky notes aid my instruction?

I taught this lesson the day after a snow day, so students seemed to be a little chatty today. I didn’t have a problem with the chattiness that was going on right at the beginning because students seemed to be getting their bell ringer done. But I should have jumped on students right away for it so the chattiness did not continue after the bell ringer. Students complained at the beginning of the lesson about already knowing about bar graphs, but found out they didn’t know some of the vocabulary terms and the lesson was a good refresher for many. Students seemed to really enjoy making a bar graph about their favorite ice cream flavors in class with sticky notes as well. This lesson I was definitely struggling to get the right words out of my

X. Coop’s Comments: -Jump on chattiness earlier so they understand your expectations right away. -After the bell ringer they listened better -Be sure everyone is listening when you give next task -Good job getting around room while students completed their notes -Notes were helpful for students to copy down -Good job having students talk about what graphs are used for with a partner. Students did a good job of sharing and some showed knowledge of them. -Good job facing students as you wrote on the board -Good sense of humor throughout lesson -Sticky notes on board allowed for students to get out of chairs (brain break). -Having students get up by rows helped

mouth, but was able to joke about it and students enjoyed having a laugh with me.

keep it organized -Instead of saying “I think” just say “you guys understand”

Worksheet 1 in packet: Students put in data and interpret graph

Worksheet 2 in packet: Students label all parts of the graph and put in data.

Day 2: Line Graphs

State Standard: MA 6.4.1 Display and Analysis: Students will organize, display,

compare, and interpret data. Subject: Math

Name of Lesson: Line Graphs Period / Time: 42 minutes

I. Goal: Students will compare and interpret data sets and their graphical representations.


II. Objectives: When given a set of data students will be able to form and interpret line graphs, along with labeling the important parts of the graphs.






V. Materials: Laptop, worksheets, white board marker,


VI: Procedure: A. Set / Hook: I will have one to two short bell ringer problems pulled up onto the board for students to start working on as they come into the classroom. These problems will be problems they will see on their state test (5-8 min). B. Transition: Go over the bell ringer and answer any questions that may have come up (5 min). C. Main Lesson: Go over the homework from the previous day. As we start our main lesson I am going to ask students: What does a line graph represent? Answer: A line graph reflects changes in a set of data over a period of time. We can then use line graphs to make predictions/estimations about what will happen in the future. We will then move on to look at a line graph on the board in a PowerPoint and interpret the data on the graph together and review the different parts of the


graph together in class. Students will be given a worksheet and work with a clock partner and be asked to write in the scale, titles, plot points, label the x-axis and y-axis, and plot points and connect the line graph along with answering a set of questions. I will let students know that if they work well in groups together that their partner worksheet will be their assignment for the day. I will talk around and monitor groups and answer any questions students may have (25 min). D. Transition: Tell students to head back to their seats and to get a pen out to check the worksheets we just did (2-3 min).

E. Conclusion: Go over answers on worksheets with students and explain things as needed for the remainder of the period.

Students will work with clock partners on their worksheets. The second worksheet requires a double line graph and students will need to make a key to differentiate between the two lines.

VII. Assessment: Formative assessment-observing work as we go through making line graphs together, questions students have, and observing work as students work on their worksheets


VIII. Assignment: None


IX. Self-Evaluation: Did I pace my lesson well? Did I speak at an appropriate level? Was working in clock partners an effective form of instruction? Did I have students engaged throughout the lesson? Did students understand the worksheet? I think I did a better job today of jumping on chatty students and making sure they were on task on their bell ringers right when the lesson started. Students enjoyed having the PowerPoint to work through together as their notes to have better visuals than having me just write on the board. I think it helped to review pieces of the graphs we worked on the day before and talked about the difference with line graphs being the time period on the x-axis. Students also seemed to enjoy working with clock partners

X. Coop’s Comments: -Putting students in partners was a good way to switch up the instruction for the day. -Students were engaged and were able to tell that line graphs show change over time. -Looking at the graphs prior to putting students in clock partners was a good way to reinforce things they had learned on the concept in the past. -Be thinking about alternative activities/things you can do for groups that get done before others.

instead of on their own to mix up instruction for the day. I did have some students that flew through their worksheet packets where other students took right up to the bell to finish. I should have been more prepared and had another enrichment activity for those students to work on to challenge them even more beyond having them make a double line graph.

PowerPoint slides that I showed in class and talked about the differences in increasing

and decreasing line graphs and how we can use line graphs to predict data in the future.

Worksheets that students work on with clock partners and finish for homework what

they don’t get done in class.

Name_________________________ Period______________

The table shows how the fifth grade class’s field trip fund grew

over five weeks. Make a line graph to represent the data.

-Your graph should include a title and axis labels.

-You should show the scales on your graph.

-Your data should be graphed accurately.

-Then answer the questions on the following page.

Week Amount in Fund

1 $50.00

2 $105.00

3 $145.00

4 $190.00

5 $220.00

1. In what week did the 5th

grade class have the greatest increase in the

amount of money raised?

2. Make a prediction of how much money you think the class will raise

in week 6.

3. In what week did the 5th

grade class have the least increase in the

amount of money raised?

4. If the class raises $500 in week 8 and then they go on their field trip,

what is going to happen to the line graph if they spend half of their

money?

5. What is the difference between the amounts of money raised in week

2 to week 5?

Paul and his brother Alex put part of their allowance in their

savings account each month. The table shows how much money

was in each boy’s account for four months.

-Your graph should include a title and axis labels.

-You should show the scales on your graph.

-Your data should be graphed accurately.

-Then answer the questions on the next page about the graph.

Paul Alex

January $10.00 $8.00

February $16.00 $18.00

March $22.00 $24.00

April $30.00 $28.00

6. What is the difference between Paul and Alex’s savings accounts in

February?

7. Make a prediction of how much money you think both Paul and Alex

may have in May.

Alex—

Paul—

8. Based on the data who will reach $40 first? Explain your reasoning.

9. Who had the most money in their savings account in March?

10. Describe the change in Paul’s savings account and Alex’s savings

accounts in the months of January through April.

Day 3: Mean and Median

State Standard: MA 6.4.1.c Find the mean, median, mode and range for a set of data

Subject: Math

Name of Lesson: Mean & Median Period / Time: 42 minutes

I. Goal: Students will compute the mean and median.


II. Objectives: When given a set of data students will be able to find the mean and median.






V. Materials: Laptop, worksheets, white board marker, candy, candy recording sheets, cups for candy, yellow foldable, scissors


VI: Procedure: A. Set / Hook: I will have one to two short bell ringer problems pulled up onto the board for students to start working on as they come into the classroom. These problems will be problems they will see on their state test (5-8 min). B. Transition: Go over the bell ringer and answer any questions that may have come up (5 min). C. Main Lesson: Students will learn the difference between mean and median by counting candy and using the data to calculate the mean and median (by color). This means that students will be able to apply their learning to another collection data process from what we have been doing with the different types of graphs. Students will need to decide if they want to make a frequency chart or a bar graph to record their candy data. ****Make sure students understand that they can NOT eat their candy until they are told.

Required Adaptations/Modifications: Students will have the option of either making a bar graph or a frequency chart of their candy data.

Each student will receive a hand full of M & M’s or Skittles. First, I will have students divide the candies into their separate colors, and record them on their graphs. Then we will go over important vocabulary and talk about how we can find the average/mean of roughly how many of each color there are. Then I will move on to the word mean-is the sum of the data divided by the number of pieces of data. Important Vocabulary (we are going to start a foldable on this day to record definitions, examples, and pictures if needed): -average -mean -outlier Then we will move on median and explain how we can remember that from a median in the middle of a road. I will have a picture of a median for the students to be able to visualize that as well. Students will then calculate the mean and median of their Skittle data. I will go around and check students work as they get done. I will then talk about the outlier of a set of data and have students figure out what the new mean would be and discuss how that changes our mean. D. Transition: Ask students if they have any questions or for anything to be explained more and then give the class their homework assignment. I will now let students eat their candy (2-3 min).

E. Conclusion: Let students work on their assignment as time permits and walk around monitoring students’ work and assisting with work as needed. With a couple minutes left in class, I will ask students if they can tell me what mean and median mean again.

Show the picture of a median on a road as a clue for students to what median means.

VII. Assessment: Formative assessment-students finding the mean/average on the numbers we placed on the board and with their own candy, along with their worksheet they will do for homework


VIII. Assignment: Worksheet Pg. 41


IX. Self-Evaluation: X. Coop’s Comments:

Did I pace my lesson well? Did I speak at an appropriate level? Did I have students engaged throughout the lesson? Was the foldable an effective form of vocabulary instruction? Was the candy a good visual for students as they computed mean and median? Students enjoyed taking notes in a foldable because it was different than the notes they were used to taking. I forgot to talk about the outlier during the class period so then when students got their homework I needed to talk about it quickly before the bell rang so they could complete the couple questions they had over it. The Skittle activity worked great except it did make students a little talkative because they knew they would get to eat their candy at the end of the period.

-The foldables were a great strategy to help students remember median, mean, mode, and range and the differences between them. This was a good switch up from normal note taking. -Students went over several examples of mean and median before they practiced on own with reinforced understanding. -Make sure you cover everything that will be on their assignment. The one day "Outlier" was left out of the lesson and then students were asked to find it on assignment. -The skittles activity was engaging for students. Nice job the second time around of reminding them to include any 0's in their data if they didn't have a particular color.

Pictures I showed students in class to help them remember what the term median

means.

Choices of the different candy data collection charts students could use.

Skittles Frequency Chart

Work Zone:

Skittles Bar Graph

Work Zone:

Foldable students made in class on yellow paper to take notes and for the important

vocabulary throughout the next two lessons.

Worksheet students had for homework over mean.

Day 4: Mode and Range

State Standard: MA 6.4.1.c Find the mean, median, mode and range for a set of data.

Subject: Math

Name of Lesson: Mode & Range Period / Time: 42 minutes

I. Goal: Students will compute the mode and range for a set of data.


II. Objectives: When given a set of data students will be able to find the mode and range.






V. Materials: Laptop, worksheets, white board marker, yellow foldable, scissors


VI: Procedure: A. Set / Hook: I will have one to two short bell ringer problems pulled up onto the board for students to start working on as they come into the classroom. These problems will be problems they will see on their state test (5-8 min). B. Transition: Go over the bell ringer and answer any questions that may have come up (5 min). C. Main Lesson: We will start our lesson by going through students homework from the previous day and then by reviewing mean and its steps and practicing an example. Then we will do the same thing for the median with the same set of data. As students work through this set of data I will have them think, ink, and link with a partner to check to see if they did the same work as their partner. Example: Find the mean and median of this set of data. 28, 36, 18, 25, 12, 44, 18, 42, 34, 16, 30, 18

Required Adaptations/Modifications: Have students think, ink, and link!

Questions: -Is there an outlier in this set of data? -What if I added the number 66 to the data what happens? -How can we remember what median means? I will have students get their yellow foldables out and we will add mode and range to them with steps and examples as needed. Next, I will use the same set of data that we used above to review to have students to find the mode and range. D. Transition: Ask students if there are any questions and give them their homework assignment (2-3 min).

E. Conclusion: Give students the opportunity to work on their homework as time permits and then with a couple minutes left ask them questions about mode and range and the steps we need to do to find them.

VII. Assessment: Formative assessment- students reviewing how to find mean and median, students computing the range and mode from the same set of data, and their homework assignment


VIII. Assignment: Worksheet Pg. 49


IX. Self-Evaluation: Did I pace my lesson well? Did I speak at an appropriate level? Did I have students engaged throughout the lesson? Was thinking, inking, and linking effective? Students were very engaged today during the main lesson and the bell ringer went much better today. Students worked very hard on their problems to be able to compare them to their elbow partner. Then we were able to check their work on the board as a class and talk about where they are messing up and what steps they need to constantly focus on as they are calculating the mean, median, mode, and range of their sets of data. I think I was able to keep the class moving at a fairly decent pace today and we were able to move from one thing to another.

X. Coop’s Comments: -Students were quiet and engaged when I came back in the room -Directions are becoming more clear -Good pacing in class. Kept students engaged and moving.

Worksheet students had for homework over median, mode, and range.

State Standard: MA 6.4.1.c Find the mean, median, mode and range for a set of data & MA

6.4.1 Display and Analysis: Students will organize, display, compare, and interpret data.

Subject: Math

Name of Lesson: Performance Task Period / Time: 42 minutes (for 2-3

days)

I. Goal: Students will compare and interpret data sets and their graphical representations. Students will also compute the mean, median, mode, and range for a set of data.


II. Objectives: When given a set of data students will be able to form and interpret bar or line graphs, along with labeling the important parts of the graphs. When given a set of data students will also be able to compute the mean, median, mode, and range.




IV. Integrated Technology: Computer lab to make graphs, overhead projector and laptop to walk through directions


V. Materials: Multiplication Race Worksheets, Directions Worksheets for Computer lab


VI: Procedure: A. Set / Hook: For our bell ringer today we are going to have multiplication races and see who can answer the most multiplication questions correctly in 5 minutes on their worksheets (5 min). B. Transition: Have students count how many problems they got correct on the worksheets and give the winner a prize (2-3 min). C. Main Lesson: Students are going to start on work on their performance tasks today and then work on them for the next two days in the computer lab. I will first explain to students what their task is going to be: -they are going to be making bar or line graphs on the

Required Adaptations/Modifications: Having students choose whether they want to make a bar graph or a line graph.

computers -they will have a survey question to ask the other 6th grade periods to make their graphs -they can choose whether they make a bar graph or a line graph -when done with their graphs students will find the mean, median, mode, and range of their data Then I will divide the class into three groups and each group will need to decide what they want their survey question to be…I will give groups around 5 minutes to come up with a compromised question. Students then need to discuss the best way to collect their data so they can easily plug it into their graphs and make a chart for that. The rest of the class period will then be used for me to have a Word Document pulled up on the board and walk through the directions sheet with them on the overhead projector. ****We will come up with a system in asking the 6th grade Zap periods for their votes in each survey so that all students get to participate and collect data. The next two days will then be class time in the computer lab to work on their graphs and ask questions as needed. D. Transition: Ask students if they have any questions (2-3 min).

E. Conclusion: Make sure all students have a way to record their data before they leave the classroom and remind students we will meet in the classroom to take attendance the next two days and then go to the computer lab together.

Have students come up with their own survey questions in groups and compromising the final ones. Students will have a stepped out directions sheet of how to make both graphs on a Word Document.

VII. Assessment: Formative assessment-walking around as students discuss and compromise survey questions with their groups, making sure students have a chart to record data, the questions students ask before they leave class Summative assessment-the final product of their graphs and finding the mean, median, mode, and range of their data


VIII. Assignment: In class work-making bar graphs or line graphs of


student surveys and then computing the mean, median, mode, and range of their data

IX. Self-Evaluation: Did students understand the directions sheet? Was walking through the directions sheet by example helpful? Did we have a good system of students asking/recording their data? Were my directions accurate and helpful? I think I did a decent job of explaining directions and the rubric to students. At times I don’t give students the chance to quiet down and I start talking or giving directions with the intention of the students quieting down on their own. Sometimes it works and other times it does not, so I need to be better at giving more wait time in between tasks. My coop suggested having them print their graphs with their names on them so they know who’s they are when they get them from the printer which is something I didn’t think of. But overall the graphs turned out great and students seemed to be very engaged and excited about this project as a whole.

X. Coop’s Comments: -The graphs turned out very nice. The activity with the rubric was well explained. Just be sure that no students are having any sort of conversation as you are going over directions. -Students seemed to show understanding of their graphs and did a nice job of getting their data displayed. -Always consider the little things like typing names on graphs before printing because many graphs could look awfully similar. I have finally picked up on this after 7 years of teaching :). -You could consider adding a part on their assignment where they have to write 5-10 sentences describing the information in their graph. Always consider what you can add to make the assignment even better. This was a great performance task though, nice work!

Performance Task Assignment Directions

Name________________Survey_________

Bar Graph/Line Graph

Students will be divided into three groups.

Each group will need to pick a survey question to ask the

other 6th grade Zap periods and teachers.

Students will then work individually to make their graphs

in the computer lab following the steps below.

Students will need to decide the best way to record their

data in either a bar or line graph.

Follow the steps below:

1. Open Microsoft Excel

2. Open Excel Workbook

3. Go to the Charts Tab

4. Plug your categories/names into column A

5. Plug your data into column B

6. Select and highlight your data

7. Then choose either a bar graph or a line graph

8. If you choose to make a bar graph follow these directions:

i. Use the first option for a bar graph-the clustered

column graph

9. If you choose to make a line graph use these directions:

i. Use either the first option or the one below it-either

line or marked line graph

10. Once your graph is made go to the chart layout tab and

add:

i. A chart title

ii. A horizontal axis (under axis titles)

iii. A vertical axis (under axis titles)

iv. In the chart tab you can change the color or your

bars or lines

v. In the format tab under the chart elements tab you

can change the background colors of your charts

11. If you want to make teachers votes an extra column in

your bar graph or an extra line in your bar graph you can, just

add their data to column C.

12. No matter what graph you choose you need to make it

colorful and your OWN!

13. Don’t be afraid to ask questions!

14. Make sure to SAVE your work!

15. Have fun and don’t be afraid to mess around with Excel and the

formatting a bit!

****Once you are done with your bar or line graph PRINT it off

and put your NAME on it. You will need to check the print

preview before you print to make sure your graph fits on the

page.

********Then you need to calculate the mean, median, mode,

and range of your data either on another sheet of paper or at

the bottom of your graph. Show your work!

Performance task rubric: Name________________________________

CATEGORY 4 3 2 1

Neatness and

Attractiveness

Exceptionally

well designed,

neat, and

attractive. Colors

that go well

together are used

to make the graph

more readable.

Neat and

relatively

attractive.

Graph appears

quite plain.

Appears messy and

“thrown together”

in a hurry.

Title Title is creative

and clearly relates

to the problem

being graphed. It

is at the top of the

graph. All axes

are labeled and

intervals.

Title clearly

relates to the

problem being

graphed and is

printed at the top

of the graph.

Some axes and

intervals are

labeled.

A title is present

at the top of the

graph.

A title is not

present.

Labeling of x-axis

(horizontal axis)

The x-axis has a

clear, neat label

that describes the

units used for the

independent

variable (Ex:

days, months,

participants,

names,

categories).

The x-axis has a

clear label that

describes the units

used for the

independent

variable.

The x-axis has a

label.

The x-axis has no

label.

Labeling of y-axis

(vertical axis)

The y-axis has a

clear, neat label

that describes the

units and the

dependent

variable (Ex: %

of dog food eaten,

degree of

satisfaction, or

number of votes).

The y-axis has a

clear label that

describes the units

and the dependent

variable.

The y-axis has a

label.

The y-axis has no

label.

Type of graph

chosen

Graph fits the data

well and makes it

easy to interpret.

Graph is adequate

and does not

distort the data,

but interpretation

of the data is

somewhat

difficult.

Graph distorts the

data somewhat

and interpretation

of the data is

somewhat

difficult.

Graph seriously

distorts the data

making

interpretation

almost impossible.

Mean calculated Correct steps

were followed to

Correct steps

were followed to

Correct steps

were not followed

The mean was not

attempted at all.

find the mean and

the mean is

correct.

find the mean but

the mean is

wrong.

to find the mean

and the mean is

wrong.

Median calculated Correct steps

were followed to

find the median

and the median is

correct.

Correct steps

were followed to

find the median

but the median is

wrong.

Correct steps

were not followed

to find the median

and the median is

wrong.

The median was not

attempted at all.

Mode calculated Correct steps

were followed to

find the mode and

the mode is

correct.

Correct steps

were followed to

find the mode but

the mode is

wrong.

Correct steps

were not followed

to find the mode

and the mode is

wrong.

The mode was not

attempted at all.

Range calculated Correct steps

were followed to

find the range and

the range is

correct.

Correct steps

were followed to

find the range but

the range is

wrong.

Correct steps

were not followed

to find the range

and the range is

wrong.

The range was not

attempted at all.

Used time

wisely/Came to

class prepared

Brought

directions sheet to

class, data to plug

into graphs, and

on task when

working on the

computers.

Did not bring

instructions sheet to

class, data to plug

into graphs, and

was not on task

when working on

the computers.

Totals (40 points

total):

Here are some student samples of the work they did in class. Students also calculated the mean, median, mode, and range of their data as well:

Data and Graphing Unit

Michala Maurer

Michala taught a data and graphing unit in my classroom in the spring semester of

2015. This unit was well planned and kept the students engaged throughout. Ms. Maurer

tied examples to real world situations throughout the unit as well, which helped students

learn the importance of each concept. Students went over line graphs, bar graphs,

frequency charts, stem and leaf plots, line plots, mean, median, mode, and range

throughout the unit.

The unit started with a pretest, which was designed to show prior knowledge for

each student. Many of these concepts were learned in prior grades, but students showed

understanding in some areas, but it was evident that they needed to be exposed to the

concepts again. Ms. Maurer used many techniques of teaching throughout the unit.

Students worked individually, in partners, small groups, and whole group on worksheets

and activities. There was the right amount of movement with students, as they were able

to come up to the board to create data plots and graphs.

When students got to the lessons over mean, median, mode, and range, they were

given “foldables” to help them remember the differences between each vocabulary term

and concept. This was a different method than the usual note taking, and kept students

organized with the topics.

Overall, students showed great growth and understanding on their posttest at the

end of the unit. Ms. Maurer was able to track growth for specific students from the

pretest to the posttest. Her final assessment was to have students create graphs on the

computers in the lab using Microsoft Excel. Students were broke into groups and

surveyed classmates during our study hall period. The graphs that students made were

creative and showed understanding of a bar graph. They were also asked to find the

mean, median, mode, and range of their data, where they showed clear understanding.

Overall, Ms. Maurer and I were pleased with their progress throughout the unit.

The prior understanding helped, but the overall teaching was what helped them grasp

onto the concepts for understanding. Michala did a fantastic job covering these concepts!

Brad Vancura

6th

Grade Math and Writing Teacher

Seward Public Schools

Reflection

Student Learning Progress

1. When you look at the pre-assessment and the post-assessment you see a drastic change in the understanding that the students have in regards to mean, median, mode, and range. Some students had an idea of what they were and just mixed up the concepts, and other students didn’t have a clue how to calculate them at first; but after we covered the topics and made a foldable to differentiate between the four terms students clearly understood exactly how to find each of them. Students who still had trouble on the post-assessment were sick or gone a couple days and still mixed up two concepts with each other. So even though not all students were able to grasp all of the concepts, there was still improvement in all their abilities as math students which can be seen previously when comparing the pre-assessment and post-assessment graphed data.

2. I believe the unit objectives were met. Students were exposed to the differences between bar graphs and line graphs and can interpret and analyze the information within them. Student were also exposed to the definitions of mean, median, mode, and range and taught the differences between them and the different steps taken to calculate each. Through the post-assessment we see that their overall understanding of these concepts has been enhanced.

3. There was a bit of a lack of growth in a couple students but it was a dramatic lack of growth. A couple students were sick for a couple says and we had a hard time catching them back up to the rest of the class as a result. Then we had two snow says in the mix and I think that resulted in a couple other students falling behind because they lost the school structure for a couple days that they desperately need. Other than that this was the upper level math class and not many students struggle to bad in the class. There are a couple students that just get lazy with their work possibly from a lack of being challenged enough. I made sure as I gave examples in class and on most of their homework to pick challenging worksheets to make the class as a whole think harder and work more for their answers. As I said earlier, a majority of the students had decent background knowledge in this chapter they just mixed up and confused terms for each other, which we clearly hashed out looking at the pre-assessment to the post-assessment. Students that clearly showed on their pre-assessment that they didn’t know what a term meant clearly showed they understood on the post-assessment except for the couple students who were sick and as a result of snow days.

4. If I were to teach this unit again, I would incorporate more hands on learning activities or foldables where I could. The students in my class seemed to be sick of taking notes and wanted and liked more variety. I think it can also be very

helpful in a math classroom to help students understand concepts better. I did do group work, clock partners, the Skittle activity, and the think, ink, and link concept but I think if I could have found a way to review material such as bar graphs and line graphs before the activities it would have been helpful. I also would have done a better job of finding enrichment material for this particular class. I was worried to an extent that some students would have started seeing the enrichment activities as more busy work though because my coop takes a lot of completion grades for a small amount of points. But it would definitely be something to consider when I have more control over the gradebook.

Personal Professional Growth

1. What did you learn about effective instruction as a result of this experience?

Effective instruction can make or break a lesson. As a teacher I need to be present my lesson with excitement even if what I am teaching is not that exciting because it will make my students more amped for the lesson. I also need to think about what I am going to say and what examples I want to put on the board ahead of time to an extent. I don’t want to be stuck on my feet at the board at any given time, and I also want to be prepared to answer my students’ questions. Being prepared and rehearsing a little bit can also help make my lesson clearer. Effective instruction also involves having fun! I think the best lessons I taught were when I couldn’t get words out of my mouth and I started to make fun of myself. It lightened up the mood in the room and students instantly seemed to more engaged because we made something like talking about bar graphs a little more exciting.

2. How has this experience changed your perception of yourself as a teacher? I think this experience has made me even more passionate for my future profession that is not so far down on the road now. I love working with students and getting to know them more and more every day. I also learned that I can be a pretty flexible teacher even though I normally am not a flexible person at heart all the time. I dealt with multiple snow days and an epidemic of students being absent and sick for a while and was able to help students get caught back up with their peers. I also dealt with my coop being sick and gone for basketball games and my substitute being pulled out of the room to help another sick teacher. I know I haven’t dealt with everything that is going to come my way as a teacher but I am getting my foot in the door and am ready to learn and improve every day right along with my students. I am very ready for this journey to continue!

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