My Teaching Philosophy

          I am an essentialist. I believe that teaching through direct contact with the environment and using task-oriented projects is the most effective instructional method. Basically, my belief is that students learn through hands-on experiences that connect subject-based content into practical uses in everyday life. Also, I think that focusing on today’s society rather than emphasizing on the classics is effective and more relevant to students’ lives. The main focus of essentialism is teaching students the basics to survive and be successful in society. I bring to teaching a belief that current events are much more applicable to students’ lives rather than reading a novel based in a different time period with different values. For example, Nathanial Hawthorne’s The Scarlet Letter is not nearly as relevant to current classrooms because students are unable to make connections between the novel and modern culture. Focusing on more recent literature like The Hunger Games allows students to make connections between current events, their own lives, and the novel. In order to be a successful educator, I must present material in a relevant, hands-on way for students to understand and make worthwhile connections. Although essentialists are subject-focused, I believe that through focusing on relevant topics I will be able to reach my students more effectively.

            As an essentialist, I belief that one way children learn is through observations in their environment. If children learn morals by watching adults or family members in their lives, I would argue that they have this ability to learn through observation at school as well. An engaging lesson that allows students to observe the content rather than reading out of a textbook allows students to draw their own conclusions, and can be much more effective. Obviously, students learn through their environment without acknowledging it, and I wish to bring this type of natural learning into the classroom. One way of presenting information through this observational theory is by providing multimedia in the classroom. Through technological and environmental observation students will learn without traditional textbooks and study guide assignments; the lessons will be more engaging. Additionally, I see myself assessing student progress through observational, informal assessments more rather drilling students with quizzes and tests. In the classroom, I see myself giving more project-based assignments rather than unit tests, because it is important for students to work together as a group and overcome problems as a team. In most careers, employees are presented with projects, not tests, and students need to be aware of group dynamics prior to entering the work force. By observing effective group work in school settings, students will feel comfortable in their communication and group-work skills. Allowing students to make their own connections to the world around them and the content areas gives ownership over their education; the teacher is a facilitator rather than a dictator in the classroom. By observing their environment, students will learn the content naturally.

            Also, current events are more applicable in modern day classrooms than classics. During any subject, I believe students want to know how the information relates to their future endeavors. If teachers cannot make the connection between the standards we have to teach and the student’s life, the information is worthless. Without those connections to current events, politics, and applications in careers, I do not believe that teachers are fulfilling their job of educating young minds. I think that learning is something that can be fun and relevant to society, but does not require studying classic ideologies. Current events relate vocabulary and content to the world. This is a concrete connection that students can see and hopefully become more engaged and interested in the material being presented. I believe that students are curious about the world around them, and by relating topics to something concrete like current events we give students the tools to draw their own conclusions. Additionally, information is better retained, in my opinion, if the content areas focus on real-life scenarios. If I were to teach a lesson on budgeting, for example, I would give students an assigned weekly income and have them create a budget that would ideally cover bills and extra expenses such as groceries, insurance, clothing, dining… etc. By giving the students an actual instance of budgeting, they are forced to problem solve an ideal budget based on their given income. Learning is through relevant experiences such as the budgeting project, not passing a standardized test.

            Overall, I believe that the main goal any teacher has is taking a child from the known to the unknown. Through effective teaching methods, however, the students are bound to make stronger connections between the content and their future endeavors. I think that teaching through task-oriented projects and hands-on experiences students will retain a more memorable experience to learning. Not only will their learning experience be more fun and challenging, it will prepare them for the real world. Using current events and natural learning, students will pick up on the material without memorizing and regurgitating information for an exam or test. Overall I want my students to learn, not remember something long enough to pass a test. 

Everyday Math 6th Grade Unit 5 Lessons

Lauren Nearhoof

1/28/14

Mathematics Unit 5

Lesson 5.1

Standards:

M6.B.2.3.1: Define, label and/or identify right, straight, acute and obtuse angles.

M6.B.2.1.3: Measure angles using a protractor up to 180⁰ - protractor must be drawn - one side of the angle to be measured should line up with the straight edge of the protractor.

Essential Question:

How can you demonstrate that you understand the classifications of angles according to their specific properties?

Assessment Prompts:

1. How are angles labeled?

2. With a partner, explain each step of how to measure an angle using a protractor in a bulleted list.

Materials:

1.      Copy from the previous day’s closing activity on transparency

a.       Choose an example that demonstrates clear and precise thinking

2.      Student journals

Activating Strategy:

1.      Show students the chosen answer from previous day’s closing activity

a.      Choose an example that demonstrates clear and precise thinking

b.      White out name

c.       Make a transparency

2.      Remind students of prompt

3.      Have students read the selected assignment

4.      Discuss with students what was good about the writing assignment

5.      Discuss ways to improve writing in math

6.      Hand back individual writing assignments

Teaching Strategy:

1.      The students will have to participate in “Ms. Nearhoof Says.”  In this game, the students will have to show the different angles of right, acute, obtuse, and straight (the angles they just learned).  I will be able to assess the students’ knowledge when they demonstrate with their arms the different angles.

a.       Have students stand-up during this activity

b.      Ensure that students have enough room to safely move arms without touching another student

c.       Use as an assessment

2.      Ask students to get out Math Journal page 162

a.       Use this as a guide for teaching

b.      Discuss how an angle is labeled

                                                              i.      By the vertex

                                                            ii.      Go over what a vertex is again

                                                          iii.      Refer to vocabulary notebook if needed

                                                          iv.      Complete number 1 and 3 together

                                                            v.      Have students complete 2, 4, and 5 with a partner

                                                          vi.      Go over answers

3.      Ask A.P #1

4.      Introduce protractor to students

a.       Show large one up on board

b.      Compare to geometry template

c.       Explain how to measure angles

5.      Practice measuring angles together doing number 6 part a and b together as a class

a.       Explain each step

                                                              i.      Place the center of the protractor on the vertex

                                                            ii.      Line up the straight edge of the protractor on one of the lines

                                                          iii.      Approximate what each angle is

1.      Be sure to use the correct measurement

a.       Ask yourself, “is it acute or obtuse?”

b.      Have students complete c and d by themselves

6.      Ask A.P. #2

7.      Teach students how to draw angles by completing number 8 part a together

Summarizing Strategy:

1.      Using a ticket out the door, have students complete the following prompt:

a.       1 thing you learned today

b.      1 thing you are still struggling with

Homework Assignment:

Students must complete the remaining questions on the 5.1 worksheet for the following day.

Reflection:

            Overall, the lesson went well! The students responded to the Simon Says game, and I was able to formatively assess the student’s knowledge from the previous class. I must have done a good job teaching this concept because every single student was able to identify the different types of angles. Additionally, I believe that offering sample writing from the class was very beneficial because everyone was able to see what his or her classmates were capable of doing. One thing I would change about this is referring to the student as simply “student.” During my explanation, I referred to the student writer as a “her” and it was then easy for the others to pinpoint whose writing assignment it was. I know that the work was being praised, but I didn’t want to embarrass the specific student or make him/her feel bad.

            One thing that I would change is training the students to be prepared for a starter during every class. If this was my classroom, I would like to emphasize how important it is not to waste class time, and it often takes several attempts to get the class focused after 7^th period resource. Also, the class period was shortened because of report card distribution, and I was not able to finish the entire lesson as planned. One thing that I would like to work on is timing during a lesson. Sometimes I struggle with trying to figure out how long a specific activity will take. Lastly, I think that I didn’t assign enough practice problems because many of the students were finished with the assignment before the class was over. If I was able to, I would have assigned another worksheet for homework to ensure that students understood how to measure angles and label them accordingly.

Lauren Nearhoof

1/29/14

Mathematics Unit 5

Lesson 5.2- Angle Relationships

Standards:

M6.C.1.2.2: Identify, draw and/or label points, planes, lines, line segments, rays, angles and vertices

Essential Question:

How can you apply your knowledge of supplementary, vertical, and adjacent angles to identify the unknown angles in a graphic without a protractor?

Assessment Prompts:

1. How are adjacent and supplementary angle relationships related?

2. Are you able to find angle “r” without using a protractor?

3. What are the differences between a supplementary angle relationship and a vertical angle relationship?

Materials:

·         White paper (for a foldable)

·         An overhead sheet/ access to Smartboard

·         Scissors

·         Student Math Journal

·         Copies of Student Study Link 5.2

·         Transparency of 5.2 Study Link

Activating Strategy:

1.      Have starter for the class on the board, “Create a step-by-step list on how to measure an angle with a protractor.”

a.       Encourage students to write this in his/her math vocabulary journal or on the whiteboard for reference later

2.      Allow students 3-4 minutes to complete this task

3.      Ask students to compare his/her list with their elbow buddy

4.      Go over how to measure an angle once more to ensure that students are understanding

a.       Take volunteers

b.      Allow students to create a list for their notes

5.      “Do you think there is a way to find out the degrees of an angle without measuring them with a protractor?”

a.       Allow students to make predictions about the answer to that question

                                                              i.      I am assuming they will say “no.”

                                                            ii.      Tell students that we will learn how to do this today

b.      Tell students that angle relationships allow us to find unknown angles through our vocabulary terms of supplementary, vertical, and adjacent angles

Teaching Strategy:

1.      Teach students how to create a foldable to help remind them of the different type of angle relationships

a.       Take white piece of paper

b.      Fold “hamburger style”

c.       Once folded take one layer and create two cuts

                                                              i.      The cuts should create 3 equal sections

d.      On the first section, write supplementary angles

                                                              i.      Open up the top

                                                            ii.      Write definition from text

                                                          iii.      Draw example

                                                          iv.      Explain to students

e.       On the second section, write vertical angles

                                                              i.      Write definition from text

                                                            ii.      Draw example

                                                          iii.      Explain to students

f.       On the third section, write adjacent angles

                                                              i.      Write definition from text

                                                            ii.      Draw example

                                                          iii.      Explain to students

2.      Give students 5.2 Study Link

a.       Go over worksheet together in class

b.      Model how to use graphic organizer/foldable to identify the unknown angles

c.       Think-aloud for students, so they are able to follow the correct thinking

d.      Take volunteers to come up and explain how to find unknown angles

3.      If students did not finish assignment/ if time runs out assignment the remainder of the worksheet for homework

Summarizing Strategy:

1.      Ask students to give a thumbs up if they understood, a middle thumb if students are “so/so,” and a thumbs down if they are totally lost

2.      Use this information for the next class

Lauren Nearhoof

1/30/13

Mathematics Unit 5

Lesson 5.3- Circle Graphs

Standards:

M6.A.1.4.1: Model percents (through 100%) using drawings, graphs and/or sets (e.g., circle graph, base ten blocks, etc)

M6.A.1.1.1: Represent common percents as fractions and/or decimals (e.g., 25% = ¼ = .25) – common percents are 1%, 10%, 25%, 50%, 75%, 100%.

Essential Question:

How can you demonstrate your knowledge of percents, decimals, and angles to create a circle graph?

Assessment Prompts:

1. What is 10% as a decimal?

2. How can you find 10% of 35?

3. How many degrees are in a circle?

Materials:

·         A prepared polling question geared towards student interest

·         A classroom size protractor

·         Math Journal

Activating Strategy:

1.      Start with a writing prompt on the board

2.      Pass out sticky notes

3.      “What is one occupation that uses angles?”

4.      Ask students to answer the writing prompt with one word on the sticky note

5.      Give 2-3 minutes

6.      When students are done with this, they may place the sticky note on the board

7.      Read over the different occupations

a.       If one sounds interesting ask the student to explain his/her answer

b.      Move into how statisticians, or people who analyze data, use angles to create circle graphs for their information

Teaching Strategy:

1.      Ask students, “What is a poll or survey?”

a.       Take volunteers

b.      Ask more than one student

c.       Ensure that students have a correct idea about the meaning of polls or surveys

2.      Poll students on favorite animals

a.       Give 5 choices

                                                              i.      Dog

                                                            ii.      Cat

                                                          iii.      Goldfish

                                                          iv.      Hamster

                                                            v.      Horse

b.      Give students 30 seconds to silently think of his/her favorite animal from the given choices

c.       Ask students his/her favorite animal

3.      Help relate this information to a table so students are able to see  how it could relate to percents and the former chapter

4.      Teach students how to find out how many degrees are each section

a.       Turn the information into a fraction

b.      Using a calculator or long division, find the corresponding decimal

c.       Multiply the decimal by 360 degrees (the amount in a circle)

d.      Explain that this is the number of degrees this section of the circle graph is

5.      Use examples from the polled information

6.      Draw the first sector as a model

7.      Ask students to come up and draw the remaining sectors in the circle graph

Summarizing Strategy:

1.      Have students analyze the graph

2.      Does it make sense that the largest part of the circle graph is __________?

a.       Why or why not?

b.      What about the smallest part

3.      Complete pages 170 in math journal.

Lauren Nearhoof

1/30/14

Mathematics Unit 5

Lesson 5.4- Coordinate Geometry

Standards:

M6.C.3.1.1: Plot, locate or identify points in Quadrant I and/or on the x and y axes with intervals of 1, 2, 5 or 10 units - up to a 200 by 200 grid. Points may be in-between lines.

Essential Question:

How can you plot points on a coordinate graph?

Assessment Prompts:

1.      Which is the x-axis?

2.      Can you locate the y-axis?

3.      Which point is (5, 5) on the graph?

4.      How can you explain the process of plotting points in 3 easy steps?

Materials:

·         Construction paper cut into circles approximately 2 inches in diameter

·         Masking tape

·         Access to a chalk board

·         A drawn coordinate plane

·         A class list

Activating Strategy:

1.      “What are some questions you have from the following day’s homework?”

2.      Have students respond to this question on his/her white board

3.      Compare/Contrast answers with an elbow buddy

a.      Does this person understand that concept?

b.      Could they help you?

4.      Allow 5 minutes for productive math conversations about last night’s homework

5.      Go over any questions that all students were confused about, if any, since the topic was completely new

Teaching Strategy:

1.      Go over vocabulary from this section with the class

a.       Axis

b.      Ordered number pair

c.       Midpoint

d.      Orign

2.      Use drawing of coordinate plane on board to explain the different parts

a.       X-axis is the horizontal line

b.      Y-axis is the vertical line

c.       A.P #1

d.      A.P. #2

3.      Teach students about (    ,     ) format

a.       The first number corresponds with the x- axis

b.      The second number corresponds with the y-axis

c.       Use the hint, “Superman must run before he can fly”

4.      Demonstrate how to plot a point

a.       Think-aloud so that students can follow what you are doing

b.      First I look at the ordered number pair

c.       Next I move along the x-axis to the first number

                                                              i.      If the number is positive, you move to the right

                                                            ii.      If the number is negative, you move to the left

d.      Lastly, I move up or down the y-axis to the second number

e.       I place a point on this part of the graph

f.       I label the point

5.      Model how to read a point on page 174 in Math Journal

6.      A.P. 3

7.      Students work on finishing the page

a.       Encourage students who have questions to ask at this time

b.      Answer questions when needed

c.       Go over answers

8.      Introduce Game to students

a.       Students will spin 3 times with his/her eyes closed and walk towards the board with a taped point

b.      The student must place the point on the coordinate grid

c.       The student must write and correctly say the point to get a point

d.      The students are in 2 groups/ teams

e.       Students at his/her seat must quietly write the answer down as well

                                                              i.      If the team at the board gets the point wrong, the opposing team can take the point

Summarizing Strategy:

1.      Ask the essential question

2.      Assign Math Boxes 5.1-5.5 due one week from today

Lauren Nearhoof

1/4/14

Mathematics Unit 5

Review 5.1-5.4

Standards:

M6.B.2.3.1: Define, label and/or identify right, straight, acute and obtuse angles.

M6.B.2.1.3: Measure angles using a protractor up to 180⁰ - protractor must be drawn - one side of the angle to be measured should line up with the straight edge of the protractor.

M6.C.1.2.2: Identify, draw and/or label points, planes, lines, line segments, rays, angles and vertices

M6.A.1.4.1: Model percents (through 100%) using drawings, graphs and/or sets (e.g., circle graph, base ten blocks, etc)

M6.A.1.1.1: Represent common percents as fractions and/or decimals (e.g., 25% = ¼ = .25) – common percents are 1%, 10%, 25%, 50%, 75%, 100%.

M6.C.3.1.1: Plot, locate or identify points in Quadrant I and/or on the x and y axes with intervals of 1, 2, 5 or 10 units - up to a 200 by 200 grid. Points may be in-between lines.

Essential Question:

How are you able to demonstrate that you have mastered the material in sections 5.1, 5.2, 5.3, and 5.4?

Assessment Prompts:

(Are assigned by station)

1.      Can you draw a 212°?

2.      Where are the vertical angles in this image? The supplementary angles? The adjacent angles?

3.      How are angle relationships different that the different types of angles?

4.      How many degrees should 78% be in a circle graph?

5.      Can you demonstrate how to draw 38% in a circle graph?

6.      Can you plot the point (-6, 4)? Demonstrate.

Materials:

·         4 groups previously divided into an equal number of students

·         4 group leaders chosen

·         Math templates/ protractors

·         Note cards with angle measurements written on them

·         Worksheet of angles cut out

·         Table of surveyed information

·         Worksheet of angles that contain vertical and supplementary angles

·         Graph paper

·         Markers

Activating Strategy:

1.      Place quiz statistics on PowerPoint or on chalkboard

2.      Have students find the mean, median, and mode of the scores

3.      What is the mean?

4.      What is the median?

5.      What is the mode?

Teaching Strategy:

1.      Coach each group leader on the information from his/her designated station

a.       Station 1: 5.1

                                                              i.      Measuring angles

                                                            ii.      Drawing angles

                                                          iii.      Classifying angles

                                                          iv.      Labeling angles

b.      Station 2: 5.2

                                                              i.      Identifying angle relationships

1.      Supplementary

2.      Adjacent

3.      Vertical

                                                            ii.      Finding missing angles without a protractor

c.       Station 3: 5.3

                                                              i.      Analyzing data

                                                            ii.      Converting a table into percentages

                                                          iii.      Graphing a circle graph using a protractor

d.      Station 4: 5.4

                                                              i.      Plotting points

                                                            ii.      Reading points

                                                          iii.      Understanding the concept of mid-points

2.      At Station 1(See directions sheet attached)

a.       Students will classify angles based on the type

                                                              i.      Acute

                                                            ii.      Obtuse

                                                          iii.      Reflex

                                                          iv.      Straight

                                                            v.      Right

b.      Students will draw specific angle measurements

                                                              i.      Have cards with angles on each

                                                            ii.      Students will pull cards and draw the corresponding angles

                                                          iii.      Have angles prepared

1.      45°

2.      87°

3.      180°

4.      354°

5.      15°

                                                          iv.      Students will trade cards and measure the angle to ensure that it was drawn correctly

3.      At Station 2 (See directions sheet attached)

a.       Students will classify the type of angle relationship based on the picture

                                                              i.      Supplementary

                                                            ii.      Vertical

                                                          iii.      Adjacent

b.      Students will find missing angles without a protractor

4.      At Station 3 (See directions sheet attached)

a.       Students will analyze the data by completing the missing parts from the table

                                                              i.      How many total people were surveyed?

                                                            ii.      What is the fraction for each possible answer

                                                          iii.      What is the decimal for this fraction?

                                                          iv.      How do you find the angle measurement?

b.      Students will create a circle graph together

                                                              i.      Graph must be labeled correctly

                                                            ii.      Graph must have a title

c.       Students will write a brief paragraph describing the data based on the circle graph

5.      At Station 4 (See directions sheet attached)

a.       Students will plot random points on graph paper

                                                              i.      Must create x and y axis

                                                            ii.      Must set up a scale for each line

b.      Students will pass paper to partner

                                                              i.      Students will identify the points

                                                            ii.      Students must write coordinate points in correct order (    ,    )

c.       Students must check the work of his/her partner

Summarizing Strategy:

1.      Hand back quiz

2.      Have students look at mistakes

3.      On a post-it note students will write one thing they learned today that could have helped them get a better grade on the quiz

Homework:

Students must fix all mistakes from the quiz and will have 3 days to complete this

Reflection:

Station 1 Directions

1. Take the pile of angles and group them based on type. For example, all of the acute angles should be in one pile. Once completed, have your group leader ensure that all of the answers are correct before moving to step 2.

2. Once your group has successfully classified the type of angles, each one of you will pull a note-card from the pile. On the note-card, you will find an angle measurement. On your whiteboard, draw the angle. When all members of the group are completed with this task, pass the whiteboards to the left.

3. Measure the angle on the whiteboard you have been passed. Write the angle on the whiteboard and give it back to the original owner. Was the angle correct? If not, try again.

Station 2 Directions

1. Look at the pictures of angle relationships with your group mates. Classify the different pictures based on the type. For example, all of the vertical angles should be placed into the same pile. Once completed, have your group leader ensure that all of the answers are correct before moving on to step 2.

            *** Supplementary angle relationships and adjacent angle relationships can be the same!

2. Each student in your group should take a worksheet and complete it to find the missing angle measurements without a protractor. Once completed, compare your answers with another person in your group.

Station 3 Directions

1. As a group, pick from the collection of data tables and answer the following questions as a group.

                                                              i.      How many total people were surveyed?

                                                            ii.      What is the fraction for each possible answer?

                                                          iii.      What is the decimal for this fraction?

                                                          iv.      How do you find the angle measurement?

2. Once you have answered the following questions, draw a circle graph representing the collection of data. Be sure to label the graph and each piece correctly. Everyone should be involved in drawing an angle!

3. As a group, write a brief 3-4 sentence paragraph describing the data in your circle graph. You may write this directly under the circle graph.

Station 4 Directions

1. Each member of your group should take a piece of graph paper. On the graph paper draw the x and y axis and create a scale for each line labeling it correctly. For example, the scale may go by ones, twos, fives, tens, or hundreds.

2. Randomly plot 6 points on your coordinate grid.

3. Pass your coordinate grid to the person to your right.

4. Once you have been given someone else’s graph paper, write out the points in correct format.

Lauren Nearhoof

2/3/14

Mathematics Unit 5

Lesson 5.5- Transformations

Standards:

2.9.6.B: Predict and describe the result of a translation (slide), rotation (turn), or reflection (flip) of a 2- dimensional shape.

M6.C.2: Identify and/or apply concepts of transformations or symmetry.

Essential Question:

What are the different types of transformations and can you identify them?

Assessment Prompts:

1.      What are the differences between a reflection, a translation, and a rotation?

2.      How can you identify a reflection?

3.      How can you identify a rotation?

Materials:

·         Access to a computer

·         This link: http://studyjams.scholastic.com/studyjams/jams/math/geometry/transformations.htm

·         Math Journal

·         Student Reference Book page 180

·         A transparency of 179, 180, and 181

·         Overhead projector

·         Overhead markers

Activating Strategy:

1.      Starter: Have students complete number 2 in Math Journal pg. 176

2.      Allow 5 minutes

3.      Used as a review from the last lesson

4.      Teach midpoint briefly

5.      Does anyone have any questions about how to plot points?

Teaching Strategy:

1.      Go over vocabulary from this section

a.       Transformation

b.      Translation

                                                              i.      Slide

c.       Reflection

                                                              i.      Flip

d.      Rotation

                                                              i.      Turn

e.       Preimage

f.       Image

2.      Read SRB 180 aloud with the class

3.      Show video to class

a.       Hand-out study guide for the video

b.      Read the directions of the hand-out aloud so students are aware of the task while watching the video

c.       http://studyjams.scholastic.com/studyjams/jams/math/geometry/transformations.htm

d.      Tell students that they must fill-out the worksheet as they watch the video as a form to take notes

e.       Students must focus on the three different types of transformations

f.       Go over the answers from the notes worksheet

4.      Ask A.P. 1

5.      Turn to page 180 in Math Journal

a.       Model number 1 and 2 on overhead projector

b.      Think aloud for the students

c.       Point out the image

d.      Point out the preimage

6.      Ask A.P. 2

7.      Turn to page 181 in Math Journal

a.       Model number 2 on overhead projector

b.      Think aloud for students

c.       Ask students which is the image and which is the preimage

8.      Ask A.P. 3

9.      Turn to page 179 in Math Journal

a.       Read the example at the top of the page aloud

b.      Model number 1

c.       Think aloud for students

Summarizing Strategy:

1.      On a note card, write 3 things you learned today, 2 things you already knew, and 1 question you still have about what we learned today

2.      Collect answers as a ticket out the door

3.      Assign the remaining problems from page 179, 180, and 181 for homework