Math Geometry Unit

“Sir Cumference” and the Beginnings of Geometry
Lauren Nearhoof, Melissa Schannauer, Patty Boland
Megan Babecki, Jessica Lowery, and Emily Reeser
6th Grade
Mathematics and Language Arts
TCH 342 Teaching Middle Level Mathematics
Dr. Ziegenfuss
 
Lauren Nearhoof, Melissa Schannauer, Patty Boland
Megan Babecki, Jessica Lowery, and Emily Reeser
TCH 342 Teaching Middle Level Mathematics
Dr Ziegenfuss- MW 3:30- 4:45 p.m.

Abstract for Integrated Unit- Mathematics and Language Arts

Incorporating a children’s picture book series, this 6th grade mathematics unit explores the basics of geometry and comprehension. Matched with common core standards in mathematics and language arts for 6th grade students, this unit plan combines skills from both disciplines. Specifically, students will learn the how to apply unknown vocabulary terms in a math setting to understand polygons and characteristics. Additionally, the unit covers fundamental formulas for area and perimeter of basic shapes.
 
Lauren Nearhoof, Melissa Schannauer, Patty Boland
Megan Babecki, Jessica Lowery, and Emily Reeser
TCH 342 Teaching Middle Level Mathematics
Dr Ziegenfuss- MW 3:30- 4:45 p.m.

Integrated Unit Table of Contents
• Integrated Unit Cover Page – Page 1
• Integrated Unit Abstract – Page 2
• Integrated Unit Table of Contents – Page 3
• Integrated Unit Graphic Organizer – Pages 4 - 5
• Integrated Unit Standards – Page 6
• Integrated Unit Content Lessons: Pages 7 - 27
• Lesson 1 Introductory – Pages 7- 10
• Lesson 2 Area and Perimeter – Pages 11- 13
• Lesson 3 Volume and Surface Area – Pages 14- 16
• Lesson 4 Volume and Surface Area – Pages 17- 18
• Lesson 5 Angles within Types of Triangles – Pages 19- 23
• Lesson 6 Summarizing and Alternative Assessment – Pages 24- 27
• Handouts for Lesson 6 – Pages 28-  31
• Integrated Unit Differentiation – Page 32
• Integrated Unit Cited Research – Pages 33- 35
• Integrated Unit Reflection – Pages 36- 37
Lauren Nearhoof, Melissa Schannauer, Patty Boland
Megan Babecki, Jessica Lowery, and Emily Reeser
TCH 342 Teaching Middle Level Mathematics
Dr Ziegenfuss- MW 3:30- 4:45 p.m.

Integrated Unit Graphic Organizer



 
Lauren Nearhoof, Melissa Schannauer, Patty Boland
Megan Babecki, Jessica Lowery, and Emily Reeser
TCH 342 Teaching Middle Level Mathematics
Dr Ziegenfuss- MW 3:30- 4:45 p.m.

Integrated Unit Standards
Language Arts Standards
• CCSS.ELA-Literacy.RI.6.1 Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text
• CCSS.ELA-Literacy.RL.6.3 Describe how a particular story’s or drama’s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution.
• CCSS.ELA-Literacy.RL.6.2 Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.
• CC.SS.ELA Literacy. L.6.4a: Use context as a clue to the meaning of the word or phrase

Mathematics Standards
• CC.SS.Math Content 6.G.A1: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes and applying to the real world
• CCSS.Math.Content.6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities
• CCSS.Math.Content.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

 
Lesson 1
Jessica Lowery & Megan Babecki
Topic: Types and characteristics of polygons
Grade Level: Grade 6, Mathematics
Common Core State Standards:
• CCSS.ELA-Literacy.RL.6.3 Describe how a particular story’s or drama’s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution.
• CCSS.ELA-Literacy.RL.6.2 Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.
• CC.SS.Math Content 6.G.A1: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes and applying to the real world
• CCSS.Math.Content.6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities

Focus Question:
How can the use of manipulatives help identify similar shapes or shapes in a real world setting?
Materials:
• Math Interactive Notebooks
• Pencils
• Vocabulary Handout
• Notecards
• Smart Board/ Overhead Projector
• Tangrams
• Tangrams handout
• Handout with pictures of shapes

Starter:
The students will complete their journey entry within the first 5 minutes of class in their interactive math notebook, which are located in the bin labeled according to the class period at the front of the classroom.  The students place their notebooks in the bin after every class period when they are finished working with them so that they do not get lost or damaged.  These interactive notebooks are never to leave the room; however, work done at home is placed in the notebook according to the section it pertains to.
Journal entry Prompt- “Imagine you and your family of 12 are at a restaurant to celebrate your 11th, 12th, or 13th birthday. The problem is the restaurant set up your table of 12 in a long rectangular shape, not allowing everyone to be involved in the party. Since you would like to be the center of attention and have everyone included, how can you solve this problem by choosing the correct shape for the table?
After the students have completed their journal entries they will share their ideas with their table mates so that they can gain different perspectives of the problem.  We will then discuss as a whole group the different ideas that the students have come up with.
Activating strategy:
1. We will begin the introduction to vocabulary of geometry by going over terms and definitions by the creation and use of flashcards
a. Each student will receive a template with blank terms and definitions.  The following terms and definitions will be on the Smartboard for the students to fill in on their blank handout- they will be given the handout to fill out so they can place the handout in their interactive math notebooks for future reference if they do not have the note cards or if they have to redo a missing note card.
• Rectangle – a parallelogram with all right angles and two pairs of parallel lines
• Regular Polygon – a polygon that has all sides the same length and all sides the same measure
• Rhombus – a quadrilateral that has all sides the same length
• Quadrilateral – polygon with four sides
• Line Segment – a straight line that has two end points
• Parallel Lines – lines that never meet no matter how long they are extended
• Parallelogram – a quadrilateral with two pairs of parallel lines. Both pairs of opposite sides are equal and parallel. Both parallel angels as well.
• Polygon – a closed flat 2-D shape whose edges are formed by line segments
• Properties of Shapes – characteristics of shapes that are always true
• Equilateral – same; equal
• Intersecting – two lines that cross
• Equilateral Triangle – a triangle with three sides the same length and all three angles the same measure
• Irregular Polygon – a polygon which has at least two sides with different lengths or at least two angles with different measures
• Isosceles Triangle – a triangle with two sides the same length
• Line – a straight line that has no end in either direction
• Trapezoid – a quadrilateral with at least one pair of opposite sides parallel
• Right Triangle – a triangle with one right angle and two acute angles
• Scalene Triangle – a triangle with no sides the same length. All sides are different lengths.
• Sides – the segments in polygons
• Square – A rectangle with four equal right angles
2. The students will then receive a paper with all the terms and definitions set up in a chart template.
a. These terms and definitions will not be set up in order and they will be expected to cut each term and definition out and match with the right term or definition.
b. Once they have them all matched up correctly they will then glue them to a flashcard. The term will go on the non-lined side and the definition will go on the lined side.
c. After they are all glued they will then draw an example of that term on the side of the definition.
d. Until everyone is finished the students will get into partners and help each other practice and understand these new terms.

Procedure:
1. Have the students explore with the manipulative of tangrams.
a. They will be creating primary shapes using an assortment of tangrams.
2. The students will receive an outline of a square and will be asked to fill in this outline using the different tangram shapes.
a. Set a small square in front of the students and ask “can you cover this square perfectly with any other shapes?” (2 small triangles) “If so, what is the relationship between the shapes?”
i. A square is twice as big as the small triangle or the triangle is half of the square.
b. Set the parallelogram in front of you. “Can you cover it perfectly with any other shapes?” (2 small triangles) “What is the relationship between these?”
i. A square is twice as big as the small triangle or the triangle is half of the square
c. “Considering this information, what do we know about these three shapes – the square, parallelogram, and medium triangle?”
i. They have the same area – even though they don’t have the same perimeter; they are the same fraction of the whole.
d. Set the large triangle in front of you. “Can you cover the shape with any other shapes? What shapes?”
i. 3 possibilities – using one of the following pieces – medium triangle, square, parallelogram – and both small triangles.
e. “What are the relationships between each piece and the large triangle?”
i. The parallelogram is half of the large triangle. The square is half of the large triangle. The medium triangle is half of the large triangle. The small triangle is the fourth of the large triangle.

Guided Practice
1. Together as a class we will be creating a tangram shape together.  The shape we will be creating is in the form of a house.  We will use the overhead projector and volunteers will come up and do it on the overhead, while other students will follow along at their seats.

Independent Practice
1. The students will be creating more shapes using the tangrams but this time they are going to pick the shapes they would like to create. They will have to chose three shapes and complete them correctly.

Homework
The students will be creating their own outline of a closed shape that they can create with the tangrams.

Formative Assessment
The students will be completing a worksheet with pictures of all the shapes on it.  They will be asked to name the shape and to list its properties that were gone over in the activating strategy.

Closing Activity

Exit Slip – the students will be asked to pick a shape that they see in the classroom, they will then be asked to describe and name the shape they have picked.  They will be asked to hand this slip to the teacher as they leave the classroom.
a. Ex. Ceiling Tile: Rectangle because opposite sides are equal and parallel creating all right angles
 
Lesson 2
Jessica Lowery & Megan Babecki
Topic: Area and Perimeter of squares, triangles, and circles
Grade Level: Grade 6, Mathematics
Common Core State Standards:
• CC.SS.Math Content 6.G.A1: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes and applying to the real world
• CCSS.ELA-Literacy.RL.6.2 Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.
Focus Question:
How does area and perimeter relate to one another in real world situations?
Materials:
• Sir Cumference and the First Round Table Book
• Pencil
• 10 x10 grid paper
• Math journal
• Rulers
Starting Activity:
The students will be learning about area and perimeter in this lesson. The students will start the lesson by measuring the length and width of both their desks and the classroom.  We will use the measurements to find the area of the desks and the room as a whole class.  As a class, the teacher will wait and see if any of the students already know the formula or how to get the area of a rectangle.  If the students seem to be stuck, the teacher will provide the formula to the class, and will explain later in the lesson the formula in more detail.
Activating Strategy
We will be reading the book, Sir Cumference and the First Round Table.
Procedure
1. Teach the students area and perimeter and explain the definitions of each
a. They will be writing the definitions in their interactive math notebooks.
i. Area- The amount of space inside the boundary of a flat 2-dimensional shape.
1. Formula for Area of a Square or Rectangle: A= l x w
a. l = length
b. w = width
2. Formula for Area of Circle: A= π r ^2
a. r = radius, the distance from the center to the edge of a circle
ii. Perimeter- The distance around a two-dimensional shape.
1. Formula for Perimeter of a Square or Rectangle: A= 2l + 2w
iii. Circumference- The distance around the edge of a circle (or any curvy shape.)  It is a kind of perimeter
1. Formula for Circumference of a Circle: C= 2πr
a. r = radius (see previous definition)
2. The students will then receive their exit slip back from the previous lesson, where they had to pick a shape and define it.
3. They will now use whatever shape they put on their exit slip and measure it to find its area and perimeter.
4. Once the students are finished they will get with a partner and their partner will have to check their answers.
a. The students will then find the dimensions of their partners’ shapes and check at the end to make sure they have similar answers.
Guided Practice
As a class, we will create human figures on graph paper.  Once the figures have been created, we will find the area and perimeter of the figures.  Each student will be creating their own figure and follow along with the figure on the board.
Independent Practice
As a class, students will be given a 10x10 grid.  In this grid the students will need to draw and color the first letter of their first name.  Once they have the shape of their name, they will be asked to find the area and perimeter of the shape by counting the squares the colored to form the shape.
Assessment
When they were listening to the book, they were required to find the perfect shape for the twelve knights to sit.  There were three people added to King Arthur’s table.  The students’ task will be to solve for the area and perimeter of the new round table.  For the assessment, students will be able to work with their elbow partner to think of a way to figure out how big the new table should be.

Closing Activity
Before leaving the classroom, the students will have to fill out an exit slip that asks “what is the difference between area and perimeter?”  This will be informative to know if the student comprehends the main concept taught in the lesson and if any further information needs to be covered before moving on to the next lesson.
 
Lesson 3- Enrichment Students
Patty Boland & Emily Reeser
Topic: Surface area and volume of three dimensional objects
Grade Level: Grade 6, Mathematics
Common Core State Standard:
• CCSS.Math.Content.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Focus Question
How do you find the surface area and volume of a cone, prism, cube and cylinder?
Materials
• Smartboard
• Youtube Link-   http://www.youtube.com/watch?v=R_oJqM0eXTU
• Paper for foldable
• Pencils/ Colored Pencils/ Markers
• Different Objects (party hat, pyramid, jewelry box, and can)
• Rulers, Measuring Tape
• Sticky Notes

Starter
Students have a routine of coming into the classroom every day, getting the materials they need for the class, sitting in their seats and completing the math riddle on the board. This is just to get them thinking about math in a different way and a way to get their brains geared for math class.
• “Bob is ten years older than his brother Stan.  There was a time when Bob was three times as old as Stan.  What was Stan's age when Bob was three times as old?”
After we finish going over the riddle as a whole class, we will begin the lesson.
Activating Strategy
Students will watch a YouTube video created by other students their age about the difference between surface area and volume.
http://www.youtube.com/watch?v=R_oJqM0eXTU
Teaching Strategy (Guided Practice)
Foldable (Teacher will model to the students how to make a foldable then do it with them.)
• Start with four pieces of paper
• Place each consecutive sheet about ¾ of an inch higher than the sheet in front of it
• Bring the bottom of all sheets upwards and align the edges
• Make sure all the tabs are the same distance apart
• When tabs are all equal distance apart, fold and crease the papers
• Open the papers and glue them together along the center fold
• Label the tabs accordingly (write on board the correct label for each tab.)
• Tabs & formulas:
o Volume of prisms & cylinders
 Rectangular prism: V= l*w*h
 Cylinder: V= π*r2*h
o Volume of pyramids & cones
 Pyramid: V= (1/3)*b2*h
 Cone: V= (1/3)*π*r2*h
o Surface area of prisms & cylinders
 Rectangular prism: SA= 2(w*h + l*w + l*h)
 Cylinder: SA= 2*π*r2 + 2*π*r*h
o Surface area of pyramids & cones
 Pyramid: SA= 2*b*s + b2
 Cone: SA= π*r*s + π*r2
o Last tab is for notes and any irregular formulas we add
Independent Practice
Each table group will receive an object (each group a different object): A party hat (cone), a pyramid (a triangular prism), a jewelry box (cube or rectangular prism), or a can (cylinder)
Students will measure the dimensions of the object together as a group.
Each individual student will find the surface area and volume of the object using the dimensions found.
After each student has completed their own work, they can do a think, pair, share with a partner from their table group.
Each group will tell the class their answer and how they found it.
Closing Activity: Stick it to the Wall
Students will receive a Post-it note.
Before they leave the classroom, they need to write down one thing they learned that they are unsure about—something they have not completely grasped and post it under their class board (posted on the wall near the door) as they walk out the door.




Homework
For homework the students will be asked to go through their house and find 3 objects that are the same 3-dimensional shapes as the objects we focused on in class. The 3 objects must be 3 different shapes (cone, cylinder, cube, rectangular prism, or triangular prism). Students must measure the dimensions of each figure and find the Surface Area and Volume for each.
 

Lesson 4- Enrichment Students
Topic: Real world application of surface area and volume
Grade Level: Grade 6, Mathematics
Common Core State Standards:
• CCSS.Math.Content.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
• CCSS.ELA-Literacy.RI.6.1 Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
• CCSS.ELA-Literacy.RI.6.3 Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text
Focus Question
How can you use surface area and volume to solve real-world problems?
Materials
• Smart Board
• “Sir Cumference and the Sword in the Cone”
• Sticky Notes

Starter
Starter is a math joke or riddle and will be projected on the board for the students to solve as they come into the classroom and get settled in their desks:
“If you had a pizza with crust thickness ‘a’ and radius ‘z’, what is the volume of the pizza?”
Answer: Pi*z*z*a
The goal of our starter is to get the kids thinking outside the box. We want them to see that math can be fun and that math is real in their everyday lives. The starter opens our students’ minds to math concepts and ideas.
Activating Strategy
The following statements will be projected on the board:
“Wrapping a Birthday Present”, “The cardboard of a cereal box”, “Covering an Oatmeal container in construction paper”, “The lining and cover of a swimming pool”, “Packing peanuts in a cardboard box”, “Cereal in a cereal box”, “Water in a swimming pool.”
Students will have to decide if the surface area or volume is described for every statement.
This will allow the teacher to see if the students understood what was taught the day before and if they are ready to move onto the next lesson.
Teaching Strategy
We will be reading the book “Sir Cumference and the Sword in the Cone”. This book takes the kids on an adventure through a kingdom and uses a math concept to solve a problem in the kingdom. This book in particular relates to finding the surface area and volume of figures (cone, prism, cube and cylinder).
I will read the story out loud to the students, allowing them to sit on the floor near me or in their desks (where ever they feel is most comfortable). This will enable the kids to get up and move to a new area of the room if they please. As I read I will pause at certain parts in the book where a math concept or part of a math problem is mentioned. This will prompt the students to pay attention and will remind them of the different components of math concepts that they are currently learning about.
Independent Practice
As the story is read, the students must complete the math problems embedded in the book. This will give the students practice and allow them to see how comprehension strategies learned in Language Arts class are important to know to be able to complete real world math problems.
By completing the math problems in the book along the way, the students should be able to predict how the story ends before the ending is read.
Closing Strategy
The students will be required to post on our classroom “Tweet Board” how the lesson’s activites tied math into other subject areas.
 
Lesson 5
Melissa Schannauer & Lauren Nearhoof
Topic: Angles within Types of Triangles
Grade Level: Grade 6, Mathematics
Common Core State Standards:
• CC.SS.ELA Literacy. L.6.4a: Use context as a clue to the meaning of the word or phrase
• CC.SS.Math Content 6.G.A1: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes and applying to the real world
Focus Question
How are you able to justify the type of triangle through the representation of the given visuals and angles?
Interdisciplinary
This mathematics lesson integrates both of the subjects of language arts as well as social studies.  The language art’s integration is more meaningful than the social studies integration.  Students will be using their listening and writing skills on multiple occasions throughout the lesson.  They will have to use their listening skills during the activating strategy, where they will have to use their context clue knowledge in order to predict the meaning of their vocabulary words.  The students will be required to use their writing skills for the completion of their flipbooks.  Their social studies knowledge will help aid in their understanding of the book in the activating strategy.
Materials
• Smartboard
• Interactive Notebooks
• Pencils
• “Sir Cumference” Book
Starter
There will be 8 angles with unknown values on the SmartBoard when the students enter the classroom.  They will individually be required to decide if the angle value is

1. Less than 90°
2. Equal to 90°
3. Greater than 90°
Based off of their prior knowledge that they already have on a standard, 90° right angle located in the right triangle.  This will be completed within the first 5 minutes of class in their interactive math notebook, which are located in the bin labeled according to the class period at the front of the classroom.  The students place their notebooks in the bin after every class period when they are finished working with them so that they do not get lost or damaged.  These interactive notebooks are never to leave the room; however, work done at home is placed in the notebook according to the section it pertains to.










A.) Less than E.) Greater than
B.) Less than F.) Less than
C.) Less than G.) Greater than
D.) Greater than H.) Less than


Activating Strategy
The book “Sir Cumference and the Great Knight of Angleland” will be used to activate prior knowledge of angles and shapes while incorporating listening skills and the use of context clues.
I will be reading the book aloud to the students.  While I read the book, they will be required to listen for their vocabulary words in the text.  They will not know what these words are, so they will have to use the context clues within the text to define them.  The following vocabulary words will be listed on the board and the students will have to actively listen to the story.  When a vocabulary word from the board is read aloud, the students must raise their hand to write a part of the estimated definition on the board.  The vocabulary words will be correctly defined during the lesson procedures in their interactive math notebook.
The words are: Right Angle, Straight Angle, Acute Angle, and Obtuse Angle

Lesson Procedures (Guided and Independent Practice)
A.) Students will be each be given 10 sheets of paper, first I will model how to fold a flip book so that there are 9 equal sections and then have the students independently fold their flip books.














The students will title the flip book “Triangles and Angles”
1. The first section will be titled “Acute Little Angle”
a. There will be a slide on the SmartBoard that has a picture of the angle with the correct degrees labeled.
b. The student will be required to use a protractor to draw an angle with the correct use of arrows and straight lines.
c. An acute angle is any angle that measures more than 0° and less than 90°.  Therefore, the student must draw an angle between 0° and 90°.
d. I will walk around and formatively assess the students and do a spot check to make sure they are comprehending the definitions.
2. The second section will be titled “The Obtuse Angle”
a. There will be a slide on the SmartBoard that has a picture of the angle with the correct degrees labeled.
b. The student will be required to use a protractor to draw an angle with the correct use of arrows and straight lines.
c. An obtuse angle is any angle that measures more than 90° and less than 180°.  Therefore, the student must draw an angle between 91° and 179°.
d. I will walk around and formatively assess the students and do a spot check to make sure they are comprehending the definitions.
3. The third section will be titled “Just the Right Angle”
a. There will be a slide on the SmartBoard that has a picture of the angle with the correct degrees labeled.
b. The student will be required to use a protractor to draw an angle with the correct use of arrows and straight lines.
c. A right angle is any angle that measures exactly 90°.  Therefore, the student must draw an angle exactly 90°.
d. I will walk around and formatively assess the students and do a spot check to make sure they comprehend the definitions.

Differentiation

Through the use of scaffolding the directions of the flip book will be pleasing my visual learners.  When the students are creating the flip book my kinesthetic learners will be working hands on with the new information. I will also be speaking while scaffolding the flip book, so students are able to learn through hearing me speak.

Assessment
 I will formatively assess the students throughout the lesson.
• First, the students will be assessed during the starter activity.  Their answers that they jot down in their interactive notebooks will be what I use for assessment.  If they guess the correct answers, then there is evidence that they understand what they are learning.  If the majority of their answers are incorrect, clearly I must work with that student.  However, if there are a lot of students that have a majority of the questions incorrect, I may have to go back and focus on the specific lessons again.
• Second, I can formatively assess the students that write up their definitions when I am reading aloud the book during my activating strategy.
• Third, I can formatively assess the students as they work on their flip books. When we are finished working on the flip books, I can use the finished project as a summative assessment.  With their flip books, that will be added into their interactive notebooks after grading, I can check for their comprehension of the angle measurements, drawing angles with the use of a protractor, and their definitions.
Closure: In the closure of the lesson I would like my students to be able to demonstrate their comprehension of the three different types of angles.
• The students will have to participate in “Ms. Schannauer/ Ms. Nearhoof Says.”  In this game, the students will have to show the different angles of right, acute, and obtuse (the angles they just learned).  I will be able to assess the students’ knowledge when they demonstrate with their arms the different angles.





Lesson 5 - Final Lesson/ Assessments

Melissa Schannauer & Lauren Nearhoof
Topic: Geometry Unit Assessments
Grade Level: Grade 6, Mathematics
Common Core State Standards:

• CCSS.Math.Content.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Enrichment ONLY)
• CC.SS.Math Content 6.G.A1: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes and applying to the real world
• CCSS.Math.Content.6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities

Focus Question

Combing all of your learned skills throughout this lesson, how can you demonstrate that you are able to apply properties of shapes, area, perimeter, measurement and angles in everyday applications?

Materials
• Notecards with definitions and vocabulary words written on them
• Duct tape shapes located around room
o 10 Shapes that are numbered 1 through 10
 Rhombus
 Line Segment
 Rectangle
 Isosceles Triangle
 Right Triangle
 Square
 Trapezoid
 Scalene Triangle
 Parallelogram
 Polygon
• Protractors
• Rulers/ Yard sticks
• Clipboards
• Extra Pencils/pens
• White paper 11x17
• Magazines
o Preferably old- used for collage
• Assortment of everyday objects
o Tissue Box
o Can of soup
o Ice cream cone
o Birthday party hat
o Brick
o Paper towel roll
• Tape Measure
• Sticky-notes

Starter

Students will brainstorm a list of ways he/she can apply what they have learned through this lesson in an occupation or in everyday life. A list of all of the topics we have covered thus far in the unit will be placed on the board to remind students all that was covered so it is easy for him/her to begin their journal entry. This will be completed within the first 5 minutes of class in their interactive math notebook, which are located in the bin labeled according to the class period at the front of the classroom.  The students place their notebooks in the bin after every class period when they are finished working with them so that they do not get lost or damaged.  These interactive notebooks are never to leave the room; however, work done at home is placed in the notebook according to the section it pertains to.

List:
• Properties of shapes
• Types of shapes
• Area
• Perimeter
• Types of angles
• Surface area (if applicable)
• Volume (if applicable)

Activating Strategy

Students will be given either a vocabulary word or definition on a note card and must find their partner silently to discover whom they will be working with for the final assessment. I will be strategically be handing out the partners to ensure that those of equal ability are placed together to ensure an authentic assessment.
1. Have prepared note cards prior to class
2. Hand out note cards to students
3. Explain that each person has either a definition/formula/picture or vocabulary word
4. Once every student has been given a card, students may silently walk around the room to find his/her partner
a. Students are not allowed to talk during this process
b. Students will have no more than 5 minutes to find partner
c. If students think that they have found match, they must get it approved by the teacher
5. If a pair has been approved by teacher, they may find a seat around the room and wait quietly for the rest of the students to complete the matching game
6. Once all of the students have found their pairs, each will go around and state the vocabulary word and the matching definition/picture/formula as a review for the entire class.
a. Gifted students who have been exposed to enrichment lesson will review together during this time
b. These students may sit in the back of the room and discuss the formulas and concepts prior to the assessments

Lesson Procedure

Each assessment will be administered based on mathematical competency level: Enrichment/Gifted or On Grade Level. All assessments meet the standards in a different approach that is appropriate to the needs of each group. Each student has previously been placed with a student who will be completing the same assessment during the activating strategy. All of the assessments will be completed at the same time throughout the classroom. Below is a description of each of the assessments based on mathematical level.

1. Enrichment Group
a. Stations will be created for this specific assessment.
b. Each station will have an object that can be seen in everyday life.
• Station 1: Tissue Box or brick
• Station 2: Can of soup or paper towel roll
• Station 3: Ice Cream Cone or party hat
c. Students will work in pairs to identify what shape the object has whether it is an cone, cylinder, or prism
d. Students will use rulers or tape measures to find the dimensions of the objects needed to compute the surface area and volume for the given shape at each station
e. Students will also identify the area of one of the faces of the objects and explain in a brief paragraph how they solved for it for one specific station of their choice.
• The paragraph should include the shape of the face (circle, square, etc.) and the equation used to find the specific area of the object
• This will be assessed on a 1-4 grading scale similar to the PSSAs
f. Students will fill out a chart at each station and have only 3 to complete.
2. Grade-Level Group
a. Stations will be created for this specific assessment
b. Each station will have a shape duct taped to the floor and will be labeled 1 through 10
i. List of shapes include:
1. Rhombus
2. Line Segment
3. Rectangle
4. Isosceles Triangle
5. Right Triangle
6. Square
7. Trapezoid
8. Scalene Triangle
9. Parallelogram
10. Polygon
c. Students in pairs will be assigned to start a specific number and complete the stations in order
• Example: Group will be assigned to begin at station 4. The pair will go to 5, 6, 7, 8, 9, 10, 1, 2, and 3 to ensure that only one pair is at each group
d. Students will complete a chart at each station by filling in the specific columns
• Identify the shape
• List at least 1 property of this shape
• Identify the type(s) of angles in this shape by using a protractor
• Find area by using the correct formula for the shape
o Students will only find the area for stations numbered 3, 4, 5, 6, and 8
• Find perimeter for all stations
• Students will have to write a brief paragraph identifying how they solved one area problem of his/her choice
1. The paragraph should include the shape and the equation used to find the area of that shape.

Differentiation

Throughout this assessment block period, students will be able to apply many different skills including measurement, identification of objects, and writing to demonstrate that he/she understands the standards for this geometry unit.

Closure

Students will hand-in assessments when they finish and write on a post-it note their favorite application to the unit that he/she brainstormed during the starter on the bulletin board. Once all students have completed the assessment and placed the sticky-note on the board, we will read all the applications that each student has created for the unit. This will allow students to see how what they have learned in this unit is practical and useful in everyday life and in the future. This makes the entire unit relevant to everyday life.
 
Vocabulary Word Picture/Formula/Definition
Area of Square A=l x w
Area of Circle A= π r ^2
Perimeter of a Circle (Circumference) C= πd
Perimeter of Square P= l+l+w+w
Rectangle A parallelogram with all right angles and two pairs of parallel lines
Rhombus A quadrilateral that has all sides the same length
Line Segment A straight line that has two end points
Regular Polygon a polygon that has all sides the same length and all sides the same measure
Quadrilateral polygon with four sides
Parallel Lines lines that never meet no matter how long they are extended
Parallelogram A quadrilateral with two pairs of parallel lines. Both pairs of opposite sides are equal and parallel. Both parallel angels as well.
Polygon a closed flat 2-D shape whose edges are formed by line segments
Equilateral same; equal
Equilateral Triangle a triangle with three sides the same length and all three angles the same measure
Irregular Polygon a polygon which has at least two sides with different lengths or at least two angles with different measures
Isosceles Triangle a triangle with two sides the same length
Line a straight line that has no end in either direction
Trapezoid a quadrilateral with at least one pair of opposite sides parallel
Right Triangle a triangle with one right angle and two acute angles
Scalene Triangle Triangle with no sides the same length. All sides are different lengths.
Acute An acute angle is any angle that measures more than 0° and less than 90°
Obtuse An angle that measures more than 90° and less than 180°


These will be the words and definitions placed on the note cards for the activating strategy.

 
Chart for Enrichment Assessment:

Station: Object: Shape: Surface Area: Volume: Area:


































Area Writing Assignment:
 
Chart for Assessment:
Only find area for stations 3, 4, 5, 6, and 8.
Station: Shape: Characteristic: Angle(s): Perimeter: Area:































Area Writing Assignment:

 
Writing Assignment Rubric:

4 points - The response demonstrates a thorough understanding of the mathematical concepts and procedures required by the task.

    The response provides correct answer(s) with clear and complete mathematical procedures shown and a correct explanation, as required by the task. Response may contain a minor "blemish" (e.g., missing $) or omission in work or explanation that does not detract from demonstrating a thorough understanding.

3 points - The response demonstrates a general understanding of the mathematical concepts and procedures required by the task.

    The response and explanation (as required by the task) are mostly complete and correct. The response may have minor omissions that do not detract from demonstrating a general understanding.

2 points - The response demonstrates a partial understanding of the mathematical concepts and procedures as required by the task.

    The response is partially correct with partial understanding of the required mathematical concepts and/or procedures demonstrated and/or explained. The response may contain some work that is incomplete or unclear.

1 point - The response demonstrates a minimal understanding of the mathematical concepts and procedures required by the task.

0 points - The response has no correct answer and insufficient evidence to demonstrates any understanding of the mathematical concepts and procedures required by the task for that grade level.
 
Lauren Nearhoof, Melissa Schannauer, Patty Boland
Megan Babecki, Jessica Lowery, and Emily Reeser
TCH 342 Teaching Middle Level Mathematics
Dr Ziegenfuss- MW 3:30- 4:45 p.m.

Integrated Unit Differentiation
Throughout the different lessons in our integrated unit we provided our students with multiple strategies that allow differentiation.  Four of our lessons were aimed towards proficient, basic classrooms and we provided two lessons for our enrichment students.  In our four proficient lessons we have also provided an alternative assessment for our below basic, lower leveled students.  Therefore, we hit the different leveled students in our assessments as well as the lessons that are taught and the material that is covered.
In our lessons we provided equal opportunity for learning for all of our different students.  In three out of our six lessons, we have the students listening to a read aloud, which allow our students who learn best through listening extra material as well as enjoyment.  The students are also given a visual representation when the read aloud is read.  In multiple lessons we provide our kinesthetic learners with different types of assessments, such as the use of flip books, manipulatives, and flash cards.  The students are able to use their interactive math notebooks and the activities they complete for further learning and later reference.
The students are able to complete different types of activities in order to learn and comprehend the material.  Through the different types of assessments we are also able to gauge the students’ comprehension and reassurance that the standards and focus questions have been met. 

Lauren Nearhoof, Melissa Schannauer, Patty Boland
Megan Babecki, Jessica Lowery, and Emily Reeser
TCH 342 Teaching Middle Level Mathematics
Dr Ziegenfuss- MW 3:30- 4:45 p.m.

Integrated Unit Cited Research
Throughout this entire mathematics unit plan, there have been numerous educational theories for best practice in a middle level setting incorporated to ensure that students have the greatest potential of meeting the standards. As educators, it is important to create lessons that are engaging, rigorous, and relevant to adolescent students. This mini geometry unit has implemented suggestions and research from several different psychologists and professionals to create a successful and authentic learning experience from those who are exposed to it. Below are headings from the various professional websites and readings; under each heading describes which aspects this unit plan has incorporated.
National Middle School Association, “This We Believe”
Throughout this article, “This We Believe,” this unit plan has incorporated three important aspects under the Curriculum, Instruction, and Assessment subtopic. These subtopics include number 2, 4, and 5. Subtopic number two states that “instructional practices place students in the center of the learning process… [and are able to] play a major role in their learning and education.” Throughout all of the lessons in this unit plan, students are able to create their own study tools in his/her interactive math journal. Not only does this place the students at the center of their own learning, they are also able to take what they have created and use it as a helpful study tool.
Secondly, under subtopic 4 it states, “Teaching and learning approaches should accommodate the diverse skills, abilities, and prior knowledge of young adolescents…” This math lesson incorporates multiple types of learning throughout all of the lessons provided. For example, during all of the lesson plans that incorporate the picture book, those who learn through listening and visualizing are able to hear the words and see the pictures that are associated with the book for a better understanding of the key vocabulary in this geometry lesson. Too, some of the journal entries in the interactive journal require students to fold paper; this reaches the individual needs of tactile or hands-on learners.
Lastly, under subtopic 5 it states, “Continuous, authentic and appropriate assessment measures, includes formative and summative ones, provide evidence about every student’s learning progress.” This holds true throughout the entire math unit because every lesson includes either a formative or summative assessment that measures the growth and achievement of each student throughout each lesson. One specific instance is the “Teacher Says” game after the lesson on types angles. Students are required to show acute, right, obtuse, and straight angles with his/her arms. This is a formative assessment that allows the teacher to see if students understood the lesson and vocabulary involved with a fun Simon says game.
Dr. Howard Gardner’s Multiple Intelligences
Similar to the forth subtopic in “This We Believe,” Gardner believed that, “human beings have nine different kinds of intelligence that reflect different ways of interacting with the world” (Howard’s). The nine different types of intelligences include linguistic, Logical, Musical, Bodily, Spatial, Naturalist, Intrapersonal, Interpersonal, and Existential. This unit plan has attempted to reach as many of these intelligences as possible to ensure that all students have the opportunity to succeed through all of the lessons.
Linguistic intelligence can be measured through the use of language to express thoughts; this unit incorporates small group discussions and journal entries. Additionally, one aspect of the assessments includes a mathematical writing assignment that allows students to prove how they got an area problem through words and explanations. Logical or mathematical intelligence is incorporated throughout the entire unit plan since it is geometry. Also, bodily or kinesthetic intelligence is reached through various activities throughout the unit. For example, during the starter of the final assessment lesson plan, students are required to get out of his/her seats to find their partner based on note cards given to them. This allows the students to move around and find his/her partner through movement. Lastly, interpersonal intelligence, or the ability to work well with others, is obvious during group work, small group discussions, and overall behavior in class. This is something that is easily placed in any of the lessons provided. http://www.pbs.org/wnet/gperf/education/ed_mi_overview.html
 
Lauren Nearhoof, Melissa Schannauer, Patty Boland
Megan Babecki, Jessica Lowery, and Emily Reeser
TCH 342 Teaching Middle Level Mathematics
Dr Ziegenfuss- MW 3:30- 4:45 p.m.

Integrated Unit Reflection
Benefits
Overall, we believe that our unit plan offers several benefits to the students. All of our lessons are uniform; every starter is similar which allows students to create an understanding of what is expected of him/her when entering a math classroom. In addition, every lesson incorporated a unique way of taking notes and understanding the new concepts in the geometry lessons. Since geometry is predominately vocabulary and formulas, it was essential to create lessons that had students writing and working with the terms in several different ways to ensure that all students had the opportunity to succeed. For instance, students created his/her own note cards, graphic organizers, and vocabulary list within an interactive math journal. Not only does this expose students to the terminology in fun and unique ways, it also teaches students how to create study tools. Overall, we want our students to be able to create effective study guides and tools to succeed in other aspects of their education as well as in math. Lastly, all of the lessons incorporated a book from the “Sir Cumference” series. This created cohesiveness throughout the entire unit plan.
Challenges
There were various challenges that our group had to overcome when creating this unit plan. To begin, it was difficult picking math standards that could be applied to language arts standards. We wanted our cross-curricular unit plan to show strong evidence of language arts skills, and it was difficult creating lessons that met both of the subject standards. Applying the unit plan to the students, it might be a challenge teaching geometry to 6th grade students since it is only their second year exposed to basic ideas of shapes and characteristics of polygons. Also, time constraints may pose an issue for schools that do not implement block scheduling in math and language arts. All of the lessons presented in this unit plan are intended to be taught in a ninety minute block period, and it is likely that the lessons would not be fully completed if in smaller time frames.
Relevance
Throughout this mini geometry unit plan, we believe that our lessons are made relevant to sixth grade students through our use of activities, examples, and choice of math-related literature. Playing “teacher says” and using examples that involve pizza are likely to excite the students more than filling out a worksheet or KWL chart. Additionally, our literature series is specifically written for this age group of students. It involves parent/child boundaries, adventure, and an adolescent character that is likely to engage the students. Not only does the literature introduce basic ideas and terminology, it has a fun story line that students can follow along while relating to the main character Radius. Generally, we feel that the lessons we created reach the specific learning needs and interests of students in sixth grade.