Apartment Proportions 7.G.A.1

Apartment Proportions

Problem:

Congratulations! You just got your first apartment. It’s located right in the heart of downtown Ellensburg. You just realized you do not have anything to put in your new living room which is 14’ by 12.5’.

Sadly, the store you want to get your furniture from only has a few options but they come in multiple proportions. Make sure you have at least one item from each of the categories. If an item is too large or small, use ratios to change the proportions. You are only allowed to have ten of the following items in your living room!

Hint: Do some of the sizes seem odd? You should probably use ratios to change the size.

Show your work!

Below are the furniture you can select from with the measurements.

Seating                                                            Misc

Couch 8’x4’                                                    Lamp 4’x4’

Chair 2’x3’                                                     Fan 4’x2’

Bean bag square 3’x3’                                  Bookshelf 3’x2’

 

Table                                                              Entertainment

Coffee Table 16’x9’                                       TV with stand 12’x10

Side Table .5’x.5’                                           TV 10’x2’

                                                                           Gaming Consoles 4’x6’

Rug

Fuzzy Rug 15’x8’

Rug 14’x6’

 

This picture was found at Clipart-Library. This lesson will focus on the CCSS.Math.Content.7.G.A.1 which is solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

I would teach this culturally by understanding that all students come from different cultures and different cultures have different housing expectations.

Other standard:

CCSS.ELA-Literacy.W.7.4
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

Yeah He Caught It, But How Far Was It? 8.G.B.7

Problem: For this lesson, students will be doing an extreme version of utilizing the Pythagorean Theorem. The number in the picture, 400ft, is the distance from home plate to dead center field at Miller Park in Milwaukee, Wisconsin. The goal of the lesson is for students to find the distance of the ball when it is caught by Keon Broxton. Almost all of the information is present in the picture without much background knowledge, but they will also be told that he was estimated to be about 4ft off of dead center when he caught the ball.

The beginning of the lesson will have students discussing what information they have and what information they will need to complete the assignment. The groups will realize that they need to use the Pythagorean Theorem to solve the problem. The groups will come together for a class discussion and asked what information they still need.

After that, students will do their own research to find the missing components. These components are things like where in the stadium the ball was caught, where the ball was when it was caught, etc. The students will use this information to solve the problem, and present to the class how they solved the problem and how they found the missing information.

Connected Math Standards:

CCSS.MATH.CONTENT.8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

CCSS.MATH.CONTENT.8.G.B.8
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Extension: If students are grasping the content quickly, have them estimate the angle at which the ball entered Keon Broxton’s glove. This can be done using basic trigonometry, which is referenced in the standard CCSS.MATH.HSG.SRT.D.10. While this is technically beyond their grade level, they have a lot of the background knowledge needed to solve the problem so long as they have the height of the ball at the apex of its flight.

Cultural Relevance: This lesson is culturally relevant because baseball is widely played around the world, especially in Hispanic cultures like Mexico, Puerto Rico, Costa Rica, and especially in the Dominican Republic. Plus many students idolize baseball players in a way that they will like the opportunity to do extra research with certain players in them.

Standard from Another Content Area:
WA.EALR.5.4.1
Uses sources within the body of the work to support positions in a paper or presentation.

This standard will be used when students are finding extra information for the assignment.

Build a playground 7.G.B.6 and MP4

By: Kimberly Younger, Rachel Van Kopp, Lizzie Englehart and Naomi Johnson

This lesson is focused on a 7th grade standard CCSS.Math.Content.7.G.B.6 but could be used for 6th through 8th grade depending on the application. This lesson focuses on the use of formulas to find area and problem solving of a real-world problem with the use of technology.

The prompt is “The school district is building a new playground for the new elementary school down the road. They have hired Playgrounds R’ Us to build it, but the supervisor wants to know what students would want on a playground. Create a playground with the following requirements.”

The students are building on their knowledge of area and perimeter formulas and applying it to a problem. The students are given a square footage for the playground, they must use three or more different shapes to represent their equipment, and the total square footage of the equipment must cover 30% of the playground’s area or more.

The students are given a packet which includes direction, a rough draft grid paper, final draft grid paper (submitted for approval), a screen shot of their Geogebra playground and a write up about their playground.

Below is an example of the packet students received. (link to the packet)

Below is a student’s sample playground

Rough Draft Blueprint                                Final Draft Blueprint                               Geogebra Blueprint

Table for Blueprint

Extension for “Build a Playground”:

As an extension to this lesson, students will later be able to work with 3 dimensional figures and nets to build the playground they have constructed in our lesson. This lesson emphasized finding and working with area of various geometrical figures and special reasoning. Using the knowledge, they have gained through our lesson, the students will be able to create the net that would best fit the equipment shape that they have presented to us on their “blue prints”.

In order to create the appropriate net, students will need to understand that the 3-dimensional shapes base will be the shape they have placed on their map in the lesson “Build a Playground”. This extension will cover CCSS.math.content.7.g.b.6 which states “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.” This extension will help students make connections to the relationships between 2-dimensional figures and 3-dimensional figures, and connect the concepts of surface area and volume to real-world scenarios.

How to Prove Two Triangles are Similar G.CO

 

High School: Geometry I


Proving Geometric Theorems

By Emily Ivie

This learning progression was designed primarily for students who are in a traditional classroom
setting and have similar mathematical abilities. This class consists of 28 students, mainly
sophomores, who are studying geometry as part of their graduation requirement. The geometry
class has been designed to cover topics at a pace that meets the state requirements of content
topics in high school geometry. Since the class is set up on a semester system, the majority of the
students in this class have been a part of this class since the start of the school year and have had
the same exposure and background knowledge about geometry. Many students enjoy talking and
taking part in discussions during class, that is why I am going to teach this learning progression
in a student-lead conversation.

Standards:
The Common Core State Standards that will be satisfied are from the High School Geometry:
Congruence: Prove Geometric Theorems cluster. In the Congruence domain we will cover
CCSS.MATH.CONTENT.HSG.CO.C.9. Prove theorems about lines and angles and we will also
prove theorems about triangles and parallelograms with standards
CCSS.MATH.CONTENT.HSG.CO.C.10 and CCSS.MATH.CONTENT.HSG.CO.C.11. In this
course, students focus on mastering basic geometry knowledge that is required by the state, while
integrating in common core standards and mathematical practices. In this learning progression
the students will use four mathematical practices including: MP4, MP5, and MP7.
The curriculum these students are learning is based off the McDougal Littell: Geometry by
Larson, Boswell, and Stiff. This textbook is a resource used to design lectures, find worksheets,
and create practice problems through. The start to each class day will begin with a warm up
problem, followed with an introduction to a new topic with notes, classroom activity, and then
discussion. The notes are put up on the projector at the beginning of class so that students who
finish their warm up activity early can start writing the notes.

Accommodations:
Throughout the learning progression accommodations are made for students with IEPs and ELL
students. For the students who need a longer amount of time to write down their notes, they are
able to get the notes from me a day early so that they do not fall behind during lecture and are
able to participate in the discussion during note. Another accommodation made is that I let my 2
ELL students sit next to each other because they feel most comfortable working in partners this
way. In addition to these accommodations, the learning progression designed has activities that
are accessible to all learners. They do not require internet or any other tools beside from the
classroom whiteboards, pen, and paper.

Central Focus:
The central focus of this learning progression is for students to understand how specific theorems
about lines, triangles, and parallelograms were proved and how you can apply them. Students
will also have an understanding as to why it is important to know these theorems when applying
them to everyday life situations.

Lesson 1: Lines
We will start with an introduction to lines: parallel, transversal, and perpendicular. Since many of
the students have already had an introduction to this topic, it will be much easier to engage in a
class in student lead discussion when I ask them, “What does it mean for two lines to be parallel/
transversal/perpendicular?” This discussion of defining certain types of lines will begin to build
their mathematical thinking and conceptual understanding that they will use again during their
partner tasks. During the entry task students will demonstrate MP 7 looking for a way to identify
structure. After reviewing the entry task and understanding these definitions, I will give students
different geometric pictures and we will play a game of “I Spy”, students will be given colored
pencils and required to make a key. We will go around the class and identify specific types of
lines and angles. Once each student has identified and color marked one type of each line and
angle, I will show the students how to prove theorems about line angles. My example I will show
in class will be proving how vertical angle are congruent. I will ask students specific questions to
guide their learning such as: “What do we know about the lines and angles in this diagram? Are
their any linear pairs? What about supplementary?” These questions will formatively assess my
students knowledge about how well they conceptually understand how to identify lines and
angles. When students answer these questions, I will be looking for them to make the connection
between the next steps such as, “since we have angles that are linear pairs, we can use the linear
pair postulate.” This assessment will show students understanding of
CCSS.MATH.CONTENT.HSG.CO.C.9. proving theorems about lines and angles. After students
have worked through the vertical angle theorem, I will ask them to prove that alternate interior
angles are congruent. They will turn in their proof as part of their summative assessment. Once
looking at their proof, I will give feedback based on their reasoning and mathematical thinking.

Lesson 2: Triangles
My next activity will start with reminding my students about the properties of triangle. We will
be expanding our proof knowledge of triangles building off of the prior lesson where students
learned about proving lines and angles and we will try to prove properties about triangles. I will
work through one property about triangles and hold a discussion. After this, we will break up into
groups and I will give each group one theorem about triangles to solve. Then once enough time
has passed, each group will go up to the front board and give a presentation about the theorem
they proved. This lesson aligns with the following standard
CCSS.MATH.CONTENT.HSG.CO.C.10 proving theorems about triangles. Finally once groups
have put their proof up on the whiteboard, I will ask questions to assess their understanding such
as “What does this theorem tell us?”, “How can we apply this postulate to our problem?”, and
“Where do you start when proving this theorem?” These questions are important to ask students
to make sure that they are using tools (such as theorems) appropriately MP5. These
presentations will be a formative and summative assessment to make sure that students can
properly use the new information we just learned as well as explain their answers using old
vocabulary.

Lesson 3: Parallelograms
We will be expanding students understanding of proving line angles and triangles by introducing
parallelogram theorems. Ideally this lesson should be a fun activity that helps students with their
understanding of parallelogram proofs. Students will begin the lesson with a warm up in which
we will cover material learned in the previous day. Students will find a partner and share their
proof completed from the homework the night before. After we finish the entry task I plan to go
over the learning outcomes for the day, which is, students will be able to use their learned
understanding of parallelogram proofs. Shortly after that we will have a class discussion about
what a parallelogram is and I will encourage the use of specific vocabulary words like length,
adjacent, and angle. During our discussion I will hand out 4 parallelogram figures made from
construction paper to each student. We will go through each theorem about parallelograms:
labeling, folding, and drawing on each figure to show understanding for each theorem. Then I
will have the students take the time to try about write up their proofs of these theorems. While
the students working on folding there diagrams I will be walking around the classroom asking
questions about the theorems and how they proved the theorem. During this activity students will
achieve their learning target of CCSS.MATH.CONTENT.HSG.CO.C.11 and MP 4: “Model with
Mathematics” because students will use their parallelogram cuts outs to model their proofs.

Polygons and Parallelograms G.CO

High School Geometry: Polygons and Parallelograms

This learning progression will be taught at Ellensburg High School in a Geometry course. The students in the class this learning progression is being taught in are all good students. By that I mean each student is a diligent and hard worker. The course text is Geometry: Reasoning, Measuring, Applying by McDougal Littell. The learning progression covers sections 6.1-6.3, after which will be a summative assessment. Section 6.1 covers the basics of Polygons; what they are, definitions related to them, procedures for determining a figure is a polygon, and the different types of polygons. Section 6.2 covers the properties of parallelograms; related theorems and proofs. Section 6.3 covers the theorems and proof of parallelograms being quadrilaterals. I have planned to spend a single lesson on each section with another lesson afterward designated to a quiz. Below are the prior CCSS which have been covered that are related this learning progression:

Experiment with transformations in the plane

CCSS.MATH.CONTENT.HSG.CO.A.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Prove geometric theorems

CCSS.MATH.CONTENT.HSG.CO.C.9

Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Make geometric constructions

CCSS.MATH.CONTENT.HSG.CO.D.12

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

The students have mastered these concepts and CCSS through activities and tasks assigned in earlier learning progressions. Thus, the students are prepared and have the appropriate academic knowledge to begin learning CCSS.MATH.CONTENT.HSG.CO.C.11 which covers proving theorems about parallelograms. As I explain the tasks within the learning progression I will explain how the students’ prior academic knowledge was necessary; as well as, how the new concepts build off of the students’ prior knowledge will help them gain a deeper understanding of the new concepts. However, before beginning the explanation of the tasks and assessments I would first like to discuss my instructional strategies.

When teaching the learning progression I will use direct instruction and the use multi-media to communicate the learning targets, the concepts, and the directions for the tasks. The initial discussion will not provide examples. I want the students to struggle and make their own inquiries about how to solve the posed problems. I will then make use of grouping to have students work together on the tasks and make inquiries as a group or as an entire class. I will also allow students who have figured something out to travel to another group and share what they know after they first share with their own group (not a requirement though). This will work effectively because I know that my students are diligent workers and that they have proven they work well in groups. I also know that it will promote them to work together and share procedures and reasoning if I give them the opportunity to do so. Lastly, this learning progression will only include formative assessment except for the last quiz since all work will be done in groups and I want to assess discussion and inquiry not mathematical correctness. For the most part answers will be gone over as a whole class so students that I ca make sure all students have the correct solutions, procedures and reasoning to be studying.

Lesson 1: Polygons

The first lesson does not touch a CCSS but teaches the students the necessary prior-academic knowledge needed to learn HSG.CO.C.11. As stated above my lessons do not begin with lectures or examples of how to solve the related problems within the lesson’s tasks. I will begin this first lesson with some light-hearted dialogue with the students to ease them into a learning-mindset. Afterwards, I will hand out a worksheet which I created. I devised the worksheet so that once finished it can be used as a resource tool for studying and review. The worksheet has this prompt, “[d]irections: For the figures 1-13 state which figures are polygons and why. If it is a polygon name it based upon its number of sides and state whether it is concave or convex. Lastly, state whether or not the polygon is regular or not.” Attached to the worksheet is a sheet with 13 figures; some are polygons and some are not, some are concave polygons and some are convex polygons, and some are regular polygons.

How this activity will work is once I have handed it out students will be directed to tackle the first part of the prompt in their groups without help from me. Students have been working with polygons for quite a while but without me explicitly telling them that have been. Thus, it is my hope that through inquiry some of the students will be able to determine which figures are polygons and which are not. Then those students can share their reasoning with the class. If after about 2 minutes not students have made any progress I will pick a figure and state whether or not it is a polygon. Students will then have an example to go off of. By 4 minutes, whether students are finished or not, I will ask the class to quiet down and for any volunteers to share which they chose to be polygons or not to be polygons. Once all of the students had shared I will go over the definition of a polygon and then go through which are and are not on the worksheet. Just like how we as a class went through this part of the prompt so too will we with the other parts. By the end students will have helped each other create a resource tool with visual representations connected to descriptive details. Students will have examples to study and use as reference on homework problems. Which leads me to the last part of this lesson; a homework assignment which has students answering 5-10 questions picked from the section 6.1 of the text.

Lesson 2: Properties of Parallel Lines

As stated above students have gone over parallel lines and have also constructed parallel lines. Thus, I have decided to begin this lesson by having student construct a parallelogram without actually telling them that. I will direct them to construct two parallel lines on a sheet of paper and extend the lines across the whole sheet. Then I will direct students to create two more parallel lines that are not parallel to the other lines and also extend the lines across the whole sheet. Lastly, I will ask the students if any of them know what they had just created. Hopefully a student might know and share but if not I will explain what they created and how it relates to what we are in the lesson.

The next step in the lesson would be to direct students to discover any properties about the parallelogram they just created; for instance any congruent angles or sides, any supplementary angles, or the fact that their diagonals bisect each other. I will designate 10 minutes to this part of the lesson and while students are discovery the properties I will be walking from group to group posing specific questions to promote the right inquiries. Once those 10 minutes are over I will present the 4 related theorems and ask the students how many of the 4 theorems they discovered and make a tally up on the board (a little competition never hurt). I will then go over two examples of how to use these properties to solve proofs relating parallelograms. The end of the lesson would be designated to their homework assignment which would incorporate basic problems from section 6.2 and 2 hand-made, two-column proofs. Students would only have in-class time for their homework if as a class we went through the example proofs in the time allotted for it.

Lesson 3: Proving Quadrilaterals are Parallelograms

This lesson will be set up exactly the same as the second but with a different introduction. Since the students have already constructed a parallelogram there is no sense in repeating that. Instead, I will open the lesson with this question, “[w]hat are the properties of a quadrilateral?” I will give students some time to discuss this. After a while, 2-3 minutes or so, I will ask students to volunteer what their group concluded the properties of a quadrilateral are. After all of the students have shared what they wanted to I would then go over the properties of a quadrilateral and reference to the properties of a parallelogram we went over the day before. Students should be starting to make the connections in their head that these properties are the same or share similarities. To finish the introductory I would ask the students if a parallelogram is a quadrilateral. Hopefully I would get a volunteer to share their reasoning thus creating a discussion. If not I would lead a discussion as to why it is a quadrilateral. Then as I said before the rest of the lesson would follow the same structure as the one before.

Quiz

            All of the assignments, tasks, and activities in the lesson were solely graded upon participation and completion. This is because I always gave the students the answers to the in-class activities at the end which meant I graded only the students’ participation in discussions and group work. The homework assignments were only graded on completion and not correctness because I wanted to promote students to at least provide work for a problem even if they thought they could not do it. A student who does not think they can solve a problem won’t even start it but if completion is the only grade then they will at the least attempt it. Therefore, I have decided to give a quiz half way through chapter 6 so that the students and I have an accurate measure of the conceptual and procedural understanding and reasoning skill that should have been learned in section 6.1-6.3. This assessment will help me determine whether or not the students are ready to move on and it will help the students self-reflect on what they have learned and plan out what they still need to.

HSG.CO.A.5 Transformations

This learning progression focuses on the first half of a unit on Transformations in a high school Geometry class, consisting of mostly 9th and 10th graders. The first lesson will cover 7.1 Rigid Motion in a Plane, which will just briefly introduce the concepts of transformations and what each transformation means. The second lesson will cover 7.2 Reflections, and will give students a more in depth understanding of reflections, and how to use them to find coordinates in a plane. The third lesson covers 7.3 Rotations more in depth, and then for the final lesson in the learning progression, students will have a review to make sure they understand these concepts before moving on to the second half of the chapter.

 

CCSS Content Standards:

CCSS.MATH.CONTENT.HSG.CO.A.5

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g. graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

 

CCSS Mathematical Practice Standards:

CCSS.MATH.PRACTICE.MP1

Make sense of problems and perservere in solving them.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6

Attend to precision.

 

Throughout this learning progression, students will be getting new notes in the first three lessons, while also working on practice problems and homework assignments in every lesson. I will be implementing a lot of group work during this learning progression, because it is helpful for students to compare their answers with peers so that they can work together to figure out the correct answers. For the last lesson, they will do an activity for the review, where they are put in groups, and rotating through different stations that will be focusing on the main ideas from each concept. I will be giving them entry tasks daily as their formative assessments in this learning progression to check their understanding, along with checking their homework assignments, and going over the most missed problems so that they can see common errors.

The full learning progression is attached here: edTPA Learning Progression

Art from a Different Angle 7.G.B.5


This math problem is one in which students are using their knowledge of different kinds of angles (supplementary, complimentary, vertical, adjacent) to find as many angles as they can within some sort of abstract art.

The main idea is to locate as many angles of each time as they can within the art-piece, as well as give reasoning in written form of how they know they are correct, based on the different laws of angles and not just a protractor.  Students can also be expected to identify patterns during discussions as well as in written forms, and can present their arguments to the class.  Students can be given various samples of art to work with, and be separated into groups, so that at the end of the lesson the groups can present their art and which angles they found and where.

This lesson is an integration of math into art, and a great way for students to explore how math really is a part of more than most would believe.  This lesson could also lead into the idea that there are different kinds of math within all art, and students could begin trying to identify the various mathematics involved in art and widen their understanding of mathematics in the real world.

CCSS.MATH.CONTENT.7.G.B.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP6 Attend to precision.

CCSS.ELA-LITERACY.W.7.1.B
Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.

7.G.B.6 Volume and Surface of 3D figures

poolpool-2

Who would not like to have a swim in this pool? This is the biggest pool in the world with  1,013 meters in length and a total area of 19.77 acres and it is located in a resort in Algarrobo, Chile. Can you imagine how much water does this pool holds? How will you find out?

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.

Using pictures to explain and illustrate concepts help students connect those concepts from the classroom to the real world and develop higher thinking skills. In the case of this pool, volume and surface area are some of the concepts that students can learn. By showing students an “useful and fun” use of this concepts, students will develop a different thought process and connect their thinking into answering the question, how much water does this pool holds?

By challenging students to think how to answer this question, given that the pool is an irregular shape, before the concepts are introduced will help the students to start developing a thought process that go beyond the use of formulas to find the surface area/volume of prisms .

GMD.B.4-Play Time with Play-Doh

play-doh

There is something very therapeutic about playing with play-dough. All children of all ages whether they admit it or not enjoy playing with play-dough and what better than to incorporate it into learning math. Using playdough in a subject that stresses many students can be very beneficial and making visualizing math concepts making the problems easier to approach.

For example, given the high school geometry standard:

CCSS.MATH.CONTENT.HSG.GMD.A.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
We can work on solving problems like:                           play-dough-diagram
Given that the radius of a sphere of play-dough is 8 cm.
If the cylinder it needs to fit into is only 6 cm, what is the minimum height the cylinder must be in order to fit all the play-dough inside of it?

 

Allowing students first to try the problem hands on will work on engaging the students and with the visualization solving the problems will become less of a stressful situation. And from this, we can create other similar problems in which the shapes the problem works with changes. Such as what could change if we had a pyramid shape of play-dough that needed to fit into a cone shape container.

ƨnoiƚɔɘlʇɘЯ : Reflections

flying-air-ballons-reflections

Can You See It : ƚI ɘɘƧ uoY nɒƆ

This learning progression will be taught in a 10th grade High School Geometry classroom and the following three Common Core State Standards will be used as goals: HSG.CO.A.3, HSG.CO.A.4 and HSG.CO.A.5. Additionally, the mathematical practices that align with this learning progression are the following: MP5 Use appropriate tools strategically, MP7 Look for and make use of structure, and MP8 Look for and express regularity in repeated reasoning. The textbook this class uses is CORD Geometry 1 Learning in Context 4th edition. Specifically, I will be using chapter 4 on polynomials and factors.

Pyramid
Students have previously been introduced to patterns and relationships between two things. For example, in previous classes they have discussed series of geometric functions and more recently similarities in triangles. Specifically, students have worked with distances on the coordinate plane is relation to the origin and a point and how this constant equidistance moved around the origin would rotate a point which was a topic discussed in chapter 3. In this learning progression students will be once again looking at these rotations of points with the larger and focused picture of rotations, reflections, and translations of various geometric figures. The first skill and portion of this lesson will be to examine how to manipulate an object/shape on the coordinate plane through reflections that will maintain its original form. The various reflections, which will depend on the geometric object used at the time, will include over the y-axis, x-axis, y=x and y= -x. The students will practice this process with a variety of shapes and discover which shapes can or cannot use one of the above mentioned reflections. For example, a square can be both reflected across the y= x and y= -x, but a rectangle cannot. The second lesson will then discuss rotations of the same geometric objects and once again help students investigate which rotations certain shapes can and cannot rotated x number of degrees. The third lesson in this progression will be to consider translations of objects so as to still maintain shape, size, and angles. The third lesson will also help clarify the previous topics with practice with all of the movements as well as help students understand notation for the actions, like T(2, 3) referring to a translation of all vertices of an object to the right by 2 and vertically by 3.

Thus, this learning progressions is all about helping students see both with physical pictures and in their minds eye the mirrors, rotations, and translations found everywhere in mathematics and life. As can bee seen from the pictures above reflections are as common as looking into a pool of water. Therefore, modeling such actions with mathematics can help students understand its importance to our everyday life and aspiring to teach this beautiful concept as a guided lesson and at a pace that will not overwhelm any of our students.

High School Geometry 1 Learning Progression edTPA

edTPA Reflections Worksheet

Lesson Plan Transformations_Reflections