wordpress.clarku.edu file · Web viewTitle and brief description: Give a title and short description. What, briefly, will students be doing in this unit of study? (2-3 sentences)

Hayley CunninghamGeometry CUP

“Two-dimensional figures”

I. Title and brief description : Give a title and short description. What, briefly, will students be doing in this unit of study? (2-3 sentences)

Students will engage in a variety of activities to learn the various properties of two-

dimensional figures. Students will then use this knowledge to learn how to identify and classify

two-dimensional geometric figures.

II. Big Idea/Essential Question : Explain your “big idea” and/or essential question.

This unit revolves around two-dimensional figures. Throughout this unit students will

focus on answering two essential questions: 1.How can you draw and identify lines and angles?

2. How can you can you classify shapes? Students will be expected to draw and identify lines,

line segments, rays, acute, obtuse, and right angles, and parallel, perpendicular, and intersecting

lines. Additionally, students will take away an understanding that geometric figures (our focus

will be on triangles and quadrilaterals) can be analyzed and classified based on their properties,

such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

III. Learning Goals : Explain what learning goals you have set for students’ investigation of the big idea/essential question. Consider the following areas:

a. Development of content understanding (key concepts and ideas) Students will be able to identify, draw and define:

o Point: an exact location in space.o Line: a straight path of points that continues without end in both

directions.o Line segment: part of a line between two endpoints.o Ray: a part of a line that has one endpoint and continues without end in

one direction.o Angle: formed by two rays or line segments that have the same endpoint.

The shared endpoint is called the vertex.o Intersecting lines: lines in a plane that cross at exactly one point.

Intersecting lines form four angles.o Parallel lines: lines in a plane that are always the same distance apart.

Parallel lines never intersecto Perpendicular lines: lines in a plane that intersect to form four right

angleso Acute angle: an angle that is smaller than a right angle (less than 90

degrees)

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o Obtuse angle: an angle that is greater than a right angle (more than 90 degrees, but less than 180 degrees)

o Right angle: forms a small square corner (measures 90 degrees)o Straight angle: a straight line (measures 180 degrees)o Quadrilateral: a polygon with 4 sides and 4 verticeso Square: a quadrilateral with sides are the same length, 4 right angleso Rectangle: a quadrilateral in which opposite sides are parallel and the

same length, 4 right angleso Parallelogram: a quadrilateral with two pairs of parallel sideso Rhombus: a quadrilateral with 2 pairs of parallel sides, all sides are the

same length o Trapezoid: a quadrilateral with 1 pair of parallel lineso Symmetrical: when a shape has symmetry; when you can fold it and it

has matching partso Asymmetrical: when a shape has no symmetryo Right triangle: a triangle with one right angleo Acute triangle: a triangle with three acute angleso Obtuse triangle: a triangle with one obtuse angleo Equilateral triangle: a triangle with 3 equal sideso Isosceles triangle: a triangle with 2 equal sideso Scalene triangle: a triangle with no equal sides

Students will be able to draw and label figures. Students will be able to label a figure using symbols. Students will be able to use kinesthetic movement to help enhance

understanding/recall of vocabulary words. Students will be able to work collaboratively to complete a review packet. Students will be able to monitor understanding and ask clarifying questions. Students will be able to classify triangles by angles and number of sides. Students will be able to classify the different types of quadrilaterals. Students will be able to explain that symmetry is when an image can be folded

along a line into two matching halves. Students will be able to classify geometric shapes as symmetrical or

asymmetrical. Students will be able to define line of symmetry as the line that cuts an image

exactly in half horizontally, vertically or diagonally. Students will be able to draw a line of symmetry.

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b. Enabling students to experience the power of their minds and their capacities as learners and doers (powerful learning)

This unit will enable students to experience the power of their minds by asking students

to embody the role of mathematician and become thinkers, collaborators, and problem solvers.

They will become creators of their own knowledge through hands-on, minds-on thinking.

Students will be immersed in challenging thinking that culminates in intellectually, challenging

content understanding. Students will get the opportunity to engage in a learning experience that

invites individuals to construct and negotiate deep conceptual understanding. With the support of

the classroom community, learners can meet more strenuous challenges than they might succeed

at alone. Within this unit, students will have multiple opportunities to engage in peer

collaboration and substantive discourse. Through various sorting activities and worksheets,

students will be encouraged to use their minds and work together to determine how to classify

various polygons. Students will compare solutions and explain thinking to one another. This type

of learning is powerful as discourse promotes thinking, builds community and invites

metacognition. Discourse is a life skill and math is a wonderful opportunity for the listening,

critical thinking, and cooperation that discourse requires.

c. Development of intellectual and academic habits of mind, work, and discourse, including habits of independent or collaborative thinking and doing typical of readers, writers, speakers, creators, researchers and thinkers in the discipline (ways of knowing)

This unit will develop academic habits of mind primarily by asking students to take on the

role of a mathematician. It is the mathematician’s role to analyze and utilize given information to

problem-solve, come up with a solution, and interconnect mathematical ideas and patterns. As

mathematicians, students will utilize critical thinking strategies throughout various sorting

activities. Students will need to extend their knowledge of the various properties of two-

dimensional geometric figures to creating classifications of polygons. Throughout this process,

students will be asked to monitor understanding and ask clarifying questions. Students will have

opportunities to work as a whole-class, in small groups, in pairs, and individually to help aid in

their production of knowledge. Students will be asked to read and write as mathematicians do.

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For instance, students will be asked to be able to use the correct symbolic notation to identify

lines, rays, segments, parallel, perpendicular, and intersecting lines, acute, right, and obtuse

angles and be able to use this notation interchangeably- being able to create it and read it to

identify a property in a figure.

d. Literacy development, including capabilities of proficient readers, writers, and speakers

Students will develop primarily as speakers throughout this unit. Students will have

multiple opportunities for substantive talk. Students will be asked to engage in a range of

collaborative discussion and be expected to express the ideas of themselves and others clearly.

Students will develop as readers by being asked to read a math problem, and determine what the

question is asking and create an appropriate pathway to solve it. Students will also engage in an

interactive read aloud and see how literacy can develop in math. Students will develop as

mathematical writers in this unit by being asked to write solutions to math problems. Students

will be asked to write math with symbols and notations. Students will need to explain their

thinking and reasoning in words.

e. Development of trust and the classroom as a learning community

This classroom will continue its development of trust, as students will engage in

collaborative work. Students will be expected to actively listen to one another’s ideas and extend

thinking through discussion. Students will be offered a comfortable space to share student

thinking. Students will be encouraged to share their ideas, which fosters student valuing and

becoming understanding of different perspectives. Students will also be reminded of their talk

moves, such as the appropriate means to agree or disagree with someone else’s opinion.

Furthermore, working as a whole class also serves to foster community building in our

classroom. Our classroom dynamic is already set up in a way where students are encouraged to

collaboratively work as well as engage in classroom discussions. It is an opportunity for students

to reflect, question and monitor their understanding. Students are well aware on how to be good

listeners and respect one another’s ideas. Students will get to practice this throughout the unit

and further extended our classroom community building.

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IV. Personal, social, and cultural factors (yourself, your students, and learning) a. What assumptions are you making about why your plan will connect to your

Main South students? How are you taking into account any differences in your socioeconomic, cultural, or racial background, gender, personality, approach to learning, or view of the world?

Math exists all around us whether we see it or not. Math affects everyone regardless of

socioeconomic status, cultural affiliations, racial background, gender, or personality. Throughout

this unit, students will learn to see and appreciate the math that exists around us. In

accomplishing this, I will utilize the various learning styles, academic capabilities and

personalities of my students to create a unit that is accessible and comprehensible to each

student.

b. How are you activating your students’ personal, social, and cultural capabilities and capacities in this plan?

I am taking measures to make this learning authentic to show students how to extend our

math concepts into daily life. For one, students will have the opportunity to identify parallel,

perpendicular, and intersecting lines in a map of the Main South area. Students will also be given

the opportunity to identify these features as well as the angles and symmetry that surround them

each day. Finally, students will be given the opportunity to find geometry in their name giving

them more of a personal connection with the content.

V. Rationale : Your rationale should show clearly your careful consideration of a full range of factors in planning your unit to ensure equitable support and meaningful, authentic, and substantial learning for all students, taking into account:

a. Learning goals : Explain why your big idea/essential question and your learning goals are important for your discipline and meaningful for your students.

Learning about the properties of two-dimensional figures and using those properties to

classify geometric figures is essential for students to know. Students will extend some of the

knowledge in this lesson, such as acute, right, and obtuse angles in our next math unit on

measuring angles. Being able to identify whether an angle is acute right or obtuse is foundational

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and will be a good resource to help students when they are using protractors and determining the

measure of an angle. Additionally, this unit is foundational, as students will extend this

knowledge in later grades to analyzing and classifying three-dimensional figures.

b. Curriculum standards : Explain how the big idea/essential question connects to the Guiding Principles in the MA curriculum frameworks. Identify which learning standards are addressed and how.

4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.-In the first 3 lessons, by means of a variety of activities, fluency drills and worksheets, students will learn how to draw and identify and label all these various properties in two-dimensional figures.

4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presences or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.- Students will have practice identifying and classifying triangles and quadrilaterals based on their geometric properties in lessons 4-8.

4.G.A.3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.-In the final lesson, through a read-aloud, use of manipulatives, and group work, students will learn how to recognize and draw a line of symmetry in a geometric figure and classify a shape as symmetrical or asymmetrical.

CCSS.ELA-LITERACY.SL.4.1Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others' ideas and expressing their own clearly.

CCSS.ELA-LITERACY.SL.4.1.ACome to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.

CCSS.ELA-LITERACY.SL.4.1.BFollow agreed-upon rules for discussions and carry out assigned roles.

CCSS.ELA-LITERACY.SL.4.1.CPose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others.

CCSS.ELA-LITERACY.SL.4.1.DReview the key ideas expressed and explain their own ideas and understanding in light of the discussion.

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- Students will engage in a range of collaborative discussions throughout the entirety of this unit.

Mathematical Practice Standards:

MP3 Construct viable arguments and critique the reasoning of others-Throughout every lesson, students will engage in substantive discussion and be able to create arguments with claims to support their reasoning and be able to reason to critique the reasoning of others.

MP4 Model with mathematics- Students will be able to show their thinking using appropriate models, labels and notation. They should be able to utilize many different ways to show their learning.

MP5 Use appropriate tools strategically-The end of this unit will have exposed students exposed to a variety of math tools, such as using a right angle template (in the form of a post-it note), using a straight edge to construct lines, and using manipulatives in the form of cut out geometric figures, specifically triangles and quadrilaterals. Students will be able to use these tools and be able to explain why they chose them.

MP6 Attend to Precision-In this unit, students are introduced to the terms point, line, line segment, ray, angle, right angle, acute angle, obtuse angle, and straight angle.

Students must distinguish between endpoints and arrows to identify and describe lines, line segments, and rays. Students learn that while a line and line segment can be names in two ways, a ray can be named in only one way. Students learn that two rays that have a common endpoint form an angle. An angle can be named by its vertex or by using three points, with the vertex being the second point named.

Students will need to develop the understanding of how intersecting and perpendicular lines are the same and different. Need to explain that both types of lines cross at one point, forming 4 angles. Only perpendicular lines form 4 angles that are right angles.

By understanding and using precise definitions, students can communicate their mathematical reasoning clearly.

MP7 Look for and make use of structure.-Students will be expected to use what they know about geometric math properties to solve new problems, in the class of this unit, the identification and classification of geometric figures based on properties.

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c. Students’ backgrounds and readiness : What strengths, capacities, and interests, in terms of their content understanding (prior knowledge), academic and literacy development, personal and cultural abilities, and development as a learning community, are you taking into account in planning this unit?

Throughout the year students have been creating anchor charts in their learning logs and

using those anchor charts are reference. As this unit is heavily focused on vocabulary

development, I am planning on utilizing this technique to help my students and give them a

reference tool. Additionally, we will utilize a word wall and multiple larger anchor charts that

will hang on the walls of the classroom to serve as resources for students throughout the unit.

In terms of prior knowledge, I am aware that some of my students have been exposed to

acute, right, and obtuse angles in 3rd grade. I’m not sure how in depth their math unit on these

terms was, but I do know that many students are eager to revisit them.

d. Student needs : What particular needs of your students—academic, social, personal, language (ELLs)—have you taken into account in planning the unit?

Throughout this unit I tried to meet the needs of diverse learners on a variety of different

levels. For instance, I tried to incorporate activities that reached out to the various types of

learners present in my classroom: verbal, auditory, visual, kinesthetic, social, solitary and

reading/ writing learners. Each learning type responds best to a different method of teaching. For

my visual learners who prefer to see info, I relied heavily on drawing images and figures as well

as on Brain Pop videos. For my auditory learners who prefer to hear information rather than

reading it or seeing it visually, I tried to implemented lectures, discussions, peer collaboration,

and Brain Pop videos. For my verbal learners who need to use word in speech and writing to

understand a concept, I utilized peer collaboration and turn and talks. For my reading/writing

learners who learn best when interacting with text, I utilized anchor charts where students filled

in and read definitions. For my social learners, I employed peer collaboration (as

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aforementioned) in the form of sorting activities and in worksheets. Finally, for my kinesthetic

leaners who learn best using sense of movement and touch to learn, I used cut out of shapes to

help demonstrate concepts. I also implemented a Simon Says kinesthetic movement game for

these students to learn the concepts and vocabulary. Overall my unit was set up to accommodate

a variety of learners and to support what Gibbons deems as “high support and high challenge”.

For my lower ELL students this unit is challenging but contains a support that caters to their

personal learning style to enable them to access the content in the least restrictive environment.

Overall, I hope to foster an environment with a low affective filter (Krashen) to give students the

confidence to participate in the content.

e. Research- and evidence-based best practice ideas : Explain how research and best practice ideas have informed your plan.

After reading research from Pauline Gibbons, I differentiated my design to provide a

variety of means for students to access the content. The students in my classroom have very

distinct ways of learning and of extracting information. I needed to provide different means for

students to understand the concept presented in this study of two-dimensional figures. It is my

job to provide modifications to meet the needs of students in terms of learning styles and

preferences. My goal was to reach distinct types of learners when introducing our unit of study

while at the same time giving them the support needed to make this unit more comprehensible

(Gibbons, 133) and optimizing the learning potential of all students.

One means of to optimize the learning potential for all students came in the form of peer

collaboration. According to Christine Moynihan, student collaboration is paramount as it serves

to not only have students view themselves as learners, but also as teachers. Students learn that

having two (or more) minds come together will allow students to come into the zone of proximal

development (Vygotsky), thus enhancing individual learning (Math Sense 64). They may be able

to problem solve in a manner which they couldn’t reach if they were working alone.

Furthermore, according to Koch, author of Science Stories: Science Methods for

Elementary and Middle School Teachers, “Extensive research has been done on cooperative

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learning, which can be defined as students working together in groups to accomplish shared

learning goals. Studies have shown both social and educational benefits from cooperative

learning” (329). A cooperative learning environment helps students build conceptual knowledge

while at the same time fostering classroom climate. Students in my class excel in peer

collaboration hence building up our classroom community. Based on this evidence, while

creating this unit, I provided ample opportunities for students to work collaboratively in pairs, in

small groups, and as a whole-class.

Students will also be benefitted in this unit by having more opportunities to engage in

substantive conversation. According to Pauline Gibbons, students need to engage in substantive

conversation. That is, they need to be involved in extended talk around big ideas. The process of

taking part in substantive conversations leads to an increased understanding of subject content,

since it creates space for students to explore new ideas, clarify their understandings, initiate

questions, and make their reasoning visible to peers (Gibbons 25). Not only are students

developing content understanding, but also they are developing language skills. This unit is

heavy on mathematical vocabulary. Students are introduced to a variety of new terminology and

math concepts. The opportunity for extended talk allows students a chance to practice vocabulary

and grammar and enhance their language development.

VI. Assessments : It is essential for both you and your students that your formative and culminating assessments clearly show the extent to which students have achieved learning goals.

a. Explain your main assessments and why they are appropriate for your learning goals.

The primary assessment in this unit comes in the form of a pre-test and a post-test.

Students will be given a pre-test prior to instruction. Once instruction is completed, students will

be given a post-test. I will able to use the pre and posttest to assess gains in student development

and knowledge. I will be able to compare data and be able to see with concepts students

understood and struggled with. Overall this form of assessment is paramount, as it will give me

insight as to whether students met my learning goals or not.

Throughout the unit students will also have many minor assessments that come in the

form of worksheets and homework. This will allow me to track progress throughout the unit and

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give me insight into what concepts students are struggling with and what concepts they are

confident in. It will allow me to adapt my instruction to meet the needs of my students.

b. How will students know what to expect and the criteria for good work?

Students will know expectations, as we will discuss the objective for the lesson prior to

beginning each lesson. It will also be posted in our weekly objective under the math category.

c. How will students and parents learn about students’ overall academic progress from these assessments?

Parents will learn about student’s academic progress in progress/report cards and also

through communication with the agenda. I will also be willing to share information with parents

that I see at arrival. Students will also get to bring home all completed work at the end of the

unit.

VII. Unit Calendar a. Provide a calendar of key learning activities, learning strategies, and

assessments for your anticipated timeframe for the unit.Teacher Will Student Will Assessment

LAP 1“How to identify and draw points, lines, line segments, rays, and angles”.

DAY 1

Tell class that today we’re going to begin a new unit on geometry.

Turn & Talk: What is geometry?

Discuss the definition of geometry as the study of points, lines, shapes & space.

Show pictures of a polygon (triangle, quadrilateral, pentagon, hexagon, heptagon/septagon, octagon, nonagon, and decagon) one by one.

Turn & Talk with a partner about what geometry is.

Actively listen, ask clarifying questions, monitor understanding

(f): Whiteboard activity, anchor chart, Go Math problems, homework(i): Turn & Talk, active participation, engagement, ability to remain on task

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Ask students how many sides the polygon has.Ask students how many vertices the polygon has.Ask student to find the pattern.

Facilitate Whiteboard Activity

Model filling out anchor chart: define, draw a picture, read it, and write it sections for point, line, line segment, & ray. Complete one-by-one with wait time in between for student questions.

Guide students through question 1 while modeling on Elmo.Ask for questions.

Ask students to work together to complete number 2

Distribute Engage NY worksheet for homework

Raise hand and respond

Follow along with activity, ask clarifying questions, and monitor understanding.

Copy down definition, ask clarifying questions

Cut out & paste in learning log

Monitor understanding, ask questions

Work independently or with a partner to complete number 2.

Ask questions on homework

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DAY 2

Play Brain Pop JR: Points, lines, segments, rays.

Ask students to draw: a line, a line

segment, a ray, an angle, a point

Ask students to identify each of the following drawings: a line, a line

segment, a ray, an angle, a point

Ask students to write the name and write the symbol for the following figures that are drawn: Line AB/BA Ray AG* Line segment

FG/GA Ray HI

After each problem, go over as a whole-class and discuss the characteristics.

*Re-stress the importance of only reading a ray starting at the endpoint!

Guide students through Go Math p.551 #1, 2, 5, 7, 10, 12, 13 andPg.552 #20

Write homework problems on Elmo

DAY 2

Watch video

Engage in activityAsk clarifying questions

Work through Go Math problems, monitor understanding, ask clarifying questions

Copy down homework problems

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and project to board:

Draw the figure:1. Line FG2. Ray HI3. Line Segment

FG4. Point A5. Line JK

Name the figure*:6. Line LM/ML7. Line Segment

NO/ON8. Ray PQ9. Point B10. Ray RS

*These were drawn for students, they were to look at the figure and identify it using appropriate notation.

LAP 2“Parallel and perpendicular, and intersecting lines”

Play Brain Pop JR. Points, lines, segments and rays

Model filling out anchor chart: define, draw a picture, read it, and write it sections for parallel lines, intersecting lines, and perpendicular lines. Complete one-by-one with wait time in between for student questions.

Discuss the definitions in depth and ask if there are

Rewatch the Brain POP JR video from the previous day focusing on parallel, intersecting, and perpendicular lines.


Cut out & paste in learning log

(f): Anchor chart, in-class worksheet(i): active participation, engagement, ability to remain on task

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questions.

Distribute worksheets to class.

For each of the following figures ask students to identify parallel lines. Provide wait time. Highlight answers. Write the notation on the side using the correct symbols. *

Do the same thing a second time, but instead of searching for parallel lines, search for perpendicular lines.

Project printout of the streets in Main South Worcester

Ask students to look for parallel, perpendicular, & intersecting lines.

Work through the worksheet as a whole class to identify parallel lines and perpendicular lines.

Ask questionsMonitor understanding.

Look for parallel, perpendicular, and intersecting lines in a map.

LAP 3“Mid-unit Review”

Teach a Simon Says review game using the movements of point, ray, line, line segment, intersecting lines, perpendicular lines, and parallel lines.

Distribute review worksheets for students to work through to practice the concepts they’ve

Learn movementsAsk questionsEnjoy the game

Work in pairs to complete worksheet;Ask questions

(f): review worksheet(i): Simon Says game, active participation, engagement, ability to remain on task

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learned.

Filter through room answering questions and probing student thinking.

LAP 4

“Identifying angles”

Review Hand movements

Facilitate Game

Model filling out anchor chart: define, draw a picture, read it, and write it sections for straight angle, acute angle, right angle, and obtuse angle. Complete one-by-one with wait time in between for student questions.

Creating new movements to go along with our angles.

Distribute worksheet- Asks students to determine if the figure has an angle less than, equal to, or more than a right angle.

Distribute post-it notes for students to use to compare angles to a right angle.

Distribute Engage NY Worksheet

Participate in Simon Says game, have good sportsmanship


Learn movements; ask questions

Work through worksheet; engage, ask questions

Ask questions on homework

(f): anchor chart, in-class worksheet, homework(i): Simon Says game, active participation, engagement, ability to remain on task

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LAP 5

“Finding geometry in your name”

Remind students the movements, including the new movements we create the previous class

Facilitate game

Ask students a variety of questions either asking them to draw or identify a straight, obtuse, right or acute angle

Explain that students are going to be looking for geometry in their names; lines, line segments, rays, and angles.

Show model using first name.

Distribute Paper

Participate in Simon Says game

Engage in whiteboard fluency drill,Ask questions, monitor understanding

Write first name in capital letters on blank paper.

Find geometry in name and either label or make a key to make it easier for the reader to understand.

(f): Finding geometry in your name final product(i): active participation, engagement, ability to remain on task

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LAP 6

“Classifying Triangles”

Conduct line, ray and angle Simon says game.

Pass out packets

Facilitate Discussion:How did you and your partner classify the pack of triangles? Why did you classify them that way?

Show Brain Pop Video on classifying triangles; ask follow up questions

Facilitate sorting as a whole-class

Prompt students to fill in their anchor charts; guide them through while answering questions

Distribute Classify Triangles Worksheet

Respond with movement when teacher says: “Simon says make a (ray, line, line segment, parallel line, perpendicular line, intersecting line, acute, obtuse, and right angle.

In pairs, observe triangles and classify them into categories

Participate in whole-class discussion; be actively engaged; remain on task

Watch Brain Pop video on classifying triangles, ask questions

Students will engage in a whole-class sorting activity; students will classify triangles*

Fill in anchor chart based on the model; cut out & glue into math learning log.

Ask questions about homework if needed

(f): sorting activity, anchor chart, homework(i): Simon Says game, active participation, engagement, ability to remain on task

LAP 7“Classifying Quadrilaterals”

Pick a number of the day.

Filter through the room aiding students.

Pick student checkers.

Distribute cut out of quadrilaterals

Work on answering number of the day in learning log

Students work in pairs to classify triangles based

(f): Sorting activity, Go Math problems, homework(i): active participation, engagement, ability to remain on task

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Facilitate discussion on quadrilaterals while modeling how to fill in anchor chart

Guide students through Go Math 568-571 (dependent on time)

Distribute Quadrilateral Worksheet

on properties; try to find the attributes of each quadrilateral and recordFill in anchor chart according to classroom model, cut out and paste in learning log

Work in Go Math Book,Participate,Monitor understanding,Ask questions

Ask questions if needed

LAP 8“Symmetry”

Put students in pairsDistribute Packets

Ask students to take out the square rugs and examine thing.

Facilitate discussion: What do you notice about the rugs?

Interactive read aloud of Seeing Symmetry by Loreen Leedy

Introduce the terms symmetrical and asymmetrical.

Find one other person to work with.

Examine the rugs

Participate in discussion

Actively listenParticipate when askedMonitor Understanding

Participate in whole-class discussion; be actively engaged; remain on task, monitor understanding, ask questions.

(f): sorting activity, ABC sheet(i): active participation, engagement, ability to remain on task

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“Say symmetrical” x3

Explain: a shape is symmetrical when it has matching parts when you fold it.

Explain that the fold is called the line of symmetry.

“Say asymmetrical” x3

Explain: When a shape has no symmetry it is called asymmetrical.

Tell students that they will be working with their partner to classify shapes as symmetrical or asymmetrical.

Model on shape, showing how to fold.

Give students time to look at shapes and manipulate them to determine whether or not they have symmetry.

Facilitate sorting as a whole-class: Hold up a shape Ask if it’s

symmetrical or asymmetrical

If symmetrical, ask if the line of symmetry is

Actively listen and participate; monitor understanding, ask questions

Sort pieces with partner

Participate in sorting shapes into symmetrical and asymmetrical categories

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horizontal, vertical or diagonal

Distribute worksheets with the alphabet.

Ask students to draw lines of symmetry for each letter (Demonstrate how to draw the line of symmetry)

Draw lines of symmetry for each letter of the alphabet, ask questions, monitor understanding

b. Explain your sequence of activities—why does this particular order make sense in light of your learning goals and rationale for the unit?

This unit focuses on two-dimensional figures. In the first half of this unit, students will

focus on drawing and identifying lines, line segments, rays, right angles, obtuse angles, acute

angles, parallel lines, perpendicular lines and intersecting lines. In the second half of the unit

students will use these properties to analyze and classify geometric figures. Overall, learning

how to identify the properties of geometric figures and shapes is paramount for students to be

able to classify them.

VIII. Family and Community Involvement : a) Are there possible ways for you to actively involve parents in their child’s academic

activities and performance, and communicate clearly with them?

Parents will learn about student’s academic progress in progress/report cards and also

through communication with the agenda. Students will be given homework assignments that will

be written in the planner. Additionally, any incomplete assignments will be sent home for

homework with a note to the guardian. Finally, all completed work will be sent home at the end

of the unit.

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b) Are there possible resources—such as guest presenters, A/V, field trips, and material artifacts—from colleagues, families, and the community for you to draw on to enhance learning?

ResourcesGrade 4 Go Math Teacher Guide & Student Workbook 2

Chapter 10Engage NY: Angle Measure and Plane Figures

Module A (Lines and Angles) B (Angle Measurement)

SuperTeacherWorksheets.com for various worksheets

BooksSeeing Symmetry- Loreen Leedy

IX. Post-Teaching Reflection Based on your culminating and other assessments of learning goals, analyze the extent to which students achieved your learning goals. To what extent did different students achieve the learning goals? What do you learn from differences in performance, or puzzling student

performances (hard for you to explain), about the particular challenges of learning in this unit?

What do you learn from differences in performance about the effectiveness of your planning for the needs of different students?

What would you change to improve this plan and why?

Overall, I think this unit was a success. By the end of this unit, students were able to

identify the properties of two-dimensional figures and were able to take away an understanding

that geometric figures can be analyzed and classified based on their properties. On the pre-test

for this unit, the average test score was 7% with a range of 36 points. On the post-test for this

unit, the average grade was 69% with a range of 82 points (see appendix for data). 100% of

students made growth with the average growth being 62 points. Students significantly improved

and demonstrated an increase in content knowledge throughout this unit.

Two students who showed the most growth were Sebastian Delgado and Diana (see

student samples). Both Sebastian and Diana received a zero on their pre-test, but consistently

worked hard during the unit. Both students were active agents in creating their own knowledge.

They were able to monitor their understanding and ask for help whenever needed throughout the

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unit. Diana made a growth of 91 points whereas Sebastian grew 99 points. Both demonstrated

immense content knowledge in the area of two-dimensional shapes.

My students that are still acquiring English did phenomenal as well! Johannis (see

student work) scored an 82% with an 82-point growth. She came into this unit with no

knowledge, but came out being able to identify lines, rays, line segments, angles, and able to

classify triangles by angle. Her confidence with math grew significantly and she always wants to

play the Simon Says geometry game. Johannis did awesome with symmetry although missing

problem 6 (One explanation is that Johannis struggles with reading English and has anxiety with

word problems. I am assuming seeing all the writing made her anxious). But Johannis excelled

with problem 11 and 13. She demonstrated knowledge of finding lines of symmetry in geometric

figures. And on problem 17, she was able to identify F as asymmetrical. One aspect of this unit

Johannis struggled with, as indicated from her post-test, was identifying types of quadrilaterals.

Question 9 and 10 were challenging for Johannis, as well as question 19, which will be discussed

in further detail later.

Another ELL student, Mee scored a 79% on his post-test with a 66-point growth.

Throughout this entire unit, I have been absolutely amazed with Mee’s output (as

aforementioned in LAP reflections). Similar to Johannis, he showed strength in identifying lines,

rays, line segments, angles, and classification, but struggles with symmetry still! One final ELL

student, Van, also did better than anticipated (see student samples)! On the pre-test she scored a

3% whereas on the post-test scored a 67%! Her strength lied in identifying properties of two-

dimensional figures including rays, lines, and angles and using that knowledge to classify

triangles. She struggled with question 6, which pertains to symmetry. Van is a very low ELL

student who reads significantly below grade level with low comprehension. It can be assumed

that for question 6 she couldn’t fully comprehend what was being asked. The question asked

students to look at the date drawn (2/13) and identify if all the numbers had line symmetry. Van

answered the question: “Debbie birthday is February 12 and Debbie have a 2 moth line

symmetry is 13”. Overall, I contribute some of Van’s misconceptions in math in part to not being

able to fully comprehend what the question was asking. Despite this, Van did significantly better

on this math test than any other test throughout the year.

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Prince was the least successful student on this exam in my opinion. Despite making

growth from pre-test to post-test, Prince still only scored a 51% on his post-test. He was unable

to identify angles, and classify triangles (on question 2, he was only able to identify 3, but it

appears to be through trial and error). On questions 3, he couldn’t identify the angles that identify

an obtuse angle. He circled every answer. On question 9, he didn’t recognize that GH and IJ

were parallel lines. He simply wrote, “there not” to advocate that there wasn’t a true statement.

Prince also significantly struggled with symmetry. On question 6, he identified all the numbers

as having symmetry. On question 6, he was only able to correctly identify the lines of symmetry

in 2 geometric figures. On 13, instead of drawing a line of symmetry through the figure, he wrote

intersecting line (I have no explanation why he did this besides he didn’t know what a line of

symmetry was and he tried to utilize something he knew.) The only aspect of success in this unit

he had was with question 4 and 5. He could identify lines, segments and rays. Overall, Prince’s

lack of success with this lesson was directly correlated to his behavior throughout the unit. Prince

was not focused, unable to remain on task, fooled around, could not follow redirections, and

rarely completed class work. Despite multiple attempts to get him engaged in the lesson and

notes home to mom, nothing motivated him to try harder and make positive choices to create a

positive learning environment. All these factors played a large role in his poor performance.

Overall, students did exceptionally well in this unit, as indicated by post-assessment

grades. There was one question that a large majority of the class missed. That was question 19

Part A & B. The question asks students to look at two figures and either agree or disagree if both

figures represent a square or a rectangle. Many students couldn’t conceptualize that a square can

be classified as a rectangle. Most answers fell along the lines of “rectangles are longer, squares

are smaller”, or “one’s a rectangle the other is a square”. I needed them to be more specific. If I

had the opportunity to teach this lesson (Rebecca taught a lesson related, but not quite in depth,

due to me being sick- refer to LAP 7), this is an aspect I had anticipated addressing and coming

back to multiple times. If I had the opportunity to teach my planned lesson, I would have hoped

to have seen this misconception and addressed it. I can’t dwell on this and can only hope that if

in the future, if I have the opportunity to teach this unit again, I could address this before a unit

exam and maybe create some activities to build critical thinking students to help students address

questions similar to this.

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Students succeeded in achieving an overarching larger learning goal: to be able to

engage in a range of collaborative discussions. Students were able to work in a whole class,

small group and one-on-one setting to critically think about the topics at hand. Throughout the

lessons you could hear productive talk buzz through the air. Students were excited about the

content and collaborative working. Students worked amazing together. They were able to pool

their resources to problem solve and create classifications during their sorting activities. Students

in my class who usual don’t do well with social interactions did amazing. For instance, Carlos

was able to collaboratively work with Angellyse during the unit to meet the content objectives.

He did exceptionally well on his post-test, scoring a 67%. This was big for Carlos because most

of the time he is fooling around, having a tantrum, or leaving the classroom to go to the office.

He doesn’t usually produce a great amount of output, but Carlos did great throughout this unit.

Overall, if I were to implement this unit again, I would add another lesson focused on

symmetry to give students the extra practice they needed, as indicated from the post-test.

Additionally, I wish I focused the class more on the essential questions. I posted them and we

went over them periodically, but I didn’t follow through in explaining the end goal of being able

to classify geometric figures. If I were to explain the goal of the overarching unit, I may have

been able to give more students ownership of their unit. Additionally, throughout each lesson, I

needed to have a more summative/reflective component to my lesson where I bring students

together to reflect on the content. This would provide my students with an opportunity to reflect

on growth and connect learning to our broader learning goal.

Time was also a major issue in this unit. This unit was jam-packed in regards to content.

The whole 4th grade was given the same content standards, which followed closely to Chapter 10

of Go Math! A unit that should’ve had at least 3 weeks (due to the various linguistic differences

and learning styles present in my classroom) was implemented in 2 weeks. Students, specifically

my lower achieving students, could’ve used more time to develop the skills needed to succeed on

the test. This was also a shift in a content area. Students were fresh off of fractions and decimals.

Geometry required a whole paradigm shift and for students to refocus their brains toward

acquiring a completely different skill set. Additionally, because of the time constraints, I wasn’t

able to address patterns (which almost seemed unrelated in terms of the learning goals of this

specific unit). On the test, which came from Go Math- this is the test that the 4th grade decided to

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use, students were expected to answer questions regarding finding patterns and creating a rule for

the pattern. I allowed students to skip these questions. If they wanted to attempt them and they

succeeded I would give extra points. Some students succeeded on this questions, while others

either didn’t attempt or wrongly attempted. Despite the challenges of this unit, I think I managed

quite well with the time that I had. I was able to use a gradual release model and various

mediums to present content and make the unit as accessible and comprehensible as possible.

Another major component of this unit that I would change relates to the kinesthetic

component of this lesson. I think that completely redoing my lesson 1 (refer to LAP 1 reflection),

and including the kinesthetic component earlier in the unit would’ve benefited my students

greatly! Looking back, I relied more on “skill and drill” in the earlier lessons, which was

definitely a large lapse in judgment on my end. At the time, I felt that introducing the movements

would have been too overwhelming for my students. I was wrong. I wish that I had started off

with them to help my students acquire the academic language quicker. Once I introduced the

Simon Says game, student learning took off! Students weren’t as confused as they were in the

beginning. By introducing these movements earlier, I may have eliminated a lot of stress and

confusion on the end of my students and may have help students acquire the vocab faster. If this

were the case, we could’ve spent more time on developing the skills needed to classify

quadrilaterals and symmetrical figures.

In the end, students were able to meet my learning goals. Students were able to identify

the properties of two-dimensional figures and utilize their knowledge to classify geometric

figures. I attribute student growth due to the fact that I was able to differentiate my learning to

meet the varying degrees of needs of my students. I was able to utilize different techniques to

address the different learning styles of my students. Content was made accessible and

comprehensible. Throughout this unit, visuals, peer collaboration, audio, video, images,

kinesthetic movement, reading and writing with anchor charts, and tiered worksheets were

utilized to help support learners.

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Appendix

Pretest Post TestGrowth (Points)

Carlos 0 67 67Noelani 5 77 72Angellyse 0 28 28Tayen 3 78 75Van 3 67 64Kevin 0 23 23Dashaun 10 82 72Huy 10 67 57Paola 3 91 88Prince 13 51 38Samantha 3 56 53Gilmary 0 64 64Vanceia 5 18 13SebDiaz 15 95 80Gianni 18 90 72Mee 13 79 66Alkawthar 35 100 65Jasmine 36 78 42Johannis 0 82 82Anthony 0 73 73Han 0 44 44Ezekiel 0 62 62Seb Delgado 0 99 99Diana 0 91 91

7.166666667 69.25 62.08333333

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

20

40

60

80

100

120

PretestPost Test

Test Scores

Student

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