Fourth Grade Geometry Lesson: Drawing and Classifying Geometric Figures, Study notes of Geometry

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Getting to the Core

Geometry

Fourth Grade

1

Fourth Grade Geometry

• Unit Overview Table of Contents
• Van Hiele Theory of Geometric Thought
• Preparing the Learner A – Collaboration and Pre-Assessment
• Lesson 1 – Open Sort
• Lesson 2 – Parallel and Perpendicular
• Lesson 3 - Angles
• Lesson 4 - Precision with Vocabulary
• Lesson 5 - The Greedy Triangle
• Lesson 6 - Shape Deconstruction
• Lesson 7 – Map Project
• Special Education Appendix

Designing for Opportunities for Standards for Mathematical Practice happen at the Unit Level From: Bill McCallum, Ph.D., University of Arizona

21 st^ Century

Skills:

Learning and Innovation:

Critical Thinking & Problem Solving Communication & Collaboration Creativity & Innovation

Information, Media and Technology:

Online Tools Software Hardware

Essential

Academic

Language:

Tier II:

∑ Clarification

∑ Collaboration

∑ Norms

∑ Argument

∑ Parallel

∑ Perpendicular

∑ Angle

∑ Acute angle

∑ Obtuse angle

∑ Right angle

∑ Presence

∑ Absence

∑ Vertices

∑ Equilateral

∑ Isosceles

∑ Scalene

Tier III:

∑ Piggyback

∑ Compass Rose

What pre-assessment will be given?

Geometry Pre-Assessment

How will pre-assessment guide instruction?

The Geometry pre-assessment will inform the teacher with the data

needed that will show what students already know, what they don’t

4

know, and what possible misconceptions there might be.

Standards Assessment of Standards (include formative and summative)

Common Core Learning Standards Taught and Assessed ( include

one or more standards for one or more of the areas below. Please

write out the complete text for the standard(s) you include.)

What assessment(s) will be utilized for this

unit? (include the types of both f ormative

assessments ( F ) that will be used throughout

the unit to inform your instruction and the

summative assessments ( S ) that will

demonstrate student mastery of the standards.)

What does the

assessment tell us?

Common Core Mathematics Content Standard(s):

**4. G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two- dimensional figures.

4. G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right angles. (Two dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.)**

F: Collaboration throughout the unit of study.

F: Picture Sort Activity

F: Shape Handout Activities

F: Note Taking Guide

F: Student Math Journal

S: Geometry Term Book

S: Culminating Town Activity

S: Pre-Assessment

S: Post Assessment

Ongoing evidence

of students’

understanding of

concepts presented.

Diagnostic

information for

intervention or

acceleration.

Student

comprehension of

unit concepts and

the Big Idea:

Objects can be

described,

classified and

analyzed based on

their attributes.

Opportunities for listening, speaking, reading, writing, and

thinking ( Cite Literacy Standards (as applicable):

Listening and Speaking : Engage 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. 4.1.a Come 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 discussions. 4.2. b Follow agreed-upon rules for discussions and carry out assigned roles.

Teacher evaluation of student speaking and

listening:

F: Ask and answer questions in pairs and

collaborative groups during and after lessons.

F: Work collaboratively using Collaborative

Conversation sentence frames to create

classroom norms for the unit of study.

When talking about

mathematics in

pairs and

collaborative

groups, do students

follow

protocol/rules/

5

Differentiated

Instruction:

Based on desired student outcomes, what instructional

variation will be used to address the needs of English

Learners by language proficiency level?

∑ Sentence frames are provided in varying degrees

of difficulty to facilitate academic language and

conversations.

∑ Use of visual organizers to assist processing

mathematical ideas.

∑ Scaffolding by teacher as necessary to support

the English Learner.

∑ Explicitly teach key academic vocabulary.

∑ Use of manipulates to facilitate conceptual

understanding.

Based on desired student outcomes, what instructional

variation will be used to address the needs of students

with special needs, including gifted and talented?

Special Needs-

∑ Inclusion of Appendix to provide additional

resources to help prepare students. *

∑ Opportunities for verbal rehearsal of concepts.

∑ Use of visual organizers.

∑ Explicitly teach key academic vocabulary.

Accelerated Learners-

∑ Concepts of each day’s lessons have been

extended to include a higher level of depth of

complexity.

∑ Accelerated students can create their own

representations as an extension to deepen their

understanding of the mathematical concepts.

7

Fourth Grade Geometry

4

th Grade Unit- Theory

The 4th grade Geometry Unit was based on research that explains how students develop their

understanding of geometric concepts. In order to ensure students success in geometry and to develop

their ability to think and reason in a geometric context, The van Hiele Model of the Development of

Geometric Thought was utilized. The van Hiele model is a sequential model that has a five-level

hierarchy of geometric thinking. In this unit we will be addressing the first three levels.

The van Hiele Levels of Geometric Thought Summary

(From Elementary and Middle School Mathematics, Teaching Developmentally , by John Van de Walle,

Karen Karp, and Jennifer Bay-Williiams. Pearson Education, Inc., Boston (2010).)

Level 0: Visualization - Students know vocabulary, can identify shapes by its appearance, and can begin

to classify shapes by similarities and differences.

Level 1: Analysis- Students begin to recognize parts of shapes, and as they look at them they make

generalizations to understand the properties of shapes. Students refine their understanding of symmetry,

angle classification (right, obtuse, acute), parallel and perpendicular.

Level 2: Informal Deduction - Students begin to understand the relationship between properties. For

example, “If all four angles are right angles, then the shape must be a rectangle. If it is a square, then all

angles are right angles. If it is a square, then it must be a rectangle.” If-then reasoning is established to

lead to logical arguments of properties.

Level 3: Deduction- Students begin to develop definitions, theorems, corollaries, and postulates to

establish geometric truths. Students are able to make conclusions based on abstract statements about

geometric properties.

Level 4: Rigor- “The objects of thought at level 4 are deductive, axiomatic systems of geometry.”

(Generally the level of college geometry courses)

The levels are sequential, hierarchical, and not age dependent. Our goal is to guide students through the

progression of these levels.

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Lesson: Prep A Lesson 1 Lesson 2 Lesson 3

Activities * Pre-Assessment

• “Sierpinski Triangle”

*Collaborative Conversation

*Compare and Contrast a triangle with a rectangle *Geometric figure sort

• Presentation of sort *Create a Geometry word bank

*Perpendicular Picture Sort *Parallel Picture Sort *Collaborative Conversation

• Math Talk with ST Math *Color code angles utilizing ¼ of a circle as a reference for a right angle.

Materials

to

Compile

*Pre-Assessment

*Post Content and Language Objectives

*Sierpinski Triangle Handout

*Collaborative Conversations Sentence Frames- 1 per group

*Chart paper

*Math Journals

*Post Big Idea and Essential Questions

*Post Content and Language Objectives *Geometry Figure Handout *Construction paper ( piece per group) *Scissors *Glue for each group *Chart Paper

• Collaborative Conversations Sentence Frames

*Post Content and Language Objectives

• Collaborative Conversations Sentence Frames *Glue for each group
• Parallel T-Chart handout *Parallel picture sort handout *Perpendicular T-chart handout *Perpendicular picture sort handout *Math journals *Highlighters

*Parallel video Clip *Perpendicular video clip

Content>Test Drive Games> 4 th^ grade> Optional Objectives> Line and Angles>Parallel or Perpendicular

*Post Content and Language Objectives

• Collaborative Conversations Sentence *Shapes handout *Construction Paper
• Crayons: red, blue, yellow *Circle cutout (each student will use a ¼ piece)

Homework Journal Entry^ Lesson 1 Homework

Handout

Lesson 2 Homework Handout

Angles Homework Handout

4

th Grade Common Core Unit Overview: Week 1

Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8

Activities *^ Math Talk with ST

Math

• Geometric Terms video

• Create a geometric terms foldable

• Watch a video and take notes on how a shape changes when a side is added

*”Pick Up Stick Game”

• Students will create shapes using sticks and marshmallows *Students will draw the shape and label its parts in their journal

*Geometry Performance Task: create a map *Write two sets of directions from one place to another

Assessment

Materials

to

Compile

Content> Test Drive Games> 4 th^ grade> Optional Objectives> Line and Angles> Which Angle> Level 1

*Post Content and Language Objectives

• Post Collaborative Conversations Sentence Frames *Construction paper (1/student) *Tape or glue *Scissors
• Math journals

Video

*Greedy Triangle video

*Note taking guide *Post Content and Language Objectives

• Post Collaborative Conversations Sentence Frames

*Post Content and Language Objectives

• Post Collaborative Conversations Sentence Frames

Stir sticks per student: 5-whole stir sticks 5- 2 ½ inch stir sticks 5-3 ½ inch stir sticks

*Mini Marshmallows- 20 per student

*baggies

*Math journals

*Greedy Triangle note taking guide- for reference

*Post Content and Language Objectives

• Post Collaborative Conversations Sentence Frames

*12x Construction paper (1/student) *Rulers *Geometric Performance Task sheet

*Assessment (same as Pre-Assessment)

Homework Lesson 4 Homework^ Greedy Triangle Homework handout Lesson 6 homework^ Take map home andpractice

4 th^ Grade Common Core Unit Overview: Week 2

Fourth Grade Geometry

Preparing the Learner A

Academic Vocabulary(Tier II & Tier III)

TEACHER PROVIDESSIMPLE EXPLANATION

(^) KEY WORDS ESSENTIAL TO UNDERSTANDING WORDS WORTH KNOWING Clarification Collaboration Norms Argument

Piggyback

STUDENTS FIGURE OUT THE MEANING

Expand Evidence

Interrupting Respect

Pre-teaching Considerations

Student desks should be arranged in collaborative groups of four for the entire unit. Student should be able to work successfully in collaborative groups.

Lesson Delivery

Instructional Methods

Check method(s) used in the lesson: Modeling Guided Practice Collaboration Independent Practice Guided Inquiry Reflection

Lesson Opening

Prior Knowledge, Context, and Motivation: The purpose of this lesson is to practice how to work

together in collaborative groups. Students will have a collaborative discussion which may include argument.

Body of the Lesson: Activities/ Questioning/ Tasks/ Strategies/ Technology/ Engagement

Lesson Overview

Teacher Directions

∑ Pass out pre-assessment and explain to the students that the purpose of the test is to see what they already know. They should not worry if they don’t know the answers, just do the best they can. The same test will be given at the end of the unit to measure growth. ∑ Introduce Content and Language Objectives. ∑ Discuss ways to have a respectful discussion. Explain that in a discussion it is ok to agree and disagree, but that it must be done in a respectful way. To facilitate this we will be using sentence frames. Pass out the sentence frames for collaborative conversation and review them.

∑ Pass out “Sierpinski Triangle” to each student. Ask each student to count how many triangles are in the picture. Give students 5 minutes to count the triangles on their own, and then ask them to discuss their answers with their collaborative group. Students should be able to give an answer and justify or explain how they got it. If the students have different answers, (which is expected), have them use the sentence frames to debate the answer.

Differentiated Instruction:

English Learners: Collaborative sentence frames are provided on Collaborative Conversations handout.

Students Who Need Additional Support:

See Appendix

Accelerated Learners:

Allow students to create their own shape-like version of the Sierpinski Triangle. This activity can be extended over two days. 11

Fourth Grade Geometry

Preparing the Learner A

∑ To continue practicing collaborative conversations, have the students pair up with a second collaborative group to again debate their answers. After approximately 10 minutes, open a discussion with the whole class comparing/contrasting their two discussions. What issues came up when working in a larger group as opposed to a smaller group? How did the group handle disagreement? What norms need to be established for collaborative talk? Work with the students to create a list of 4- 6 norms o Suggested norms ß We listen to one another. ß We share our own ideas and explain them. ß We respect one another’s ideas, even if they are different. ß We respectfully disagree and try to see the other view. ß We let others finish explaining their ideas without interrupting. ß We take turns and share time. ∑ Explain that throughout the unit the class will be using the norms in their collaborative groups and have them copy the norms into their math journal. ∑ Review Content and Language Objectives. ∑ Homework – In student math journals, students write a paragraph describing a successful collaborative group. (What would you see? What would you hear?)

Lesson Reflection Teacher Reflection Evidenced by Student Learning/ Outcomes

12

Fourth Grade Geometry

Preparing the Learner A

Collaborative Conversation Sentence Frames

What to say when you want clarification…

∑ Will you explain that again?

∑ I have a question about what you said

about _____________.

∑ Do you mean that __________?

∑ Could you expand a little bit on what you

said about _____________?

∑ Could you give an example of what you

mean by ______________?

What to say when you want to build

on another’s idea…

∑ You made a good point when you said

_________.

∑ My idea is related to _______’s idea. I

think _________.

∑ I see what you’re saying. I agree

because ______________.

∑ My idea builds on _______’s idea. I think

_________.

∑ I’d like to piggyback on that idea. I think

__________.

What to say when you disagree…

∑ I see what you’re saying, but I think that

___________.

∑ Another way to look at it is ________.

∑ I do agree with what you said about

____________, but I think _________.

∑ I see it another way. Based on ________,

I think _________.

∑ Another possibility might be _______.

∑ I have a different answer. I wrote down

What to say when you want to cite

evidence from the text…

∑ On page____, paragraph _______, the

author says ___________.

∑ When I read _______ on page _______, I

thought that _________.

∑ I think the text supports my thinking on

page _______, paragraph ______, by

stating that ________.

∑ Another example of ______ is on page

_____, paragraph , where the author

states_____________.

14

Fourth Grade Geometry

Preparing the Learner A

Sierpinski Triangle

15

Fourth Grade Geometry

Lesson 1

Academic Vocabulary(Tier II & Tier III)

TEACHER PROVIDESSIMPLE EXPLANATION

(^) KEY WORDS ESSENTIAL TO UNDERSTANDING WORDS WORTH KNOWING

STUDENTSFIGURE OUT THEMEANING Pre-teaching Considerations

Student desks should be arranged in collaborative groups of four for the entire unit. Student should be able to work successfully in collaborative groups. Review posted norms.

Students should be familiar with creating a Double Bubble Thinking Map (Compare and Contrast). Students should have background about triangles and rectangles.

Lesson Delivery

Instructional Methods

Check method(s) used in the lesson: Modeling Guided Practice Collaboration Independent Practice Guided Inquiry Reflection

Lesson Opening

Prior Knowledge, Context, and Motivation: Students will be familiar with classifying shapes based on their properties.

Body of the Lesson: Activities/ Questioning/ Tasks/ Strategies/ Technology/ Engagement

Lesson Overview

Math Warm-up Display the triangle and rectangle and ask the students to compare and contrast them using a Double Bubble map in their math journal. Possible student answers shown below.

Differentiated Instruction:

English Learners:

We sorted our shapes by ________ because ______.

Students Who Need Additional Support:

See Appendix

Accelerated Learners: Have the students resort the shapes in another way and explain their reasoning.

17

Fourth Grade Geometry

Lesson 1

Teacher Directions ∑ Introduce Big Idea and Essential Questions. Once you have introduced them please display them throughout the entire unit. ∑ Introduce daily Content and Language Objective ∑ Review Collaborative Conservation Frames ∑ Pass out one piece of construction paper, geometric figure handout, glue, and scissors. ∑ Tell the students that they will be sorting their geometric figures into groups after they have cut them out. Each group will decide how to sort the figures based on a common geometric property (their choice). ∑ Remind students to follow group norms. ∑ Tell students that they will be presenting their completed sort to the class, and the class will guess how the shapes were sorted. ∑ Give students 5-10 minutes to discuss, sort cards, and glue them on the construction paper. ∑ Collaborative groups will write the property they used to sort the figures on the top of the construction paper so that it can be folded and hidden from view. ∑ All groups should present one of their groupings. Each collaborative group will guess how the shapes were sorted and write the group answer on a student whiteboard or piece of paper. When all groups have attempted to guess, the presenting group will explain how they sorted. ∑ As groups are presenting the teacher will create add the following terms to the word bank of geometric terms as they are generated by the students: line segment, point, ray, line, angle. ∑ After all groups have presented, the students should answer the essential question “What properties do geometric figures have in common?” in their math journals.

Closure Review Content and Language Objectives

Homework ∑ Lesson 1 homework handout

Lesson Reflection Teacher Reflection Evidenced by Student Learning/ Outcomes

18