Georgia Performance Standards Framework

S Kindergarten Mathematics C

I Frameworks

T Unit 2 Patterns, Shapes, Spatial

A Relationships M E H T A M Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Unit 2:Patterns, Shapes, and Spatial Relationships (4-6 Weeks)

TABLE OF CONTENTS

Overview...... 3

Key Standards and Related Standards...... 4

Enduring Understanding...... 7

Essential Questions...... 7

Concepts and Skills to Maintain...... 7

Selected Terms and Symbols...... 8

Classroom Routines...... 9

Strategies for Teaching and Learning...... 9

Evidence of Learning...... 9

Performance Tasks

 Task Chart...... 10  Animal Moves...... 11  Copy Cat...... 13  Where is Teddy?...... 15  Seeing and Hearing Patterns...... 22  Patterns are Everywhere...... 25  Culminating Task 1: Floor Patterns...... 28  What Shape is This?...... 34  Shape Search...... 39  A Poem and a Picture...... 42  Geoboard Museum...... 44  Marshmallow Shapes...... 47  Tangram Shapes...... 50  3-D and Me...... 54  Culminating Task 2: Shapes All Around Me...... 58

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 2 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition

OVERVIEW

In this unit, students will:  recognize, name, build, draw, compare, and sort simple two- and three-dimensional shapes  describe attributes and parts of two- and three-dimensional shapes  group objects according to common properties  investigate and predict the results of putting together and taking apart simple two- and three-dimensional shapes  describe, name, and interpret relative positions in space and apply ideas about relative position  create mental images of geometric shapes using spatial memory and spatial visualization;  recognize and represent shapes from different perspectives  recognize geometric shapes in the environment  create and extend patterns  investigate and predict the results of putting together and taking apart two and three- dimensional shapes  pose information questions  collect data  organize and display results using objects, pictures and picture graphs

Although the units in this instructional framework emphasize key standards and big ideas at specific times of the year, routine topics such as counting, time, money, positional words, and patterns should be addressed on an ongoing basis through the use of calendar, centers (tubs), and games.

To assure that this unit is taught with the appropriate emphasis, depth, and rigor, it is important that the tasks listed under “Evidence of Learning” be reviewed early in the planning process. A variety of resources should be utilized to supplement, but not completely replace, the textbook. Textbooks not only provide much needed content information, but excellent learning activities as well. The tasks in these units illustrate the types of learning activities that should be utilized from a variety of sources.

STANDARDS ADDRESSED IN THIS UNIT

Mathematical standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.

KEY STANDARDS

MKG1. Students will correctly name simple two and three-dimensional figures, and recognize them in the environment. a. Recognize and name the following basic two-dimensional figures: triangles, quadrilaterals (rectangles, squares) and circles. b. Recognize and name the following three-dimensional figures: spheres and cubes. c. Observe concrete objects in the environment and represent the objects using basic shapes. d. Combine basic figures to form other basic and complex figures into basic figures; decompose basic and complex figures into basic figures. e. Compare geometric shapes and identify similarities and differences of the following two and three-dimensional shapes: triangles, rectangles, squares, circles, spheres, and cubes.

MKG2. Students will understand basic spatial relationships. a. Identify when an object is beside another object, above another object, or below another object. b. Identify when an object is in front of another object, behind another object, inside another object, or outside it.

MKG3. Students will identify, create, extend, and transfer patterns from one representation to another using actions, objects, and geometric shapes. a. Identify missing elements within a given pattern. b. Extend a given pattern and recognize similarities in different patterns. c. Create a pattern in a different context with attributes similar to a given pattern.

MKM1. Students will group objects according to common properties such as longer/shorter, more/less, taller/shorter, and heavier/lighter. a. Compare and order objects on the basis of length. b. Compare and order objects on the basis of capacity. c. Compare and order objects on the basis of height. d. Compare and order objects on the basis of weight.

MKD1. Students will pose information questions, collect data, organize, and display results using objects, pictures, and picture graphs.

RELATED STANDARDS MKN1. Students will connect numerals to the quantities they represent. a. Count a number of objects up to 30. b. Produce models for number words through ten. c. Write numerals through 20 to label sets. d. Sequence and identify using ordinal numbers (1st-10th). e. Compare two or more sets of objects (1-10) and identify which set is equal to, more than, or less than the other.

MKN2. Students will use representations to model addition and subtraction. a. Use counting strategies to find out how many items are in two sets when they are combined, separated, or compared. b. Build number combinations up to 10 (e.g., 4 and 1, 2 and 3, 3 and 2, 4 and 1 for five) and for doubles to 10 (3 and 3 for six). c. Use objects, pictures, numbers, or words to create, solve and explain story problems (combining, separating, or comparing) for two numbers that are each less than 10.

MKM2. Students will understand the measurement of calendar time. a. Know the names of the days of the week, as well as understand yesterday, today and tomorrow. b. Know the months of the year. c. Know the four seasons.

MKP1. Students will solve problems (using appropriate technology). a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems. d. Monitor and reflect on the process of mathematical problem solving. MKP2. Students will reason and evaluate mathematical arguments. a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.

MKP3. Students will communicate mathematically. a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely.

MKP4. Students will make connections among mathematical ideas and to other disciplines. a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics.

MKP5. Students will represent mathematics in multiple ways. a. Create and use representations to organize, record, and communicate mathematical ideas. b. Select, apply, and translate among mathematical representations to solve problems. c. Use representations to model and interpret physical, social, and mathematical phenomena.

ENDURING UNDERSTANDINGS

 Properties determine when shapes are alike or different.  Shapes are everywhere.  Shapes have names.  Shapes have sides and angles which can be counted.  Patterns can be created and extended using geometric shapes.  Words can be used to describe the location of an object.  Pictures can be used to show what is counted.  Some shapes are flat (2 dimensional) and can cover up things while other shapes have a body/thick/tall/volume (3 dimensional) and can be filled.

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  How do shapes fit together and come apart?  How do we identify patterns?  How do we describe a pattern?  How can shapes be sorted?  What shapes can we see in our world?  How can we organize information?  How can we describe the location/position of an object?  How can you describe the triangles?  How are quadrilaterials and triangles different?  How can we describe location in our everyday life?  How are patterns used in everyday world?  How do we use shapes in school?

CONCEPTS/SKILLS TO MAINTAIN

Although many students may have attended pre-school prior to entering kindergarten, this is the first year of school for some students. For that reason, no concepts/skills to maintain will be listed at this time. It is expected that teachers will differentiate to accommodate those students that may enter kindergarten with prior knowledge.

SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, teachers should pay particular attention to them and how their students are able to explain and apply them.

The definitions below are for teacher reference only and are not to be memorized by students. Teachers should present these concepts to students with models and real life examples in discussions with students. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers.

 Above: in a higher place; overhead; a positional word

 Behind: in the back of; a positional word

 Below: in a lower place; under; a positional word

 Beside: by the side of; a positional word

 Circle: the set of all points in a plane that are the same distance from a given point

 Cube: a regular polyhedron whose six faces are congruent squares

 In front of: a positional phrase meaning in the place before

 Inside: the part within; inner surface

 Outside: the side or surface that is the outer part

 Quadrilateral: a closed shape with four straight sides (rectangles and squares are quadrilaterals)

 Rectangle: a special quadrilateral with four sides and four right angles

 Square: a quadrilateral that has four right angles and four equal sides

 Sphere: the set of all points in space that are of equal distance from a fixed point, called the center

 Triangle: a closed shape with three straight sides

CLASSROOM ROUTINES

The importance of continuing the established classroom routines cannot be overstated. Daily routines must include such obvious activities as taking attendance, doing a lunch count, lining up in a variety of ways (by height, age, type of shoe, hair color, eye color, etc.), daily questions, and calendar activities. They should also include less obvious routines, such as how to select materials, how to use materials in a productive manner, how to put materials away, how to open and close a door, how to do just about everything! An additional routine is to allow plenty of time for children to explore new materials before attempting any directed activity with these new materials. The regular use of the routines are important to the development of students’ number sense, flexibility, and fluency, which will support students’ performances on the tasks in this unit. See Unit 1 for suggestions concerning specific ideas for classroom routines.

STRATEGIES FOR TEACHING AND LEARNING

 Students should be actively engaged by developing their own understanding.  Mathematics should be represented in as many ways as possible by using graphs, tables, pictures, words, and finally symbols.  Appropriate manipulatives and technology should be used to enhance student learning.  Students should be given opportunities to revise their work based on teacher feedback, peer feedback, and meta-cognition which includes self-assessment and reflection.  Math journals are an excellent way for students to show what they are learning about a concept. These could be spiral bound notebooks that students could draw or write in to describe the day’s math lesson. Students love to go back and look at things they have done in the past so journals could also serve as a tool for a nine week review.

EVIDENCE OF LEARNING

By the conclusion of this unit, students should be able to demonstrate the following competencies:

 Count objects and show the quantity by drawing pictures.  Count objects and show the quantity by using other objects to represent the quantity.  Sort shapes into groups made up of members sharing the same attributes.  Find and name shapes in the environment.  Use shapes to create representations of items in the environment.  Compose and decompose shapes.  Use a graph to represent real data about themselves and their classmates.

TASKS The following tasks represent the level of depth, rigor, and complexity expected of all Kindergarteners. These tasks or a task of similar depth and rigor should be used to demonstrate evidence of learning. It is important that all elements of a task be addressed throughout the learning process so that students understand what is expected of them. While some tasks are identified as a performance task, they also may be used for teaching and learning (learning task).

Task Type/ Content Addressed Task Name Grouping Strategy Spatial Relationships Learning Task Animal Moves Large Group or Small Group

Learning Task Copy Cat Spatial Relationships Partners

Performance Task Where is Teddy? Spatial Relationships Individual or Small Groups

Learning Task Seeing and Hearing Patterns Create, Extend, and Transfer Patterns Large Group

Learning Task Patterns are Everywhere Create, Extend, and Transfer Patterns Large Group or Partners

Culminating Task 1: Performance Task Create, Extend, and Transfer Patterns Floor Patterns Individual

Learning Task What Shape is This? Recognize and Name Shapes Large group or Small Group

Learning Task Recognize, Name, and Compare Shapes Shape Search Large Group, Individual Observe Shapes in the Environment

Learning Task Recognize, Name, and Compare Shapes A Poem and a Picture Large Group, Partners Observe Shapes in the Environment

Learning Task Recognize, Name, and Compare Shapes Geoboard Museum Small Group, Individual Observe Shapes in the Environment

Learning Task Recognize, Name, and Compare Shapes Marshmallow Shapes Individual Learning Task Recognize, Name, and Compare Shapes Tangram Shapes Individual Learning Task Recognize, Name, and Compare Shapes 3-D and Me Individual Observe Shapes in the Environment Culminating Task 2: Performance Task Recognize, Name, and Compare Shapes Shapes All Around Small Groups or Individual Observe Shapes in the Environment

STANDARDS ADDRESSED

MKG2. Students will understand basic spatial relationships. a. Identify when an object is beside another object, above another object, or below another object. b. Identify when an object is in front of another object, behind another object, inside, another object, or outside it.

MKP1. Students will solve problems (using appropriate technology). a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems. b. Monitor and reflect on the process of mathematical problem solving.

ESSENTIAL QUESTIONS

 How can we describe the position of an object?  How can we use words that describe location in our everyday life?

MATERIALS

 student chair  small stuffed animal

GROUPING

Large Group

TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

 Place the student chair on top of the table.  Put the box on top of the chair.  Use this arrangement to pose questions about the location of the stuffed animal.  Move the stuffed animal around asking “Where is it now?” questions  Have students answer with a variety of positional words (above, beside, below)  Give students an opportunity to come up and move the animal and describe its location

The teacher should model the activity using appropriate vocabulary before having the students participate. “The animal is beside the chair. Now it is behind the chair.” As the animal is moved around ask the students “Will the position words always work the same way?” Continue in this manner, eventually giving the students a chance to move the animal.

Position words are difficult for students to follow through with when given directions to locate something in the classroom. As the school year progresses students can use this information to organize papers, cubbies, backpacks, folders, etc.

Knowledge of these positional words is a life skill. Encourage parents through weekly newsletters, to use this vocabulary in their home life. Students will benefit from the school/home connection that applies these concepts to their everyday life.

Questions for Teacher Reflection  Do students place the animal randomly with no regard to vocabulary?  Do students need multiple prompts to get the right answer?  Can the students differentiate between above and below?  Can the students complete the task independently?  Are students able to use the positional words correctly in a sentence about the animal?

DIFFERENTIATION

Extension  This task could be extended by adding it to the calendar routine. A student could place the animal or other object in specific positions and then challenge the others to describe where the animal is being placed. “The animal is above Jacob’s head. He is beside him. Jacob has the animal between his feet.”

Intervention  If students have a difficult time with this task, practice by playing “Simon Says” emphasizing the words above, beside, below, behind, inside, and outside. The familiarity of this game may provide a link for some students.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 12 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task: Copycat

STANDARDS ADDRESSED

MKP1. Students will solve problems (using appropriate technology). a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems. d. Monitor and reflect on the process of mathematical problem solving.

ESSENTIAL QUESTIONS

 How can we describe the location of an object?  How can we describe location in our everyday life?

MATERIALS

 Tiles or connecting cubes  Folders or something to obstruct view of partner’s pattern creation  Pattern by Henry Arthur Pluckrose or similar book

GROUPING

Partners

Gather students on the carpet for a game of copycat. Read a story such as Pattern by Henry Arthur Pluckrose. Discuss the patterns shared in the story. Next, model for students how to create a pattern using the manipulatives and manila folder to hide the pattern on the other side of the folder. It is important to model for the students how to complete this task. You may want to model for the students sitting in a way that the students can see the pattern that has been created, as well as the work of the student who is creating the “copycat” version. The modeling of this process is very important to the overall understanding of giving explicit, concise directions for the spatial relationships. Have a child build a design using different colors (connecting cubes, color tiles, etc.) and allow the child to describe to the teacher using directions to recreate the design using spatial or positional words. Say to students “Tell how your partner could make a design exactly like yours without your partner seeing your design. Only use words to help. Be sure not to point, signal, or touch anything to give additional clues.” The partner may only put a block in their structure when verbal directions are given. For example, the child might say, “Put a yellow one beside the red one. Then put a blue one above the yellow one.” Reverse roles and play again. Once a few children have learned how to do this, allow them to teach the game to others. “Beside” can be either left or right. When your partner has finished, let him/her see your design and check that the two designs are exactly the same.

Questions for Teacher Reflection  Are students able to explain how words describe the location of an object?  Are the students interpreting the correct location (below, above, beside, inside, outside) ?  Can students use words to describe location in everyday life?

DIFFERENTIATION

Extension  Once several children have become adept at this, teach them to play back to back. One builds, and then describes the design to the other child who attempts to build it without looking. When they agree that the design is complete, they may turn and look to see if the designs match.

Intervention  The student gives directions to the teacher while the teacher builds and the student observes. Then role is changed and the student builds while the teacher gives directions.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 14 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Performance Task: Where Is Teddy?

STANDARDS ADDRESSED

ESSENTIAL QUESTIONS

 How can we describe the location of an object?  How can we describe location in our everyday life?

MATERIALS

 “Where is Teddy” story mat  Teddy bear pictures  Teddy Bear booklet

GROUPING

Individual or Small Group

Teacher Note: The task assumes that students have had hands on experiences with placing objects above, below, inside, outside, between, beside, in front of, and behind another object.

The teacher may begin the task by using a stick puppet “Teddy” and a small bowl to represent a cave. The teacher may introduce the activity by telling a story about “Teddy Bear.” For example, “One day Teddy went walking in the woods. He walked on and on until he discovered a big, dark cave. He decided that he wanted to explore all around the cave.” Have children show and tell several ways that Teddy can explore the cave. The students will draw or cut apart the teddy bear pictures and glue them in the appropriate places on the story mat to show ways that Teddy can explore the cave. Students should write a position word beside, outside, and inside in each blank to complete the sentence on each page. After completing the sentences, the pages on the story mat can be cut apart and stapled together to make the “Where Is Teddy?” book. Each student should read his/her book to the teacher indicating the position of Teddy on each page. Ask the question: “Can Teddy really be under a cave? Explain your thinking!”

Questions for Teacher Reflection  Are students able to explain how words describe the location of an object?  Can students use words to describe location in their everyday life?

DIFFERENTIATION

Intervention  Students who have difficulty doing this activity may need more hands-on experiences with placing/manipulating real objects, for example, using 3D Teddy Bears and bowls for caves.

Student Teddy Bears for Story Mat

Where is Teddy?

By: Teddy is inside the cave. ______

Teddy is outside the cave. Teddy is ______the cave.

Teddy is ______the cave. Teddy is ______the cave.

Teddy is ______Teddy is ______

student waswere able able

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 21 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task: Seeing and Hearing Patterns

STANDARDS ADDRESSED

ESSENTIAL QUESTIONS

 How do we know how to identify patterns?  How do we describe a pattern?

MATERIALS

 Pattern blocks  Unifix cubes or connecting cubes  Variety of other manipulatives

GROUPING

Large Group

Draw children’s attention to patterns of shapes found in the room and in their clothing. Ask questions such as “How do you know this is a pattern?” You will want to hear answers like “A pattern is something that repeats.” Discuss how patterns are created, and how easily children can create them. After they have some free exploration with pattern blocks and connecting cubes, ask if they can create a pattern using either of these manipulatives. Allow children to share their patterns and have children clap them, snap them, or describe them using letters, such as ABABAB, etc. As students share their patterns, ask “Did anyone create a pattern similar to John’s pattern?” and “What is similar about your pattern and John’s pattern?” Once students have shared, have them group themselves by their patterns.

Choose a few children to line up in a pattern such as blue shirt, red shirt, blue shirt, red shirt, or blond hair, brown hair, blond hair, brown hair. Have other students try to guess what pattern they think is being represented by the children. When they have determined and discussed a few of these people patterns, have them attempt to record on paper, one pattern that you have already demonstrated. Share and discuss their representations.

Have children make up their own secret pattern. Partner students and see if partners can figure out what should come next in each other’s patterns. Be sure partners tell how they knew what should come next in the pattern.

Special Notes: Focus should be on the idea of repeating. Patterns begin the foundation for later number relationship, making generalizations, seeing relationships, and understanding of order in mathematics. Students will begin to see patterns in numbers through the 99s chart and other number charts. They begin with physical patterns or drawings, but will eventually move to functional representation or symbolic rule. We want to set the stage for students to begin to explore patterns in all areas of mathematics.

Questions for Teacher Reflection Listen for children to explain how they knew what would come next in the patterns. Specifically:  What are similarities that help to identify patterns?  How are they describing a pattern? How do they know it is a pattern?

DIFFERENTIATION

Extension  Allow children to take turns creating patterns, and have the other students guess the pattern. Let students represent their guess about the patterns on paper, and share and discuss their representations. Using clipboards and markers will make this task very manageable.

Intervention  Provide students with materials to make their own pattern. Have them share their pattern by clapping, singing, or by saying letters.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 24 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task: Patterns Are Everywhere

STANDARDS ADDRESSED

ESSENTIAL QUESTIONS

 How do we identify patterns?  How do we describe a pattern?

MATERIALS

 Book about patterns or book such as Beep Beep, Vroom Vroom! by Stuart Murphy, pattern blocks  pattern strips showing patterns using the shapes learned (circle, square, triangle, rectangle)  drawing paper  crayons

GROUPING

Large Group or Partners

Part I: Read a book about patterns to the students. The book Beep Beep, Vroom Vroom! by Stuart Murphy is a good example of the kind of book that is appropriate for this task. As you read the story, stop periodically asking questions such as “Did you see an example of something that repeats?” or “Describe the patterns in which the cars are placed on the shelf. How did you know?” Discuss the patterns from the book and model them using different manipulatives (cubes, shapes, students, etc.). The book uses cars for its patterning. You could cut out paper cars or have plastic cars for modeling. Various students should demonstrate pattern examples for the class. Provide each child with a bag of connecting cubes or some sort of manipulative. The teacher may choose to pre-select two or three colors for each student to have in his or her bag. As the teacher re-reads the story, have students create the patterns in the story using the cubes. Have students share their pattern creations as they create them in the story. As students share similar patterns, model for them how to group the patterns. For example, Sara created a red, blue, red, blue pattern with her cubes, which is similar to Greg’s pattern of A, B, A, B using the red and white cubes. After modeling this to the first few students, encourage other students to describe if their pattern is similar to ones shared. Next, share with students, “We are now going to find out how to create patterns using our actions.” Demonstrate a “snap-clap” pattern with your hands. Have students repeat the pattern after you. Expand the pattern to more complex patterns such as “snap, snap, clap, snap, snap, clap,” and have the students repeat after you. You can have students create their own patterns and share with the group. Once students understand the process, allow students to lead this activity.

Part II: Explain to the students that they will be creating patterns similar to the book and the “snap, clap” patterns using pattern blocks. Show a sample such as: square, triangle, triangle, square, triangle, triangle. Have students discover and describe the pattern. This is an ABB pattern. Repeat this activity several times until students understand and can complete with the pattern blocks. Have them work in groups or with partners to create patterns, and let their partners discover the patterns. Encourage math dialogue about transferring this pattern to a body action. Comment and ask questions like, “I see that you made a pattern using the triangles, squares, and circles. What kind of pattern is that? How could you describe that pattern?. Show

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 26 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition me how you could use your body actions to show this kind of pattern.” Distribute pattern strips to students. This is a blank strip of construction paper or sentence strip. Students copy the pattern on their paper and leave a blank space for another student to complete the pattern for at least five more steps. Students create their own pattern strips to be traded with partners for completion. Students should be able to verbalize the patterns they make with the shapes.

Part III: Gather students together to share their pattern strips from the previous activity. Begin the time by having students finding a new partner and completing their pattern strip. Next, teacher will share a pattern strip and discuss what information is known about the pattern. Then say, “I would like to group our patterns today by their similarities. How can we decide if patterns are similar or not? Can you help me with this activity?” Your discussion should not simply be on naming the patterns as AB, ABBA, etc but should focus primarily on the depth of patterning with different situations and the transfer to a different context. It would be helpful to have a few blank charts prepared for students to group their pattern strips. Have students share their pattern and then decide which group it belongs in and why.

Questions for Teacher Reflection Observe students as they repeat “snap, clap” patterns. Look specifically for:  Can they mimic a pattern?  Are they able to complete an unfinished pattern?  Can they create original patterns and then explain it to the class?

DIFFERENTIATION

Extension  Give students a wide variety of materials and ask them to create different patterns. They may use buttons, bears, toy cars, seeds, crayons, blocks, etc. Encourage them to create patterns other than ABAB patterns.

Intervention  Provide many opportunities for patterning practice with different types of manipulatives. Model the think aloud process for creating patterns for students. For example, “I see yellow beans and red beans in this box. I will make a pattern with these beans. Yellow is first, then red, next I need to repeat the yellow and then red and then again. I know this is a pattern because I see something that repeats. I can show another way to share this pattern by using my body actions of clap, snap, clap, snap.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 27 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Culminating Performance Task 1: Floor Patterns

STANDARDS ADDRESSED

ESSENTIAL QUESTIONS

 How do we identify patterns?  How do we describe a pattern?  How are patterns used in our everyday world?

MATERIALS

 5 square x 5 square grid to create floor pattern (2 for each student)  Objects such as paper cutouts, beads, stickers, buttons, cubes  Crayons or markers

GROUPING

Individual

Special Note: Students need to have had varied experiences with duplicating, creating and extending patterns with actions, objects, and geometric shapes.

 Tell students they are going to make a pattern for a floor rug. (Teachers may wish to supply students with grid paper similar to the one shown below.)  Have students create/color a rug picture using a pattern of their choice. (A short discussion or review of student work from previous tasks may be appropriate. A teacher may want to point out various types of patterns that have been created. Do not ask students to create an AB or ABB pattern for example. Students should use their knowledge from previous tasks to create a pattern and then describe it.)  Students then construct and explain a rug pattern they create. (Teacher will meet with each student as she circulates through the class while they are creating their rugs. Ask questions about the pattern and ask the student to show another way to create the same pattern in a different context. They could also use body movements to demonstrate their understanding of transferring patterns to different contexts. You will need to have various manipulatives available for this part of the task.)  Students should share their creations for closure of the task. Students find a pattern partner. (This part of the task will provide the teacher with further assessment of the students understanding of patterns. Students should find a pattern partner who has created a pattern rug like his or her rug. If students chose based upon color instead of pattern, ask them “What is the same about what is repeating in your pattern and your partners? Can you describe your thinking?”) Once the students find a partner, they will use math language to talk with their partner about their pattern and then share with the group why they think they are pattern partners.  After students have shared their patterns with the class, they will then place all the rugs in the center of the room and students will choose a rug other than their own rug. The teacher will use premade charts to allow students to sort these by type of pattern. (For example: The teacher would place a student’s rug who has one repeating pattern on one chart and then have the next child come up to select any rug they want that is not their own , ask a question such as “Is this rug pattern similar to the pattern Peter just shared? Should we put them in the same category? Why or why not? I see you that you said that it is different, what is different about the rug you selected than the first rug? Further questions would allow the teacher to gauge a student’s understanding of patterns.)

Special Note: Student examples shown only include using colors in the pattern. You may choose to have various manipulatives available for student use in the task. This would allow for differentiation.

Questions for Teacher Reflection  Are the students making patterns both horizontally and vertically?  Does the pattern continue as you go down the page?  Are students able to verbalize their thinking process of making a pattern?  Are students able to make connections between the pattern they have created and another student’s work?

DIFFERENTIATION

Extension  Give students opportunities to transfer patterns from one representation to another. Example: clap, snap, clap, snap, etc. could be transferred to an AB pattern made of blocks.

Intervention  Have students begin with just two colors for making their patterns.

Work samples from Georgia students are shown below.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 33 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task: What Shape Is This?

STANDARDS ADDRESSED

MKG1. Students will correctly name simple two and three-dimensional figures, and recognize them in the environment. a. Recognize and name the following basic two-dimensional figures: triangles, quadrilaterals (rectangles, squares) and circles.

MKP2. Students will reason and evaluate mathematical arguments. a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  How can you describe triangles?  How are quadrilaterals and triangles different?  How can shapes be sorted?

MATERIALS

 Circles, triangles (equilateral and right triangles), quadrilaterals (squares and rectangles of different sizes and colors). Attribute blocks could be used.  One set of above mentioned shapes for each child – 4 of each shape  Word cards labeled square, circle, rectangle, triangle  When a Line Begins…A Shape Begins by Rhonda Gowler Greene or similar book

GROUPING

Small or Large Group

Special Note: This learning task will serve as an introduction to shapes. It will take a few days.

Part I: Gather students together on carpet area. Pose this question, “What do you know about shapes? Let’s brainstorm what we know about shapes.” As students share their responses, record these on chart paper. (This group time is a chance to record all responses, we are simply gathering information at this point. A small discussion can begin, but you want to focus on gathering information for yourself as well. This is a great way to do an informal pre-assessment of the student’s knowledge of shapes. We want to quickly chart this information, we will come back to these responses after parts II and III of this task.) Once you charted their shape ideas, say “Let’s read a book to see what we can find out about shapes. This will give us information we can compare to our chart. Listen to see if you hear any of the same ideas we had in our chart or if you hear something new.” After reading a book similar to When a Line Bends…A Shape Begins by Rhonda Gowler Greene, ask students to share the new or different information they heard about shapes compared to what was listed on the chart. Use a different colored marker to add new information or mark out information that we no longer agree with based upon the story. You will need to keep this chart for future conversations with students about shapes.

Part II: Read a new book about shapes to springboard the second part of the learning task. Other examples of shape books include Shapes, Shapes, Shapes by Tana Hoban and My First Book of Shapes by Eric Carle. Give students a bag of precut shapes. You will find a student sheet below for this part of the task. Say to the students, “Group your shapes the way you think they should go together. You should be prepared to share your thinking with a partner.” Once students have sorted their shapes for a few minutes, have them glue down their sorting. Then have students partner with their elbow buddy and compare their sorting. Encourage students to discuss their sorting methods. Next, pull students together for a class discussion. The class discussion should ensue from this part of the task about the various ways to sort the shapes.

Special Note: This part of the task is another good example of assessing a student’s understanding. You want to allow for various ways to sort the shapes because this will be a way to build the student’s understanding of the properties of shapes. Some students may have sorted only by sizes of big and little, others may have sorted by shapes. Pay special attention to any examples that show all four sided shapes grouped together so you can refer back to this as the group of quadrilaterals. Also notice if any examples have separated the rectangles… Remember squares are special rectangles… from the other four sided shapes, i.e. parallelograms and trapezoids. REMEMBER, we refer to all four sided shapes as quadrilaterals in Kindergarten. AND we need to be mindful when talking about rectangles, making sure to emphasis that squares are special kinds of rectangles that have all four sides the same length.

Part III: Begin this portion of task by reviewing the work completed yesterday. This should be a quick discussion including the charts that were made in Part I of the task. Display the same set of shapes of different sizes from Part II of the task. It is important to use these same shapes, so that students can focus on the various characteristics.

The teacher will model sorting the shapes by size, asking for students to assist in this process of determining where the shape was to be placed on the chart. After sorting the shapes by size, then say “We have sorted by size and now I am wondering what other information we can use to sort the shapes in a different way. I am going to give you a moment for think time to come up with an idea. When you have an idea, give me a thumbs-up sign.” Once you have a number of students giving you the thumbs up sign, have them partner with an elbow buddy and share their idea. Have a partner set come to the front and share their ideas. (This part of the task will be fueled by their thinking. You may have discussions such as this: “Sam has sorted his shapes by the number of sides. Did anyone else sort their shapes by the number of sides? I see that you sorted them into a group that has shapes with four sides. Those shapes fall into a special group called quadrilaterals. This is a new word for us. Let’s practice saying that word together. It is special name for shapes. Who could help me group the quadrilaterals together? Wow, I see that there are different kinds of quadrilaterals. What are the names of these two types of quadrilaterals?” The answer to that is NOT rectangles and squares; it is rectangles and non rectangles! This is extremely important because squares ARE rectangles and need to be classified correctly as such early on in a child’s thinking about shapes. There should be some discussion with students about the group of rectangles and how rectangles themselves can be separated into two groups…ones that are squares and ones that are not squares) As student discussions continue with the number of sides, prepare three charts for the students. The charts should be labeled triangles, circles, and quadrilaterals. Have students give you information about each of the shapes. Refer students back to the chart that was created at the beginning of the task entitled “What We Know about Shapes.” Have students use some of the information from that chart to add more information to our more specific charts.

Part IV: Students will now practice using these clues to play a game with a partner. Have students spread their set of shapes out on their tables. Ask questions like, “Who can find a shape that is a quadrilateral? What about a shape that has three sides?” After modeling this for students a few times, allow students to play this game with a partner. Encourage students to identify the shapes based on the attributes of the shape by asking questions such as: “Which shape has three sides?” or “Show me the shape that has two long sides and two short sides. Show me an example of a rectangles that has all sides the same length? Do we have a special name for this kind of rectangle?” To close this task, discuss the similarities and differences of the shapes. Are all quadrilaterals the same? Are all triangles the same? Why or Why not?

Questions for Teacher Reflection  Can the students tell the difference between sides and corners?  Can the students verbalize the difference between a side and a corner?  Are students able to explain how they know that all quadrilaterals are not the same?  Are students able to explain how they know that all triangles are not the same?

DIFFERENTIATION

Extension  Put out a set of blocks or pattern blocks during math centers for students to explore. Using the blocks/pattern blocks to build designs of their own is a good opportunity for them to become familiar with how the geometric shapes fit together.

Intervention  As the students are exploring check for understanding by having them name a shape you point to or ask them to hand you a particular shape. Students could also show how they identify a shape by counting the sides and corners.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 38 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task: Shape Search

STANDARDS ADDRESSED

MKG1. Students will correctly name simple two and three-dimensional figures, and recognize them in the environment. a. Recognize and name the following basic two-dimensional figures: triangles, quadrilaterals (rectangles, squares) and circles. c. Observe concrete objects in the environment and represent the objects using basic shapes. e. Compare geometric shapes and identify similarities and differences of the following two and three-dimensional shapes: triangles, rectangles, squares, circles, spheres, and cubes.

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  What shapes can we see in our world?

MATERIALS

 Magazines  Large sheets of construction paper  The Important Book by Margaret Wise Brown or similar book

GROUPING

Large Group and Individual

Part I: Students should gather on the carpet to review the chart created in the previous task. These charts define the characteristics of each shape. Students will take a shape hunt or walk to find examples of shapes (i.e., circles, triangles, quadrilaterals) inside the classroom. As children explore the environment, ask the children to act as “shape detectives” as they find items or objects having the four common shapes. Provide each student with a few post-it notes for them

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 39 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition to label the shapes they find in the classroom. This will give the students a chance to practice writing the words as well. (You could adapt this by having students stand by a shape they found in the classroom)As children explore and discover items during the hunt, encourage them to describe what they find. After a short shape hunt, gather students back together to create new charts. These charts will also be labeled circle, triangle, quadrilateral. Students locate items that fit into these categories using magazine pictures. The teacher should have three tables set up with magazines and scissors. At one table, students will locate circles, at another table they will locate triangles and at the third table quadrilaterals. Each child will go to each table in the rotation. The teacher should divide class into three equal groups and then assign each group a table shape. Provide each student with a large baggie to collect their shapes. Students will be given ten minutes at each table to find that shape. (Adjust the time based upon your student’s understanding and behavior.)After ten minutes, students rotate to the next table and locate that shape and finally go to the third table. When the three tables have been completed, students bring their shape bags to the carpet. Teacher leads discussion about each shape, asking students to share their examples of that shape. (Please note that not all shapes that were cut out will be used in this part of the task. You may need to explain this to your students.) As the students share their examples, the teacher asks questions such as “I see that you have shared a picture of an envelope, how did you decide that it was a quadrilateral? What is different about the envelope and the picture of a pizza slice that Jeremy shared with us earlier?”

Special Note: If the students want to sort the quadrilaterals into two groups, rectangles and not rectangles that is fine but do not force them to do this. Likewise, if they want to distinguish further and separate the rectangles into two groups of squares and not squares allow this but make sure it is clear in the poster display that these examples are subsets of quadrilaterals and rectangles.

Part II: Students will use their left over bag of shapes to play “Guess My Shape” with a partner. In this game, one student at a time spreads out their collection of shapes. The same student asks questions to the other student like “Find a shape that has 4 sides. What is the name of that shape? Can you locate a shape picture that is round? Show me a triangle.” The students then switch places and the other student spreads out his bag of shapes. These pictures could be sent home with a note attached for the students to play the game at home with a parent for continued reinforcement. Make sure to include in the note to parents an explanation that we are identifying all four sided shapes as quadrilaterals first, and then distinguishing rectangles from non rectangles, and last distinguishing between rectangles that are squares and rectangles that are not squares. This is likely to be a very new idea to parents! Close this part of the task by asking students to share some of the good questions or clues they heard in the game.

Part III: In the third part of the task, students will use their knowledge of the characteristics of the shapes, as well as their knowledge of shapes in the environment to create a class book. The teacher reads The Important Book by Margaret Wise Brown. The class then creates their own sentences / phrases based on the important attributes of each shape. You may want to divide the class into three groups: triangles, circles, and quadrilaterals. Some examples might include The Important Thing about a quadrilateral is that is has four sides. It is a slice of cheese. It is also a

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 40 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition poster on the wall. But the important thing about a quadrilateral is that it has four sides. It is important to pull students back together and discuss pages that were created. Please pay particular importance to student’s understanding of the different types of quadrilaterals (i.e. rectangles and non rectangles and then special rectangles that are squares and ones that are not squares.) Once students have completed their pages, have them present them to their classmates and then put the book together for further discussions.

Questions for Teacher Reflection Observe students as they work sorting and labeling their groups of pictures.  Are the correct geometric terms being used as they talk/write about shapes?  Can they compare their shapes and identify similarities and differences among them?

DIFFERENTIATION

Extension  Have students work with a set of triangles of various sizes making sure to include in the set all types of triangles (isosceles, equilateral, right and scalene). Have students explain their reasoning for putting particular triangles together. For example, they may separate the right triangles out from the others because they notice a square corner; or the equilateral triangles because all sides are the same length. Ask questions like, “Why do you think these belong together? How are these you have put together different from the other triangles? How does this remind you in any way about how we grouped the quadrilaterals?

Intervention  Have students work with a set of shapes that are primarily the same size so that size is not a determining factor for grouping them. Once they notice the three categories of shapes (circles, triangles, and quadrilaterals) then add in more of these shapes that are different sizes. Also, it may be helpful to select a shape and have the students identify why the shape is NOT a quadrilateral or circle or square. They could do this with a partner that clearly understands and can identify circles, triangles, and quadrilaterals so they are hearing a peer articulate their thinking about how to classify shapes.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 41 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task : A Poem and a Picture

STANDARDS ADDRESSED

MKG1. Students will correctly name simple two and three-dimensional figures, and recognize them in the environment. a. Recognize and name the following basic two-dimensional figures: triangles, quadrilaterals (rectangles, squares) and circles. c. Observe concrete objects in the environment and represent the objects using basic shapes. f. Compare geometric shapes and identify similarities and differences of the following two and three-dimensional shapes: triangles, rectangles, squares, circles, spheres, and cubes.

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  How do shapes fit together and come apart?  What shapes can we see in our world?

MATERIALS

 copy of poem, “Shapes” by Shel Silverstein  drawing paper, crayons  2-D paper shapes in various sizes, include several different types of triangles (scalene, isosceles, and equilateral)

GROUPING

Large group or Partners

This task is based upon Lesson One of the Mathematics and Children’s Literature from the Illuminations website publication from NCTM, which can be found at the following address: http://illuminations.nctm.org/LessonDetail.aspx?ID=L202

Part I: Gather students together. Pose this situation to your students. “I have a new poem to share with you today, but guess what? It needs an illustration. I wonder if you all can listen to the poem and help me create our own illustrations for this poem? Teacher reads the poem “Shapes” by Shel Silverstein to the class. (You may want to copy this poem onto a large chart to invite students to read along with you.) Give the students a sheet of drawing paper and have them guess what the illustration of the poem would look like. Re-read the poem several times and observe as students create their illustrations. Ask question such as, “Do you think the illustration in the book will look like yours? Why or why not? When you compare the illustration in the book with yours, what do you notice? How are they alike? How are they different? What part of the poem is missing in Silverstein’s illustration? Why do you think he chose not to include it?” Have students place their shapes on the carpet and complete a gallery tour for everyone to see their version of the story.

Part II: Teacher will have a premade bag of paper shapes in different sizes for each student. Each student should have at least 2 of each shape in his or her bag. Students create a picture using their shapes. Students share their picture with the class. Encourage students to discuss which shapes were harder to use than others and why they thought so.

Questions for Teacher Reflection Observe students as they create their pictures.  Can students identify their shapes?  Can students describe their picture using mathematical vocabulary?  Are the students using all of these shapes in their picture/story?

DIFFERENTIATION

Extension  Some teachers may wish to include shapes such as ellipse or parallelogram as an extension.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 43 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task: Geoboard Museum

STANDARDS ADDRESSED

MKG1. Students will correctly name simple two and three-dimensional figures, and recognize them in the environment. a. Recognize and name the following basic two-dimensional figures: triangles, quadrilaterals (rectangles, squares) and circles. e. Compare geometric shapes and identify similarities and differences of the following two and three-dimensional shapes: triangles, rectangles, squares, circles, spheres, and cubes.

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  How do shapes fit together and come apart?  What shapes can we see in our world?

MATERIALS

 Geoboards  Rubber bands

GROUPING

Small Group or Individual

Part I Gather students together on carpet area. Discuss characteristics of a quadrilateral (i.e. that they have four sides and that some are rectangles and some are not. Also discuss that rectangles themselves can be separated into two groups, rectangles that are squares and rectangles that are not squares.), a triangle, and a circle. How are they alike? How are they different? Have students focus on the number of sides as a way to describe a shape. Give students geoboards and rubber bands. Allow students time to explore the different shapes that can be made with the rubber bands. Challenge students to come up with many ways represent the same shape. Students share the different shapes they have created. Discussions should include conversations about how the students have created their shapes.

Part II Completed geoboard designs are displayed in the classroom as Geoboard Gallery. The teacher should label each geoboard with a number. Model for students how to record the shape using dot paper. Provide each student with a student task sheet and have them record what shapes they see in each picture at the museum. This part of the task will require very clear directions and modeling. You may want to take pictures for future activities.

Questions for Teacher Reflection  Observe students as they create designs to see which students have figured out how to make designs using multiple shapes and which students use shapes to make abstract designs. We are want student to be able to create both types.  Can most students make quadrilaterals and triangles?  Are they sharing their findings?  Can they create multiple shapes within their design?

DIFFERENTIATION

Extension  Ask students “What happens if we combine more than one shape on the geoboard? For example if I put two triangles together what does it look like?”

Intervention  Some students may struggle with creating shapes on the geoboard. These students can be given cards that have examples of geoboard designs to copy.

Geoboard Gallery ______Geoboard Gallery ______

Learning Task: Marshmallow Shapes

STANDARDS ADDRESSED

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  How do shapes fit together and come apart?

MATERIALS

 Marshmallows  Toothpicks  Bowls  Black construction paper or poster board

GROUPING

Individual

Part I Gather students together on carpet area for group discussion. Begin discussion with “I have some tools to create lines. I have marshmallows and toothpicks. How could I make my line longer using these items? Do you have an idea?” After a student comes up and demonstrates how to make a line segment. Then say “We have been learning about shapes in our world. What can you tell me about the shapes we have learned? I wonder if someone has an idea about how we can use these line segments to create shapes?” According to the level of understanding of your students, you may need to guide this discussion.

Part II Allow students to explore using toothpicks to create shapes. This should be a quick discussion and exploration because students are going to have an extended time creating shapes in the next part of the task. Lead students into the task by asking questions and modeling your thinking by saying something like “What shapes can be made if I use four marshmallows and four toothpicks?” Continue modeling, making comments like “I know that a quadrilateral has four sides, so I can make a quadrilateral with 4 toothpicks. I will need four marshmallows too.” Allow the student to copy the quadrilateral with their own materials. Then ask, “Does anyone know another name for this quadrilateral that we just made?” Accept both rectangle and square, (because both are correct), but make sure to discuss how calling it a square is more specific, squares are special rectangles that have all sides the same length. Then ask, “How could we use marshmallows and toothpicks to change this shape so that it is still a rectangle but it is no longer a square?” (Note to teacher: Remember, not all rectangles are squares, but all squares are rectangles!)

Part III Divide the class into three groups. Place marshmallows and toothpicks in bowls on each table. It would be helpful to have a sign on each table that labels it as the triangle, square or rectangle table. Students can then rotate through each group, creating a few of each shape at each table. Five to ten minutes at each table would be ample time. Probe student’s thinking about their creations. Ask students to figure out a way that they could make a rectangle and a triangle using additional marshmallows and toothpicks. Students use marshmallows and toothpicks to form other shapes. Display shapes and sculptures on black construction paper. Equilateral triangles are easy to make. To make a right triangle, students will have to use lengths of three, four, and five toothpicks. Emphasize that their sculptures are going on display and they will be responsible for explaining the process for making the sculptures to others. Allow students to continue exploring with the materials until they have made several squares, rectangles, and triangles.

Part III Students gather together again on the meeting area to share their creations. Discuss what has been created and how each shape was created. Students will have created various kinds of quadrilaterals and triangles; therefore, it is important to discuss the properties of each. Discuss the steps involved in creating each shape. Also discuss which shape we did not create and why

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 48 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition we were not able to create it. Take pictures of their creations and display as student work paired with written/corresponding standards.

Ask questions such as:  How can you make your sculpture larger?  Does it have to have the same number of toothpicks and marshmallows every time? Why or why not?

Questions for Teacher Reflection  Are students able to recognize and talk about the similarities and differences of shapes?

DIFFERENTIATION

Extension  Some students will discover that if they add enough marshmallows and toothpicks they can form a cube. Provide students with enough materials so they can make 3-D sculptures. Students will recognize the relationship of the 2-D shapes within the 3-D shapes once they make a cube. Give the students plenty of time to explore and make additional discoveries.

Intervention  Provide models for students who are struggling with creating shapes or allow students to draw the shape first on paper then have them lay the toothpicks on top of the drawing in order to determine how many toothpicks to use and where to put the marshmallows.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 49 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task: Tangram Shapes

Adapted from AIMS Solve It! K-1, pp. 20-21

STANDARDS ADDRESSED

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  How do shapes fit together and come apart?  How can shapes be sorted?  How do we use shapes in school?

MATERIALS

 Tangram puzzle set – one for each child  Example of completed tangram picture  Grandfather Tang’s Story by Ann Tompert and Robert Andrew Parker or similar literature connection

GROUPING

Individual

Give each student a set of tangram puzzle pieces. Have them name and describe each piece in the set. Have them tell you something about each shape. Allow some time for free exploration with the shapes so students can see how they fit together and their relationship to each other. Next read, Grandfather Tang’s Story, and point out where/how the tangram shapes are used to build the cat and the man. Distribute the student page with the cat and man designs. Be sure everyone understands the challenges of placing the shapes in the right places to make the correct puzzle. Allow time for students to complete the cat and the man puzzles. Circulate around the room as students complete their tangram puzzles. Ask students to describe their puzzle pieces using the questions below.  What shapes are your puzzle pieces?  What do you notice about all of the triangle pieces?  What else do you notice about the puzzle piece shapes?  How did you decide which puzzle pieces to use for each puzzle?

Have students share their solutions with the class, describing how they solved the problem of fitting the pieces in the right places.

Questions for Teacher Reflection  Are students able to talk about what makes shapes different from each other?  Are students aware of how shapes fit together and come apart?  Are students able to sort shapes into reasonable groups?  Do students recognize how we use shapes in school?

DIFFERENTIATION

Extension  Have students create their own tangram puzzle picture.

Intervention  Have the students work with the tangram pieces to create either more simple pictures or to use pictures with details (line segments) filled in.

Student Tangram Puzzle

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 54 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Learning Task : 3-D and Me

STANDARDS ADDRESSED

MKP3. Students will communicate mathematically. a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  How do shapes fit together and come apart?  What shapes do we see in our world?

MATERIALS

 Geometric 2-D figures made from cardboard and pattern block examples (several different sizes of each)  Geometric 3-D examples of spheres and cubes in different sizes  Four pieces of poster board each labeled with a different shape name  Bag of various sizes of 2D and 3D shapes (circles, squares, cubes, and spheres)

GROUPING

Large Group

Part I Gather students on meeting area. Have students draw an item out of the bag and describe it to the class. Continue to share examples of the geometric figures with the class, pass the shapes around, and let students discuss the various attributes. Compare these 3D figures with the 2D figures that students have already learned. Introduce the new 3D vocabulary terms: sphere and cube.

Special Note: One way to talk about how 3-D shapes are different than 2-D shapes is to refer to 3-D shapes as having a body. This is why it is easy hold them in our hand. 2-D shapes do not have a body, which is why it is easy to draw them on paper. If you use the term “body” when talking about 3-D shapes then discussing “face” on the 3-D shape is a little easier. Our bodies have a face, and likewise most 3-D shapes have a face, some have more than one face. How funny would we look if we had more than one face?!

As students examine their shapes, ask questions such as: 1. How would you describe your shape to someone? 2. What is one thing you could say about your shape? 3. Turn to your partner and compare your shapes. How are they alike? How are they different? 4. Do any of the “faces” match with your partner’s shape? 5. Can you put your shape together with your partner and make a new shape?

Poems may be included in this lesson. Samples of poetry about figures can be found at www.canteach.ca/elementary/songspoem82.html.

Demonstrate how students can place the various 2-D and 3-D objects on the correct poster board. This can be used for small group or partner practice in comparing the various shapes. Observe as students work grouping the objects.

Part II Play “I Spy a Geometric Shape in Our Classroom” by having students sit in circle to play. Say, “I see an object in the classroom that has the same shape as a square or has four equal sides.” Have students ask “yes” and “no” questions until someone identifies the object. Once students understand the game, select a student to be the leader.

Questions for Teacher Reflection  Are they using the term square to talk about the faces of a cube?  Can they compare their shapes with a partner and identify similarities and differences?  Are they noticing where to find these shapes in the real world?

DIFFERENTIATION

Extension  Have students create a 3-D shape collage by cutting out pictures from magazines. Discuss cones and cylinders, provide examples of each and have the students participate in another shape hunt looking for examples of cones and cylinders.

Intervention  Provide students with many models of cubes and spheres that they can manipulate, trace, hold, see through (clear ones) and build whenever possible.

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 57 of 60 Copyright 2009 © All Rights Reserved Georgia Performance Standards Framework Kindergarten Mathematics Unit 2 1st Edition Unit 2 Culminating Task: Shapes All Around This culminating task represents the level of depth, rigor, and complexity expected of all kindergarten students to demonstrate evidence of learning.

STANDARDS ADDRESSED

MKP2. Students will reason and evaluate mathematical arguments. a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.

MKP3. Students will communicate mathematically. a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers and others. b. Analyze and evaluate the mathematical thinking and strategies of others. c. Use the language of mathematics to express mathematical ideas precisely.

ESSENTIAL QUESTIONS

 What makes shapes different from each other?  What shapes can we see in our world?  How can we organize information?

MATERIALS

 Student task sheet  Digital cameras

GROUPING

Initially in small groups then individually each student will fill in the task sheet

TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION Tell students they will be going on a “field trip” throughout the school and outside to search for examples of the shapes learned in this unit of study. The teacher may start with a “field trip” within the classroom and move to the inside of the building before moving outdoors. Students will record their findings on the student task sheet. This activity can be done individually, but works best if you can break the class up into small groups of 3-4 students and have a monitor with each group that can take digital pictures of the things they see around the school. Then they can sort the pictures on a poster board to be displayed. After that students can work individually to fill out the student task sheet below.

Special Note: The “monitor” does not have to be another adult; you could recruit some well behaved 5th graders to serve in this capacity.

Questions for Teacher Reflection  Are students able to identify and describe what makes shapes different from each other?  Can students recognize the different shapes (circles, triangles, quadrilaterals, spheres, and cubes) in the world around them?  Are students able to organize the information they gather on the hunt in a clear manner?

Shape Picture of Shape

Georgia Department of Education Kathy Cox, State Superintendent of Schools MATHEMATICS  GRADE K UNIT 2: PATTERNS, SHAPES, AND SPATIAL RELATIONSHIPS August 2009  Page 60 of 60 Copyright 2009 © All Rights Reserved