Unit Design For

Geometry 1st Grade

Developed by Lois Connelly

Pontiac Academy for Excellence

UBD Unit Design Worksheet / Saginaw Valley State University 1 Understanding by Design Unit Design Worksheet

Unit Title: Geometry Subject/Course: Mathematics Topic: Geometry Grade(s): 1 Staff Name: Lois Connelly

Stage 1 - Desired Results Established Goals:

Common Core Standards (GLCEs) – First Grade

1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. G.GS.01.01 Create common two-dimensional and three-dimensional shapes, and describe their physical and geometric attributes, such as color and shape.

2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter- circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.1 G.GS.01.01 Create common two-dimensional and three-dimensional shapes, and describe their physical and geometric attributes, such as color and shape. 1 Students do not need to learn formal names such as “right rectangular prism.”

3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. Not explicit in GLCEs.

Understandings: Essential Questions: Students will understand that... 1. shapes have attributes that define them and 1. How can knowing the number and length of make them different from other shapes (e.g., sides help you know the shape it will make? triangles are closed and three-sided). Some properties do not impact the shape (e.g., color, 2. How are shapes the same and different? Two- orientation, overall size). dimensional shapes: What shapes can you make by composing or decomposing squares, 2. shapes can be composed or decomposed to triangles, rectangles, trapezoids, hexagons and create new shapes. For example, two triangles circles? can be put together to make a quadrilateral. 2. Three dimensional shapes: How could you Many things in our world are constructed by compose or decompose shapes to create new combining shapes. ones?

3. circles and rectangles can be divided equally. 3. Why would you need to divide a circle or As the whole shape is divided into more equal rectangle equally? How would you do it?

UBD Unit Design Worksheet / Saginaw Valley State University 2 parts, the parts become smaller. There are What do you call the divided pieces? special fractional names for the equal pieces.

Students will know... Students will be able to...

 that plane and solid shapes have attributes that  sort, compare and describe plane and solid define them and that shapes do not change due shapes by defining attributes. (For example, to attributes such as position or color. how are squares and rectangles the same? Different?)  that shapes can be composed and decomposed to make new shapes.  name, build or draw a shape when given attributes, such as number and length of sides.  how to divide circles and rectangles into two or four equal pieces and will know the names of  recognize that shapes do not change due to the parts. position, size or color.

 find multiple ways to combine shapes to construct additional shapes. They will be able to recognize shapes that have been combined to make composite shapes in the real world. (For example, how could you make a rectangular shape if you only had square blocks? If you wanted to make a trapezoid what shapes could you use to make it?)

 divide circles and rectangles into two and four equal shapes. They will be able to name the parts using the words halves, fourths, and quarters, as well as the phrases half of, fourth of, and quarter of. They will describe the whole as two of, or four of the shares. They will explain that shapes can be decomposed into more equal and smaller shares.

Unit Enduring Understanding: Unit Question:

Students will understand that we use shapes and How do we use shapes? combinations of shapes to create objects in the world. They will understand that we sometimes need to divide objects into equal shares and will know how to accomplish this as well as how to describe the parts.

UBD Unit Design Worksheet / Saginaw Valley State University 3 Stage 2 - Assessment Evidence Performance Tasks:

Goal: Students will design a flag for our classroom. Each child will be given a rectangular piece of construction paper as well as small precut squares, triangles, circles and hexagons made from colored paper or cardstock. Have children follow the directions below to design their flag.

INSTRUCTIONS: 1. Divide your flag into 4 equal parts by folding and then drawing the lines. 2. Make a large rectangle out of small squares and glue it in one section of your flag. (This will symbolize the shape of our classroom.) 3. Make a hexagon out of small triangles and glue it in one section of your flag. (This will symbolize our 6 subjects (reading, writing, math, science, social studies, special) 4. Make a triangle out of any small shapes you choose and glue in one section of your flag. (This will symbolize that when we all come together we can create something new!) 5. Decorate one section of you flag by combining any shapes you choose into the shape of a person, place, animal, or thing to represent our class.

When complete the child will name shapes used to construct composite shapes as well as the name of the composite shapes. They will tell how many equal parts their flag is divided in to and will describe each section of the flag using the name one-fourth or one-quarter.

Role: Student is a flag designer.

Audience: Teacher

Situation: Student is a designer and must design a flag for our classroom following the instructions.

Product: Student will create a flag which is divided into quarters. Each section of the flag will contain a composite shape created from other shapes.

Standards and Criteria for Success: Student will be judged on constructing a flag which contains the attributes described in the instructions. They will correctly name the shapes that they used, the composite shapes, and will correctly write and name the fractional pieces of the flag. They will be judged on constructing and naming shapes, writing and naming fractional pieces, and combining shapes to create composite shapes.

UBD Unit Design Worksheet / Saginaw Valley State University 4 Key Criteria:

3 2 1 Criteria 1: The child correctly Criteria 1: Mistakes were made Criteria 1: The student required divided and named the fractional in dividing the flag or in naming extensive help and prompts (3 or pieces of the flag. the fractional piece. Child is able more) to fold paper. They could to explain or show how the flag correctly identify fraction only should have been divided with 1 when shown choices ¼, ½. or 2 simple cues (How could you fold the flag into 2 equal pieces? How could you fold it again to make 4?) or they could name fraction with one simple clue.

Criteria 2: The child correctly Criteria 2: The child correctly Criteria 2: The student was not created all 4 composite shapes. created 3 composite shapes, or able to create more than one they correctly created 2 and could composite shape without show how to create one or two extensive help and prompts. more given hints or prompts by the teacher. (How could you turn the triangles so they would fit together?)

Criteria 3: The child correctly Criteria 3: The child correctly Criteria 3: The child was not named all of the shapes used and named all but one of the shapes able to name two or more of the created in their flag. in their flag. shapes used in this activity.

Other Evidence:

Before During After Whole group KWL chart – Shapes Hands on activities Fill in L section of KWL chart. Complete K and W sections with Videos Assessments whole class. Read Aloud Books Daily oral math –ongoing to Pre-assessment- written review concepts and vocabulary Shape Walks Introduce vocabulary Bell work – ongoing to review Informal Assessments concepts and vocabulary Fill in attribute chart as a class as Journals children examine shapes as a whole group. Worksheets

UBD Unit Design Worksheet / Saginaw Valley State University 5 Describe the assessment/s and state the prompt if applicable. x F x S

What type of scoring tools will be used for evaluation? □ Analytic rubric x Checklist x Holistic rubric x Answer Key □ Criterion rubric □ Other

Student Self-Assessment and Reflection:

Draw a picture and write or dictate what you knew about how we use shapes before we started the unit. Draw a picture and write or dictate what you know about how we use shapes after we finished the unit.

Stage 3 – Learning Plan

WHERETO Considerations for the Learning Plan

W In this unit of study, first grade students will discover that they live in a world surrounded by shapes. They will understand that shapes can be composed and decomposed to create new shapes. Further, they will learn that some attributes define a shape and that others do not. Students will then be able to use the defining attributes to describe and sort shapes. Through hands on investigations and activities, they will learn to recognize shapes from a variety of orientations. With respect to measurement, they will develop initial understanding of fractional shares and congruence.

H Through entertaining videos, books and shape walks, students’ interest in the unit will be sparked. A variety of activities which incorporate varied learning styles will serve to enhance learning and maintain interest throughout the unit. Teacher will tailor learning to varied needs by offering the alternative learning centers and allowing students to select which one to complete. Additionally, students can be directed to activities which will help them practice and become proficient with both the knowledge and application of skills.

E Students will be equipped with skills through direct instruction, videos, books and activities in centers which are described below in the Basic section of Learning Activities. Application of the skills will take place as students sort, compose, decompose, and divide shapes. During these activities, students will have the opportunity to rethink and revise their thinking.

R Students will have the opportunity to reflect on their learning through: completing activities in the application and learning sections, discussion with peers, journaling, teacher feedback, and reviewing the results of formal assessments.

UBD Unit Design Worksheet / Saginaw Valley State University 6 E Students will self-evaluate, rethink, and revise strategies as they work independently to build, sort, and manipulate shapes. They will also have the opportunity to express what they have learned and evaluate their work as they journal, share ideas with classmates and discuss problems and solutions with the teacher.

T The varied learning styles and needs of students are addressed in the instruction of concepts by including multiple forms of instruction including videos, songs, discussions and activities such as scavenger hunts. As the unit progresses, students have the opportunity to select from numerous activities to explore and practice new skills and to demonstrate learning.

O The unit is organized to sequence the learning from simplest to more complex. Initially students will learn basic skills for plane shapes, and then progress to the more complex concepts of solids. They will then apply the skills with activities in the application section of learning activities. Again, students will begin with plane shapes and progress to solids. During this time, teacher will be conducting both formal and informal assessments which will assist him/her in directing students to next area of focus. The unit will culminate with a final project designed to allow students to showcase what they have learned and for the teacher assess learning.

Stage 3 - Learning Plan Differentiated Instruction :

Objectives: Students will compose and decompose two and three-dimensional shapes. In doing so they will understand that a shape has attributes that define it. They will also build an understanding of part-whole relationships and will be able to divided circles and rectangles into 2 or 4 equal parts, and name the fraction that the part represents.

BASIC: What basic new knowledge do I need them to know/learn?

1. Knows shape-attribute names sides, corners, faces, slide, roll, curved, flat, open, closed, edge.) 2. Knows names of shapes (Rectangles, squares, trapezoids, triangles, hexagons, circles, half-circles, quarter circles, cubes, rectangular prism, cone, sphere, cylinder, and pyramid. 3. Understands the basic concept of congruence and equal shares. Understands that things can be divided into equal pieces and that pieces have names: half, quarter and can use phrases half of and quarter of. 4. Understands that some attributes (color, size, orientation) do not define a shape.

APPLICATION: How can they apply this new information to previous information? Apply, compare, manipulate, and demonstrate.

1. Can name and compare two-dimensional shapes and organize them based upon defining attributes. 2. Can construct two-dimensional shapes given attributes. 3. Can combine two-dimensional shapes to form other two-dimensional shapes. 4. Can name and compare three-dimensional shapes and organize them based upon defining attributes. 5. Can combine three-dimensional shapes to form other shapes.

UBD Unit Design Worksheet / Saginaw Valley State University 7 6. Can identify shapes that have been combined to form composite shape.

LEARNING: What debatable issue in the real world deals with this topic? Current events, debates, leadership decisions.

Students will study the United States flag and understand the shapes and symbolism in it. They will design a classroom flag following instructions provided.

Learning Activities: (consider the WHERE TO elements)

BASIC (Level C) One-dimensional shapes and attributes  Together with teacher, students will complete a KWL chart about what they know about shapes.  Read the poem, Four Shapes by Katherine Mead and then go on a scavenger hunt in the classroom to find shapes. Labels will be placed on the shapes identifying their names.  Sing shape songs.  View and discuss United Streaming Video: The Number Crew- Shape Escape  View and discuss United Streaming Video: The Number Crew- Shape Sorting  Sort shapes by one attribute.  One shape patterns – Using only one shape, make a pattern by flipping or turning the shape.  Match game – Match shape names with shapes in learning center.  Play concentration – matching shape names with pictures.  Place three dimensional shapes in a bag. Without looking, have student reach into bag and identify what shape they are touching by “feel” - Work with a partner and tally each time your answer is correct.  Complete vocabulary worksheets: Teacher will say- color all circles blue, color all squares green… -or- Color all of the shapes with three sides yellow; color all of the shapes with 6 sides blue, cross out all of the open shapes.  Poster center: – Next to each picture of a three-dimensional shape, trace the faces of the shape. Identify how many faces and their shapes. – Next to each picture (made from rubber stamps) of a three-dimensional shape, find pictures of the shape in a magazine and glue it on the poster. Two-dimensional shapes and attributes  Together with teacher, students will complete a KWL chart about what they know about solid shapes.  Have class help with preparation of compare/contrast Venn diagram(s) to compare a plane and solid shape such as circle and sphere, or square and cube.  Introduce vocabulary: face, edge, curved, flat, roll, slide by using large shapes to demonstrate. (Beach ball, waste basket, tissue box….)  View United Streaming Video: Math Monsters: Geometry  Learn Math monster three-dimensional shape song.  Go on a shape hunt and look for three dimensional shapes and combination of shapers in the classroom.  Allow child to choose one three-dimensional shape. Use the faces as a template to trace and cut out shapes. Use the shapes to create a picture or design.  Count the edges center. Mark the edge of each three dimensional shape with a washable marker as it

UBD Unit Design Worksheet / Saginaw Valley State University 8 is counted. Count the edges and record on sheet.  Journal- Name a solid shape and draw and name a real-world object that represent the solid shape.  Make a vocabulary book – Use stamps and pictures for both two and three dimensional shapes. Fractional Parts and Names  View and discuss United Streaming Video: The Number Crew – Action With Fractions  Whole group discussion and think-pair-share of a time when have you ever had to divide something to share. How did you do it?  Classify squares, rectangles, and circles that have been divided by the categories: Equal Pieces, Unequal Pieces. (If needed, students will cut out the pieces to help them see congruence.)  Read Apple Fractions  Match fractions and fraction-words with pictures which show the correct piece shaded in. (Or – play concentration using the cards.)

APPLICATION (Level B) Sort and construct plane shapes by attribute  Place a set of plane shapes and a set of attribute cards in a center. Partners turn over first attribute card and take turns selecting shapes that have the attribute and setting them under the attribute card.  Children will be given a square, trapezoid and triangle pattern block. They will use them as templates to make a picture specified on a picture card (for example: a rocket, a boat, a house).  Place a set of plane shapes in a center. Partner 1 will organize the shapes into 2 piles based on a selected attribute. Partner 2 will guess the attribute used. Switch roles.  Child will use rubber stamps with shapes, or precut one-dimensional shapes for this activity. They will select an attribute card and write it on their 2-column paper. They will stamp or glue shapes into column YES or column NO to show if shape has the stated attribute.  Children will use pipe cleaners and clay, or marshmallows and pretzels to create two dimensional shapes and will glue them on paper with the proper shape name.  Math worksheets. Circle or color all of the shapes which have the specified attribute.  Math journal – Draw a group of shapes. Write a sorting rule and show how you would sort the shapes using the rule. Combine plane shapes to compose new shapes.  Place pattern blocks in a center and have children find as many ways as they can to cover template shapes that are provided. Trace the shapes to show how they covered it. (For example: Give students a hexagon template and have them find how many ways they can cover it using other shapes.)  Provide templates for children to cover using tangram pieces.  Provide each child in a group with a matching set of 3 or 4 pattern block pieces. Tell them to assemble the pieces so that the new shape has the least amount of sides. Compare and discuss. Sort and construct solid shapes by attribute  Place a set of three-dimensional shapes or pictures of three-dimensional shapes and a set of attribute cards in a center. Partners turn over first attribute card and take turns selecting shapes that have the attribute and setting them under the attribute card.  Place a set of solid shapes in a center. Partner 1 will organize the shapes into 2 piles based on a selected attribute. Partner 2 will guess the attribute used. Switch roles.  Math journal – Pick 2 solids. Describe how they are the same and different.  Child will use rubber stamps with solid shapes for this activity. They will select an attribute card and write it on their 2-column paper. They will stamp shapes into column YES or column NO to show if shape has the stated attribute.

UBD Unit Design Worksheet / Saginaw Valley State University 9  Children will find pictures of real-world objects that represent three dimensional shapes. They will sort the shapes into groups. They will create a poster stating the attribute that they sorted by. On one side they will all of the shapes have the attribute and the other side will be shapes that do not.  Child will use geometric solid construction set, marshmallows and pretzels, or tinker toys to build three dimensional shapes.  Children will match nets with the solid shape that they match.  Children will use two identical sheets of paper to create two different size cylinders. Combine solid shapes to compose new shapes.  Children will be given geometric solids. They will use them make a specified object (for example: a rocket, a house, a table with legs. (For example, one center may include only cubes and child must build a tall building with a chimney. Another center may include cones rectangular prisms and cylinders and the child must build a space ship.)  Look at picture of real-world objects provided by the teacher. Identify the geometric solids that were used to make each object.  Give students base shape and silhouette of a building. Have them construct the building.  A group of students will work independently using up to 24 cubes to create rectangular prisms. Compare prisms. How are they the same? Different?  Same activity as above except ask students to make their prism the tallest (longest, shortest, widest)  Design rectangular, square and round pizzas. Fold them to divide and them equally and cut them up. Label pieces with fractional shares.  Use play-doh and cookie cutters to make circles or squares. Cut them into two and 4 equal pieces. Describe what happens as the pieces get cut into more pieces. Reassemble the original shapes.  Flag center – Center will contain flags from around the world that have identifiable plane shapes, color patterns or color areas that divide the flag into equal fractional parts. Students will select a flag and present to the class, all the math it contains. Shapes it contains, Fractional parts it is divided in to. Color patterns.

LEARNING (Level A) Performance Tasks: See GRASPS activity.

Essential Vocabulary Above: in, at or to a higher place. Analyze: to examine carefully and in detail so as to identify causes, key factors, possible results, etc. Angles: two rays sharing a common endpoint. Area: the size a surface takes up measured in square units. Behind: at or toward the rear of. Below: in or toward a lower place. Beside: by or at the side of. Building: anything built or constructed Circle: a ring, circlet, or crown. Closed: forming a barrier; not open Columns: items arranged in a vertical line. Combine: to bring into or join in a close union or whole.

UBD Unit Design Worksheet / Saginaw Valley State University 10 Essential Vocabulary Compare: to examine (two or more objects, ideas, people, etc.) in order to note similarities and differences. Compose: to make or form by combining things, parts, or elements. Cone: a solid shape with a circular base and a curved surface that tapers to a point. Congruent: having the same size and same shape. Corners: point where surfaces meet – vertex. Cube: a solid shape that has 6 square faces all equal in size, 8 corners, and 12 equal edges. Curve: continuously bending line, without angles. Curved: a line that is not straight. Cylinder: a solid shape with one curved surface and two congruent circular bases. Describe: to tell or depict in written or spoken words; give an account of. Different: not identical; separate or distinct. Divide: to separate into parts, groups or sections. Equal: evenly proportioned or balanced. Having the same amount or value. Faces: flat surface of a 3-D shape. Flat: having little or no depth. Flip: to turn over. Fourths: one of four equal parts. Fraction: any part of a group, number or whole. Halves: one of two equal parts. Hexagon: a polygon with 6 sides. Identify: to recognize or establish as being a particular person or thing. In Front Of: a place or position directly before anything. Length: distance from one end to the other. Model: a representation, generally in miniature, to show the construction or appearance of something. Name: to give the name of. Next To: nearest in place or position. Octagon: a polygon with eight sides. Open: to permit passage through the opening. Oval: having the general form, shape, or outline of an egg; egg-shaped. Pentagon: a polygon with five sides. Prism: a solid three-dimensional shape with two identical parallel bases. All other faces are rectangles. A prism takes its name from the shape of its base, e.g. square prism, triangular prism, and hexagonal prism. Pyramid: a solid shape with a polygon as a base and triangular faces that taper to a point. A pyramid takes its name from the shape of its base. Rectangle: a parallelogram having four right angles. Rectangular Prism: a prism with two identical, rectangular bases. Roll: to move along a surface by revolving or turning over and over, as a ball or a wheel. Rows: items arranged in a horizontal line. Sides: the line or curve on the edge of a shape joining its vertices. Similar: having the same shape but not necessarily the same size. Size: how big or small something is. Slide: to move an item in any direction without rotating it. Sphere: three-dimensional solid that is perfectly round. A ball. Square: a rectangle having all four sides of equal length. Square Pyramid: a pyramid with a square base. Thirds: one of three equal parts. Three Dimensional: having 3 dimensions; length, width and height.

UBD Unit Design Worksheet / Saginaw Valley State University 11 Essential Vocabulary Triangle: closed plane figure having three sides and three angles. Triangular Prism: a prism with two identical, triangular bases. Turn: to rotate around a point. Two dimensional: having 2 dimensions; length and width. Vertices: a point where surfaces meet – corner. Whole: all the parts, total amount.

Sequencing the Learning Throughout unit, teacher will be monitoring individual student progress and directing student to activity choices which will help them practice and master skills required for success with the unit. Monday Tuesday Wednesday Thursday Friday Layer C (Basic Layer C (Basic Layer C (Basic Layer C (Basic Layer C (Basic activities) activities) activities) activities) activities)

Teacher led Basic Continue student Teacher led Basic Teacher testing of Teacher led Basic activities on one- activities for one- activities for solids. two and three- activities for dimensional dimensional shapes. dimensional shape fractions. shapes. Introduce and begin and attribute names. Teacher testing of student activities Introduce and begin Introduce and begin two-dimensional for solid shapes. student activities for student activities shape and attribute fractions. for one- names. dimensional Teacher testing of shapes. recognition of equal parts as well as fraction names half and quarter.

Monday Tuesday Wednesday Thursday Friday

UBD Unit Design Worksheet / Saginaw Valley State University 12 Layer B Layer B Layer B Layer B Layer B (Application (Application (Application (Application (Application activities) activities) activities) activities) activities)

Teacher testing of Teacher testing of Continue with layer Teacher testing of recognition of ability to sort and C activities ability to combine equal parts as well construct plane including more two-dimensional as fraction names shapes by attribute. direct instruction shapes to form half and quarter. for any areas not other two- Continue with layer mastered by dimensional shapes Continue with layer C activities individual students) and to identify C activities including more shapes that have including more direct instruction been combined to direct instruction for any areas not form composite for any areas not mastered by shape. mastered by individual students) individual students)

Monday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday

Layer B Layer B Layer B Layer A (Learning Layer A (Learning (Application (Application (Application activities) activities) activities) activities) activities)

Teacher testing of Teacher testing of Teacher testing of ability to compare ability to combine ability to divide three-dimensional three-dimensional circles and squares shapes and shapes to form other into halves or organize them shapes and to quarters and to based upon identify shapes that name parts. defining attributes have been combined to form composite shape.

Note: In addition to formal rubric for Layer A learning activities, teacher testing of learning will be accomplished through ongoing quizzes, tests, journals, observations, dialogs, and work samples.

UBD Unit Design Worksheet / Saginaw Valley State University 13