Second Grade Unit 5: Understanding Plane and Solid Figures3 weeksIn this unit students will: further develop understandings of basic geometric figures identify and describe plane figures and solid figures based on geometric properties expand the ability to see geometry in the real world partition shapes into equal shares by cutting, slicing, or dividing represent halves, thirds, and fourths using rectangles and circles to create fraction models compare fractions created through partitioning same-sized rectangular or circular wholes in different ways understand what an array is and how it can be used as a model for repeated addition Unit Resources:Unit 4 Overview video Parent Letter Number Talks Calendar Vocabulary CardsPrerequisite Skills Assessment Sample Post Assessment

Topic 1: Reasoning About Shapes and Their AttributesBig Ideas/Enduring Understandings: Describe plane figures according to their characteristics (sides, corners, angles). Describe solid figures according to their characteristics (faces, edges, vertices). Describe and understand the relationships (similarities and differences) between solid figures and plane figures. Recognize the relationship between geometry and the environment. Compare geometric figures to similar objects in everyday life. Identify and represent the fractional parts of a whole or of a set (halves, thirds, fourths). Recognize and represent that differently partitioned fractional parts of same-sized rectangles or circles are equal. Identify the number of rows and columns in an array and count the same-size squares to find the total. Identify and describe plane figures and solid or hollow figures according to geometric properties Develop an understanding of the relationship between solid or hollow figures and plane figures Understand that the faces of solid or hollow figures are plane figures Further develop spatial awareness of geometric solids and figures Investigate what happens when geometric figures are combined and cut apart Recognize plane and solid figures in the real world Repeatedly adding the same quantity or forming a rectangular array are strategies for repeated addition Fractional parts are equal shares of a whole number, whole object, or a whole set The more equal sized pieces that form a whole, the smaller the pieces (fraction) will be When the numerator and denominator are the same number, the fraction equals the number one or one whole (entire object or set) The fraction name (half, third, fourth) indicates the number of equal parts in the whole Equal shares of identical wholes may not have the same shape. For example, fourths can be represented in multiple ways (i.e. with diagonal, horizontal, vertical

cuts) and although they look different they represent the same amount/size piece 1

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Essential Questions: How do we describe geometric figures? Where can we find geometric figures in the world around us? How do we use the following terms: angle, vertex, face, side, and edge to describe geometric figures? How do we apply the use of fractions in everyday life? How do we know how many fractional parts make a whole? When is it appropriate to use fractions?Content StandardsContent 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.Reason with Shapes and Their Attributes MGSE2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles,

quadrilaterals, pentagons, hexagons, and cubes.

MGSE2.G.2 Partition a rectangle into rows and columns of same-size squares to find the total number of them.

MGSE2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Vertical Articulation of GeometryFirst Grade Geometry StandardsReason with shapes and their attributes MGSE1.G.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.

MGSE1.G.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.6 This is important for the future development of spatial relations which later connects to developing understanding of area, volume, and fractions.

MGSE1.G.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.

Fourth Grade Geometry StandardsDraw and identify lines and angles, and classify shapes by properties of their lines and angles. MGSE4.G.1 Draw points, lines, line segments, rays, angles (right, acute,

obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

MGSE4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

MGSE4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

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Geometry Instructional StrategiesMGSE2.G.1This standard calls for students to identify (recognize) and draw shapes based on a given set of attributes. These include triangles, quadrilaterals (squares, rectangles, and trapezoids), pentagons, hexagons and cubes. Prior to teaching the unit, you can use the plane shapes graphic organizer as a whole class assessment or give each child a copy and have them list everything they know about the given shapes.

Example:Draw a closed shape that has five sides. What is the name of the shape? Student Response - I drew a shape with 5 sides. It is called a pentagon.

Students identify, describe, and draw triangles, quadrilaterals, pentagons, and hexagons. Pentagons, triangles, and hexagons should appear as both regular (equal sides and equal angles) and irregular.

Students recognize all four sided shapes as quadrilaterals. Students use the vocabulary word “angle” in place of “corner,” but they do not need to name angle types.

Spatial sense is an important component of geometry. Spatial sense is an intuition about shapes and the relationships among shapes. Rich experiences with shape and spatial relationships help develop students' spatial sense. Students begin this experience by working with two and three dimensional shapes. As students look at how shapes are alike and different, they begin to see the properties of shapes. Students need to see shapes in different sizes and orientations. Triangles should be more than equilateral and not always show the vertex at the top. Students need to sort shapes based on their similar characteristics. Students need to experiment with composing and decomposing shapes so they can see how to form larger shapes from smaller shapes. A rectangle can be makeup of two triangles. Essential vocabulary for this standard includes: rectangle, row, column, angle, face, triangle, quadrilaterals, pentagons, hexagons, and cube.Geosticks, geoboards, interactive whiteboards, and document cameras may be used to help identify shapes and their attributes. Shapes should be presented in a variety of orientations and configurations.

MGSE2.G.2This standard calls for students to partition a rectangle into squares (or square-like regions) and then determine the total number of squares. This relates to the

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standard 2.OA.4 where students are arranging objects in an array of rows and columns. It is important to note that this standard supports the third grade work in understanding area (primarily) and fractions (secondarily). This standard may be taught in the context of geometry initially, and may move to a fractional view when student thinking leads in that direction, as connected to 2.G.3 using a square as the rectangle to be partitioned. As students partition rectangles into rows and columns to determine the total number of squares, they should recognize that there are no gaps or overlaps between the same size squares.

This is the beginning of connecting a geometric representation to multiplication and area. Students can draw arrangements using base ten blocks and then count the total number of blocks. The focus is on the geometric representation not multiplication. The concept of multiplication is introduced in grade 3. Essential vocabulary for this standard includes: rectangle, row, and column.

Example:Split the rectangle into 3 rows and 4 columns. How many small squares did you make? (Rows are horizontal and columns are vertical)

This standard is a precursor to learning about the area of a rectangle and using arrays for multiplication. An interactive whiteboard or manipulatives such as square tiles or other square shaped objects can be used to help students’ partition rectangles.

Modeling multiplication with partitioned rectangles promotes students’ understanding of multiplication. Tell students that they will be drawing a square on grid paper. The length of each side is equal to 2 units. Ask them to guess how many 1 unit by 1 unit squares will be inside this 2 unit by 2 unit square. Students now draw this square and count the 1 by 1 unit squares inside it. They compare this number to their guess. Next, students draw a 2 unit by 3 unit rectangle and count how many 1 unit by 1 unit squares are inside. Now they choose the two dimensions for a rectangle, predict the number of 1 unit by 1 unit squares inside, draw the rectangle, count the number of 1 unit by

1 unit squares inside and compare this number to their guess. Students repeat this process for different-size rectangles. Finally, ask them to what they observed as they worked on the task.

It is vital that students understand different representations of fair shares. Provide a collection of different-size circles and rectangles cut from paper. Ask students to fold some shapes into halves, some into thirds, and some into fourths. They compare the locations of the folds in their shapes as a class and discuss the different representations for the fractional parts.To fold rectangles into thirds, ask students if they have ever seen how letters are folded to be placed in envelopes. Have them fold the paper very carefully to make sure the three parts are the same size. Ask them to discuss why the same process does not work to fold a circle into thirds. Use an analog clock as a model and allow children to draw a line from the center of the clock to the place where the 12, 4 and 8 are on the clock face. This will divide the circle into three equal sections. This clock connection can also be made for discussing halves and fourths and discovering to which numbers (or hours) you would draw the lines to in order to create two or four equal parts/pieces.

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MGSE2.G.3This standard calls for students to partition (split) circles and rectangles into 2, 3 or 4 equal shares (regions). Students should be given ample experiences to explore this concept with paper strips and pictorial representations. Students should also work with the vocabulary terms halves, thirds, half of, third of, and fourth (or quarter) of. While students are working on this standard, teachers should help them to make the connection that a “whole” is composed of two halves, three thirds, or four fourths. This standard also addresses the idea that equal shares of identical wholes may not have the same shape.

This standard is the first exposure to some fractional concepts. This experience should allow students to divide circles and rectangles into equal parts. It is not necessary to define these as fractions with a numerator and denominator. Instead the focus should be on the terms halves, thirds, and fourths. When we divide a circle into two, three, or four equal parts, they can be described by half, thirds, and fourths. Emphasize that it takes two halves, three thirds, and four fourths to make the circle or rectangle. Essential vocabulary for this standard includes: equal shares, whole, halves, thirds, and fourths.

Example: Divide each rectangle into fourths a different way.

This standard introduces fractions in an area model. Students need experiences with different sizes, circles, and rectangles. These different partitions of a square afford the opportunity for students to identify correspondences between the differently-shaped fourths (SMP.1), and to explain how one of the fourths shown in these squares can be transformed into one of the “other” fourths shown. (SMP.7).

For example, students should recognize that when they cut a circle into three equal pieces, each piece will equal one third of its original whole. In this case, students should describe the whole as three thirds. If a circle is cut into four equal pieces, each piece will equal one fourth of its original whole and the whole is described as four fourths.

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It is important for students to see circles and rectangles partitioned in multiple ways so they learn to recognize that equal shares can be different shapes within the same whole. An interactive whiteboard may be used to show partitions of shapes.

Geometry Common MisconceptionsSome students may think that a shape is changed by its orientation. They may see a rectangle with the longer side as the base, but claim that the same rectangle with the shorter side as the base is a different shape. This is why is it so important to have young students handle shapes and physically feel that the shape does not change regardless of the orientation, as illustrated below:

If students are only shown equilateral triangles then when they see scalene or isosceles triangles, they do not recognize them as triangles even though they have three sides. So you must make sure you are always showing students various types of shapes and not just the regular shapes that they see in pattern blocks and on posters.

Students also may believe that a region model represents one out of two, three or four fractional parts without regard to the fact that the parts have to be equal shares, e.g., a circle divided by two equally spaced horizontal lines represents three thirds.

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DifferentiationMGSE2.G.1 – Increase the Rigor Draw a shape. Write at least 3 clues, using angles and sides. Ask your friend to guess your shape. What shapes can you make with 2 identical short straws and 2 identical long straws? Draw 2 different quadrilaterals. Compare them. What is same/different about them? Is a rectangle always a square? Is a square always a rectangle? I have six faces, what solid shape might I be? Can a shape have 4 sides and 3 angles? Explain your thinking.

MGSE2.G.2 – Increase the Rigor Frank wants to build a garden in his backyard. He wants to grow different vegetables. Draw a large rectangle and partition it into equal rows and columns.

Label each section with a different vegetable. How many different vegetables did Frank grow in his garden? The following year, Frank wants less types of vegetables. What could his garden look like?

Heather ordered a Ledo’s pizza (rectangular). She asks them to cut her pizza into 15 equal pieces, how many rows and columns will her pizza have? If you make a square cake and you cut it into 4 rows with 3 pieces in each row, how many pieces of cake will you have? If you rotate the cake 90 degrees, will

you still have the same number of cake pieces? Sally bakes a rectangle pan of brownies. How many equal pieces can she cut the brownies into? Find two other options.

MGSE2.G.3 – Increase the Rigor It’s field day at our school! Four classes must share the rectangular play area equally. Show different ways to share the field and describe the area using the

word fourth. What other shape could the play area be to be shared equally with these four classes? Enrichment: Now six classes must share the same area. Show different ways to share the field. Show how to share with eight classes.

Jane went to two different birthday parties on the same day. At the first birthday party, the cake was a square and it was cut into fourths diagonally. At the second birthday party, the cake was the same sized square but it was cut into fourths horizontally. Jane says her piece of cake was bigger at the first party. Is she right? Use drawings to support your answer.

How many different ways can you cut a rectangle into fourths? Show me. Your family is going on a vacation. You need to leave your dog at the dog care center. The dog care center is an exact square. Three other dogs will be at the

dog care center with yoru dog. Create a place for your dog to have an equal amount of space to eat, sleep, and play. What does it look like? Draw your kennel.

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Evidence of Learning

Adopted ResourcesMy Math:Chapter 12: Geometric Shapes and Equal Shares12.1 Two-Dimensional Shapes12.2 Sides and Angles12.4 Three-Dimensional Shapes12.5 Faces, Edges, and Vertices12.6 Relate Shapes and Solids12.7 Halves, Thirds, and Fourths

*These lessons are not to be completed in consecutive days as it is way too much material. They are designed to help support you as you teach your standards. All lessons should be taught at the concrete and representational level as second grade students need base ten blocks to support their learning. Even though the problems are vertical, solving problems on a number line or using a partial sums strategy is perfectly appropriate.

Adopted Online Resourceshttp://connected.mcgraw-hill.com/connected/login.do

Teacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

http://www.exemplarslibrary.com/

User: Cobb EmailPassword: First Name

Suggested Exemplars: Paleontologist Pentomino Problem How Many Vertices? Counting Corners Happy Birthday Abby

Think Math:Chapter 9: Two-Dimensional Figures and Spatial Sense.9.1 Sorting Polygons by Attributes9.3 Building with Triangles9.6 Cutting Polygons Apart

Chapter 7: Doubling, Halving, and Fractions7.1 Exploring One Half7.6 Thirds and Fourths

Chapter 14: Comparing and Contrasting Three-Dimensional Figures14.1 Two and Three Dimensional Figures14.2 Faces14.3 Edges14.4 Vertices

Additional Web Resources K-5 Math Teaching Resources (Press CTRL + Click the link to view the resources): http://www.k-5mathteachingresources.com/2nd-grade-geometry.html

Estimation 180 ~ http://www.estimation180.com/days.html

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MGSE2.G.1Geoboard Quadrilaterals

Skeletal ModelsThe Greedy Triangle

MGSE2.G.2Cover a Rectangle

MGSE2.G.3Geoboard Halves Fraction Barrier Game

Tangram ShapesMy Shape Riddle

Greg Tang ~ http://www.gregtang.com

Everyday Math E-Tool Kit ~ http://media.emgames.com/em-v2/eToolkit/eTools_v1.swf

National Library of Virtual Manipulatives ~ http://nlvm.usu.edu/en/nav/vlibrary.html

Illustrative Mathematics (Tasks listed below) https://www.illustrativemathematics.org/content-standards/2/G/A/1/tasks/1506*Press CTRL + Click the link to access each of the Illustrative Mathematics tasks:

Learn Zillion (Press CTRL + Click the link to view the tutorials):MGSE2.G.1Identify trianglesIdentify quadrilateralsIdentify pentagonsIdentify hexagonsIdentify cubesDraw shapes with a specified number of sidesDraw shapes with a specified number of anglesDraw cubesMGSE2.G.2Partition rectangles using same-sized squaresPartition rectangles into same-sized squares using toothpicksPartition rectangles into same-sized squares by creating columns and rowsPartition a rectangle into rowsPartition a rectangle into columnsFind the number of same-size squares in a rectangleMGSE2.G.3Partition a circle into equal sharesPartition a circle into two, three, or four equal sharesFind a unit fraction by dividing a shape into equal sharesCount unit fractionsDescribe fractions of rectangles

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Partition rectangles into equal shares multiple waysDescribe fractions of rectangles by counting equal sharesCount fractions of a whole using fraction stripsCompare equal shares from different wholesSuggested ManipulativesFraction StripsFraction CirclesGeoboardsAngLegsTangramsCentimeter CubesInch CubesSquare TilesGeometric SolidsPattern Blocks

Vocabulary angleattributecirclecolumncubeedgefacefourthsfractionhalveshexagonirregular polygonpartitionpentagonpolygonplane figurequadrilateralrectangleregular polygonrowshapessolid figuresquarethirdstrapezoidtrianglevertex/vertices

Suggested Literature The Greedy TriangleWhen a Line Bends…A Shape BeginsCaptain Invincible and the Space ShapesWindows, Rings, and Grapes – A Look at Different ShapesThe Shape of ThingsGive Me Half!Each Orange Had 8 SlicesIf You were a PolygonIcky Bug ShapesIf You were a Quadrilateral

State Task DescriptionsScaffolding Task Task that build up to the learning task.Constructing Task Task in which students are constructing understanding through deep/rich contextualized problem solving Practice Task Task that provide students opportunities to practice skills and concepts.

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Culminating Task Task designed to require students to use several concepts learned during the unit to answer a new or unique situation. Formative Assessment Lesson (FAL)

Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.

3-Act Task Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

Unit 5 State Tasks – Reasoning with Shapes and Their AttributesTask Name Task Type/

Grouping Strategy Content Addressed Standard(s) Task DescriptionStudents will:

Natural Shapes 3-Act TaskWhole Group Describe geometric figures MGSE2.G.1

Use mathematical vocabulary to explain discoveries of shapes within their natural world.

Shape RobotScaffolding Task

Large Group/Partners

Describe geometric figures MGSE2.G.1Identify shapes, create a robot and graph shapes used to

create robot. Technology link available.

The Shape of ThingsPractice Task

Large Group/Partners

Describe geometric figures MGSE2.G.1Identify, name, and describe 2-D and 3-D shapes found in

the world using defining attributes including but not limited to: angles, vertices, sides, faces, and edges.

Greedy ShapesPractice Task

Large Group/Partners

Describe geometric figures MGSE2.G.1Explore defining attributes of triangles and classify

polygons.

The Curious Case of the Cube

Scaffolding TaskLarge Group/Small

Group

Visualizing and creating a cube based on attributes

MGSE2.G.1Understand defining attributes of the platonic solid, cube so

as to be able to visualize it. Use understanding of defining attributes to create a cube using simple materials.

Net or Not? Performance TaskPartners Attributes of a cube MGSE2.G.1 Identify various ways to create a cube based on its defining

attributes. Technology link available.

Sharing Equally Constructing TaskPartners

Partitioning rectanglesIdentify, label, and compare

fractions

MGSE2.G.3Given a real life scenario students will explore sharing

equally to begin laying the foundation for fractions.

Grandma’s Quilts Constructing TaskPartners Partitioning rectangles MGSE2.G.2 Apply understanding of partitioning rectangles and arrays

to create a paper quilt.

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Making RectanglesPractice Task

Large Group/Partners

Partitioning rectangles(area foundation)

MGSE2.G.2Through exploration, build multiple representations of 12 square units using square ties and record number of rows

and columns for each model.

Ribbon FractionsConstructing Task

Large Group/Small Group

Identify, label, and compare fractions

MGSE2.G.2MGSE2.G.3

Apply knowledge of equal shares to cut ribbon into halves, thirds, and fourths and compare the fractional parts.

Making a CakeConstructing Task

Large Group/Small Group

Identify, label, and compare fractions

MGSE2.G.2MGSE2.G.3

Work cooperatively to explain their process/strategy of portioning a whole into equal shares.

Fraction Cookies Constructing TaskIndividual/Partner Label and compare fractions MGSE2.G.3

MGSE2.MD.10

Model how to partition circles into halves, thirds, and fourths. Create a survey, collect data, and display the data

in an appropriate graph.

Country’s Flag Culminating TaskIndividual

ArraysDescribe geometric figures

Identify, label, and compare fractions

MGSE2.G.1MGSE2.G.2MGSE2.G.3

Use knowledge of 2-D shapes to create a flag that has been partitioned into more than one part.

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