2-Dimensional Geometry



2-D and 3-D Geometry

Second Grade

|Table of Contents |Page No. |

|2-D Geometry (Plane Figures) | |

|Part 1 Polygons and Their Attributes |1 |

|Polygon Sort Cards |3 |

|Play-Doh Student Sheet |14 |

|Identifying Polygons ~ 5 to 12 sided |20 |

|Guided Practice Questions |25 |

|Part 2 Quadrilaterals |28 |

|Tracing Cards |31 |

|Part 3 Composing and Decomposing 2-D Shapes |32 |

|Guided Practice Questions |36 |

|Part 4 Additional 2-D Resources |43 |

| | |

|3-D Geometry (Solid Figures) |44 |

|Part 5 3-D Shapes Introduction |44 |

|Part 6 Building Shapes and Recording Attributes |46 |

|Triangular Prism and Rectangular Prism |46 |

|Square Prism and Cube |48 |

|Pyramids |50 |

|Cone, Cylinder and Sphere |50 |

| |51 |

|Part 7 Comparing Prisms |53 |

|Part 8 Composing 3-D Shapes |53 |

|Identify Faces on 3-D Shapes |53 |

|Discovering Nets |63 |

|Geometric Net Pattern |55 |

|Guided Practice 1 |56 |

|Using 3-D Figures to Make Other Solids |57 |

|Guided Practice 2 |58 |

|Additional 3D Resources |58 |

|Part 9 Alternative Assessment |58 |

|Guidelines |59 |

|Alternative Assessment |60 |

|Teacher Recording Sheet |62 |

|Word Bank | |

2-Dimensional Geometry

Plane Figures

TEKS 2.8 A create two-dimensional shapes based on given attributes, including number of sides and vertices;

TEKS 2.8 C classify and sort polygons with 12 or fewer sides according to attributes,

including indentifying the number of sides and vertices;

TEKS 2.8 D compose two-dimensional shapes and three-dimensional solids with given

properties or attributes;

TEKS 2.8 E de-compose two-dimensional shapes such as cutting out a square from a

rectangle, dividing a shape in half, or partitioning a rectangle into identical

triangles and identify the resulting parts.

Vocabulary: side, angle, square-type angle, polygon, triangle, rectangle, square, quadrilateral, pentagon, hexagon, octagon, nonagon, decagon, heptagon, circle, 2-dimensional, 2-D, plane shape, attribute, vertex, vertices, dimensions

A “2nd Grade Geometry Glossary - Teacher Reference” (MATH_2_A_GEOMETRY1 2014_RES.doc) contains definitions.

Note that this is a teacher reference only and is not written in “kid-friendly” language.

Part 1 Polygons and Their Attributes

Materials: Polygon sort activity - yarn or hoola hoops for circles

Labels (A, B, Not Polygons, Polygons)

Polygon sort cards (pages 3 - 11)

posters of 2-D shapes (MATH_2_A_2D GEOMETRY2 2014_RES.ppt)

Plane Shape Construction – tiny Play-Doh balls, coffee stirrers or straws (different lengths depending on the shape being built), student copies of recording sheet on pages 14-18)

“True About Me” materials –

cards- (MATH_2_A_2D GEOMETRY3A 2014_RES.doc)

questions – (MATH_2_A_2DGEOMETRY3B 2014_RES.doc)

garbage cans – (MATH_2_A_2D GEOMETRY3C 2014_RES.doc)

student copies of guided practice questions #1 and #2 on page 25-27

student copies of 2-Dimensional Geometry Practice #1

(MATH_2_A_2D GEOMETRY IP1 2014_RES.doc)

Polygon IMN Activity

(MATH_2_A_2D POLYGON IMN ACTIVITY1 2014_RES)

1. Definition of Attribute

Before the students can examine the attributes of shapes, they must understand the meaning of the word attribute. The teacher may go through the “Gingerbread Man Attributes” slideshow (MATH_2_A_2D GEOMETRY1 2014_RES.ppt) to develop understanding of this word.

2. Polygon Sort

The activity which follows is a “discovery activity.” The objective is to determine the attributes of a polygon (3 or more straight sides, 2-D, and closed shape). The shapes from pages 3-11 will be used in this sort.

Create two large circles on the floor (hoola hoops or yarn circles). Label one circle “A” and the other “B.” Circle A will hold the non-polygons and Circle B will hold the polygons. Take the shapes one-by-one and place them in the appropriate circle. As you place them, ask students to see if they can determine how you are sorting the cards, or let them tell you which circle they think a particular shape will go into.

On the board, write down students’ thoughts on the rules you are using to sort the shapes. Be sure to have the students use the word attributes when discussing their “rules.” For example, “one attribute of a polygon is straight sides.”

After the shapes are sorted and the rules have been determined, trade the label “B” for “Polygons.” Replace label “A” with “Non-Polygons.”

Take each shape from the “Non-Polygon” circle and discuss what attribute keeps it from being a polygon.

Mix up the cards and, as a class, sort them again.

IMN Activity:

Discuss and complete the definition of a polygon then glue it on the right hand side.

A polygon is a ______-dimensional shape with _____ or more ________________ sides, and is a _______________ shape.

A preprinted form can be found in MATH_2_A_2D POLYGON IMN ACTIVITY1 2014_RES

On the left hand-side students should paste the directions found in MATH_2_A_2D POLYGON IMN ACTIVITY1 2014_RES and complete the activity:

Draw a polygon that wasn’t on our cards. Explain what attributes make it a polygon.

3. Shape Construction (Play-Doh and straws)

To provide students with an opportunity to examine the attributes of polygons, they will construct them using Play-Doh and straws.

Students may work in pairs to complete this activity. Each student will need a copy of the Recording Sheet (page 14-18).

Give each table group a set of laminated plane shapes or laminated 2-D posters to use to help them with this activity. Have the students look at the plane shapes and show you examples of sides and vertices. Tell them that these are two-dimensional shapes because they are flat. (The two dimensions are length and width.) Inform students that they will be using Play-Doh and straws to build these shapes.

A. The teacher may want to pre-bag the Play-Doh balls and straws to save time.

B. Pass out the bags that contain the Play-Doh and straws. The teacher may wish to give each partner pair one napkin or paper plate also.

C. Show the students how to make a pentagon. They should use straws of the same length for all sides. Take one straw and put one Play-Doh ball on each end.

Let’s take a side and attach it to a vertex.

Take more straws and Play-Doh balls to create a regular pentagon.

D. Ask the students the following questions:

How many straws did we use for the pentagon? 5

What do the straws represent? sides

Therefore, the pentagon has 5 sides. (Have students repeat the complete sentence.) The pentagon has 5 sides.

How many Play-Doh balls did we use for the pentagon? 5

Play-Doh balls stand for ________? vertices

So, who can say that in a complete sentence? A pentagon has 5 vertices.

Is the pentagon a polygon? yes

How do you know it is a polygon? straight sides, 2-D, closed

E. Guide the students in making an irregular pentagon (one in which all the sides are not equal or one in which all the angles are not obtuse). For example,

F. Now we are going to create more polygons. The students will use the materials to build the hexagon (6-sides), heptagon (7-sides), octagon (8-sides), nonagon (9-sides), decagon (10 sides), 11-sided polygon and 12 sided polygon. (Students are not responsible for the names of the 10, 11 or 12-sided polygon. They are only responsible for creating the polygons and recognizing their attributes.) They will record their attributes and the polygons they made on pages 14-18.

The teacher should circulate around the classroom asking students about their shapes. The students should respond in complete sentences and use geometric vocabulary words.

Play-Doh 2-D Geometry

Name _________________________

G. Students can practice classifying and sorting polygons up to 12 sides by their attributes using the shapes on page 20 and 21. The teacher calls out various attributes and students sort their figures accordingly. For example the teacher may say:

Polygons with 9 or more vertices, OR shapes with an odd number of sides, OR polygons with fewer than 5 vertices. Have students sort their figures into the category you called and put the others in a group labeled NOT.

This activity may be done individually, in partners or in table groups depending on the needs of your students. To save time, you may wish to have students count and label the number of vertices and sides before you call out each category.

4. Partner Work

The students will determine which attributes describe specific shapes by doing the “True About Me” activity for plane shapes (MATH_2_2D GEOMETRY3A 2014_RES) & (MATH_2_A_ 2D GEOMETRY3C 2014_RES).

After the above activity is completed, the teacher may wish to have students answer the five pencil-and-paper questions which go along with this activity, as well. (MATH_2_A_2D GEOMETRY3B 2014_RES)

Identifying Polygons

5. Guided Practice

Together read Guided Practice Question #1 (page 25) and insert the speed bumps. There are geometric shapes which can be given to each student (page 26), if the teacher so desires.

Complete Steps 1 and 2 of the problem solving process.

Step 3: Strategy

Use questioning strategies to evaluate each answer choice.

A. Which shape is a circle? (Display the paper copy.)

How many sides are on a circle? Let's count.

Since the circle is a curved figure, there are no sides. It has zero sides. (Put zero next to the word circle on the answer choices.)

(Use this opportunity to reinforce the concept of a polygon.)

A circle is not a polygon.

B. Which shape is a triangle? Hold up the triangle.

(Students hold up the triangle.)

How many sides are on a triangle? Let's count. (Trace the sides and number them as students count.)

There are 3 sides on a triangle. (Put 3 next to the word triangle on the answer choices.)

C. Which shape is a square? (Students hold up the square.)

How many sides are on a square? Let's count.

There are 4 sides on a square. (Put 4 next to the word square on the answer choices.)

D. Which shape is the pentagon? (Students hold up the pentagon.) How many sides are on a pentagon? Let's count.

There are 5 sides on a pentagon. (Put a 5 next to the word pentagon on the answer choices.)

Go back and re-read the main idea and details.

How many sides did Jasper draw? 3

What shape did he draw? triangle

Show me that shape. ( )

Step 4: How/Why

Responses may be similar to this.

I drew each shape.

I traced and counted the sides.

Jasper drew a triangle.

A triangle has 3 sides.

Follow the same questioning process for Guided Practice Question #2 on page 27.

6. Independent Work

Students will complete 2-Dimensional Geometry Practice #1 (MATH_2_A_2D GEOMETRY IP1 2014_RES).

7. IMN Suggestions

The preprinted form can be found in MATH_2_A_2D POLYGON IMN ACTIVITY2 2014_RES-2014

What strategy or strategies do you use to decide the name of a 2-D figure?

Jenny saw the following shape. She called it a hexagon.

Explain how you would help Jenny name it correctly.

Guided Practice Questions

1. Jasper drew a polygon that had 3 sides. What polygon could he have drawn?

A. circle

B. triangle

C. square

D. pentagon

Shapes

2. Allie made the following pentagon on her paper.

How many vertices are on this pentagon?

A. 3

B. 4

C. 5

D. 6

Part 2 Quadrilaterals

Materials: set of tracing cards for each student (page 31)

a large piece of construction paper for each student

1. Definition of a Quadrilateral

The teacher should draw polygons on the board. Some should be quadrilaterals and be placed in Group A. Some should not have 4 sides and be placed in Group B. Be sure to draw both regular and irregular polygons.

For example:

Group A Group B

Ask students, “What do you notice about the shapes in these groups?” (Allow plenty of think time.) In group A, all the shapes have 4 sides and 4 vertices. Group B shapes do not have 4 sides.

All polygons with 4 sides are called quadrilaterals. (Have each student in the room say the word quadrilateral. Replace the “Group A” label with the label “Quadrilaterals”. Replace the “Group B” label with the label “Not Quadrilaterals.”)

What are the attributes of quadrilaterals? (Students should examine the shapes drawn and come up with attributes.) A quadrilateral has 4 sides and 4 vertices. It is closed, has straight sides, and 2-D, i.e. it is a polygon.

2. Examination of Square, Rectangle, Quadrilateral, and Polygon

This activity is designed to aid students in identifying the attributes of rectangles, reviewing the attributes of quadrilaterals as just discussed, and identifying squares as special rectangles.

A. The student will fold a large piece of construction paper into four quadrants. They will label them Polygon, Quadrilateral, Rectangle and Square as shown on the next page.

The student should have 4 shapes which he/she can trace, a square, a rectangle which is not a square, a trapezoid, and a hexagon. All of these shapes can be traced from pattern blocks, except the non-square rectangle. Some samples of these shapes are on page 31.

B. Pull up the Smartboard (MATH_2_A _2D GEOMETRY4 2014_RES) which lists the attributes of polygons, quadrilaterals, rectangles, and squares. For each shape, go through all four of these words, determining which apply and which do not. The student will trace the shape under the words which apply to it.

For example,

(Pull up the polygon slide on the Smartboard.)

First, let’s look at this shape. (Hold up the hexagon.)

What is it? a hexagon

Let’s go through the attributes of a polygon and see if a hexagon is a polygon. ` (Using the Smartboard slide, discuss whether a hexagon meets these criterion.

It is 2-D.

It is closed.

It has straight sides.)

Is this hexagon a polygon? yes

Let’s trace the hexagon in the polygon section. (Trace.)

(Pull up the quadrilateral slide.)

Let’s see if a hexagon is a quadrilateral.

Let’s examine a quadrilateral’s attributes.

(Using the Smartboard slide, discuss whether a hexagon meets these criterion.

It is a polygon.

It has 4 sides.

It has 4 vertices.)

So, why isn’t a hexagon a quadrilateral? It has 6 sides.

(Pull up the rectangle slide.)

Let’s see if a hexagon is a rectangle.

(Check the attributes and again rule out the hexagon.

It is a polygon.

It is a quadrilateral.

It has 4 square-type angles.)

So, why isn’t a hexagon a rectangle? because it isn’t a

quadrilateral

(Pull up the square slide and examine a square’s attributes.

It is a polygon.

It is a quadrilateral.

It is a rectangle.

All the sides are the same length.)

The hexagon isn’t a square because ……

So which of these words can we use to describe a hexagon? only polygon

Let’s say that in a complete sentence. A hexagon is a polygon.

C. Go through these same slides with each of the other shapes. Trace the shape in any section in which it belongs. Therefore, the rectangle will be traced in three sections – polygon, quadrilateral, and rectangle. The square will be traced in all four sections.

When students are finished evaluating each shape, they should state what they have found out in a complete sentence. For example, “A square is a polygon, a quadrilateral, a rectangle and a square.”

Part 3 Composing and Decomposing 2-D Shapes

Materials:

rectangles p. 34 (several per student)

hexagons p. 35 (several per student)

student copy of Guided Practice Questions (pages 36-38) and accompanying shapes (pages 39-42)

student copy of practice questions (MATH_2_A_2D GEOMETRY IP2 2014_RES)

scissors

1. Exploration

Give each student a rectangle (p. 34). Instruct the students that they

1) may only make one straight cut through the rectangle, 2) must create two shapes with their cut, and

3) must be able to name the shapes they created.

Discuss the variety of shapes they created.

Give students another rectangle. This time they will make 2 straight

cuts which form 3 shapes they must be able to name.

Now give each student a hexagon (p. 35) and then apply the same three criteria as was given for the rectangle. The teacher may wish to provide an extra hexagon that the students may cut as many times as they wish.

2. Display Guided Practice Question #1 (p. 36).

Read the question and put in the speed bumps. Write down the main idea to begin the

4-step process.

Main Idea: new shapes made

Details: hexagon

Strategy:

Pass out the paper copy of the hexagon (p.39) and the scissors. Each student will only need one hexagon to cut. The students will cut along the dotted lines to make their new shapes.

Use questioning strategies to help students identify the new shapes.

How many sides does this shape have? Let's count.

This shape has 3 sides.

Who can state in a complete sentence which shape had 3 sides? The

shape with 3 sides is a triangle.

How/Why:

We cut the shapes.

The new shapes were triangles.

Triangles have 3 sides.

3. Guided Practice Questions #2 & #3

Question #2 (p. 37):

Guide students through the 4-step process. For question #2, each student will need one square to cut apart (p. 40).

Question #3 (p. 38)

Each student will need 4 triangles (p. 41) and 2 rectangles (p. 42). After writing the main idea, let students manipulate the shapes until they can find the answer (hexagon and rectangle). A visual of how to place the shapes is below. Students should struggle with this until at least one of them finds the answer. Let the “experts” teach the other students. If no one gets the answer, guide them with questions.

4. Independent Work

Students will complete 2-Dimensional Geometry Practice #2 (MATH_2_A_ 2D GEOMETRY IP2 2014_RES).

Guided Practice Questions

1. Tracy drew a hexagon.

If you cut the hexagon along the dotted lines, what new shapes would be made?

A. circles

B. rectangles

C. triangles

D. squares

2. Robert drew a square.

If you cut the square along the dotted lines, what 2 new shapes would be made?

A. triangle and rectangle

B. triangle and square

C. pentagon and rectangle

D. rectangle and rectangle

3. Mrs. Morton has these shapes.

When she puts them all together what new shapes will she have? (Use the shapes.)

A. square and pentagon

B. rectangle and octagon

C. square and hexagon

D. rectangle and hexagon

Part 4 Additional Resources (2-D)

Mixed Practice (2-D Shapes)

(MATH_2_A_2D GEOMETRY MIXEDPRACT1 2014_RES)

“Who Can Join Me?” and “Same Name Partner Search”

These are activities which focus on the common

characteristics between shapes. In the first activity,

the teacher holds up a word or a card, and students

join him/her if their card meets the criterion. In the

second activity, students wear a shape necklace and

try to find other students in the room who have the same

name as they, e.g. “We are hexagons.”

(MATH_2_A_2DGEOMETRY5 2014_RES)

“Yarn Shapes”

Students work together to create shapes with lengths

of yarn and “vertex crowns.”

(MATH_2_A_2D GEOMETRY6 2014_RES)

Plane Geometry Smartboard

The class fills in the attributes of shapes and provides their name. (MATH_2_A_2D GEOMETRY7 2014_RES)

3-Dimensional Geometry

Solid Figures

TEKS 2.8 B classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language.

TEKS 2.8 D compose two-dimensional shapes and three-dimensional solids with given properties or attributes.

Vocabulary: solid shape, space figure, 3-dimensional, 3-D, sphere, cone, cylinder, prisms: triangular prism, rectangular prism, square prism, cube, pyramids: triangular pyramid, rectangular pyramid, square pyramid, vertex, vertices, face, edge, base, figures, net

Materials: geometric solids for each table (These should include all those mentioned in the vocabulary list.)

tiny Play-Doh balls

straws (or any type of sturdy stick-like object that can be cut into different lengths. The small straws used in the cafeteria or coffee stirrers may be good to use.)

posters of 3-D shapes (MATH_2_A_3D GEOMETRY1 2014_RES)

small pictures of shapes for sorting activity

My Geometry Book for each student

(MATH_2_A_3D GEOMETRY2 2014_RES)

student copies of Geometry Practices 1-3

(MATH_2_A_3D GEOMETRYIP1 2014_RES)

student copies of Solid Geometry Practice

(Math_2_A_3D GEOMETRY MIXED PRACT1 2014_RES)

connecting cubes, unifix cubes or base ten unit cubes

Part 5 3-Dimensional Shapes - Introduction

1. Show students pictures of 2-D shapes and review their attributes.

Why do you think these shapes are called 2-D? because they are flat; they have length and width.

2. Show students models of 3-D shapes.

These shapes are called 3-dimensional, or 3-D shapes.

How many of you have seen a 3-D movie?

How is it different from a movie that is not 3-D? Things look like they are coming out at you in a 3-D movie.

How are these shapes different from 2-dimensional shapes? (Point out that these shapes have length, width, and height. They take up space.)

Sorting Shapes

1. Give students (pairs or table groups) models of 3-dimensional shapes (cube, sphere, cylinder, cone, rectangular prism, triangular prism, triangular pyramid, rectangular pyramid, square pyramid). Ask students to sort the shapes. (Don’t give any criteria. Allow students or groups to sort any way they want.)

2. Ask groups to share how they have sorted their shapes.

If no group sorted the shapes into pyramids, prisms, and shapes that roll, tell students:

This is how mathematicians would sort these shapes...

(Sort the plastic shapes on the floor.)

3. Display 3 circles on the wall labeled pyramids, prisms, and shapes that roll. The teacher shows the students pictures of shapes, and they decide in which circle they belong. (The posters of the shapes may be used for this activity. The teacher should also model how to analyze the picture and connect it to a specific shape through “thinking aloud.” For example the teacher might say, “It has 8 vertices, 12 edges and all the faces are squares, so it must be a cube.”)

Part 6 Building Shapes and Recording Attributes

Triangular Prism & Rectangular Prism

1. Give each table group a model of a triangular prism.

Tell students that they will be doing an activity using Play-Doh and straws where they get to build shapes and record the attributes in their copy of My Geometry Book (MATH_2_A_3D GEOMETRY2 2014_RES).

2. Explain to the students that the straw will represent an edge and the Play-Doh will represent the vertex/vertices. The face on a solid figure is the flat surface. Have the students touch a face on one of the shapes.

3. Tell the students that you are going to show them how to make a triangular prism. Have students use the triangular prism on the table to use as a model.

4. Begin building a triangular prism by making 2 triangles.

A. Take one straw and place one Play-Doh ball on each end.

B. Take additional straws and Play-Doh to make a triangle.

This triangle is one of the faces of a triangular prism. (Point to one of the triangular faces on the model.) Students may notice that there are two triangular faces. If students don’t see this, point it out to them. Then have students use the Play-Doh and straws to make a second triangle just like the first.

C. Use 3 longer straws to connect the triangles.

How many Play-Doh balls did we use for the triangular prism? _____

What does that tell us about the triangular prism? A triangular prism has 6 vertices. (Have students compare it to the solid figure to see if it is true.)

Fill in the information in the booklet (p. 1). Dot the vertices and record the number.

How many toothpicks did we use for the triangular prism? ___

Who can tell me about the edges on a triangular prism?

A triangular prism has 9 edges. (Students can verify it by counting the edges on the solid figure).

Fill in the information in the booklet (p.1). Trace the edges (ask students not to trace in red, since we trace the bases in red) and record the number.

Now let's count the faces. (Have students trace on paper or make an impression of each face of the model in Play-Doh.)

How many faces does a triangular prism have? ____

What 2-dimensional shapes make up the faces of the triangular prism? 2 triangles and 3 rectangles

Now let’s look at the ends of this shape. What shapes do you see? 2 triangles

Are they the same size? yes

Mathematicians call the 2 identical faces at the opposite ends of a prism the bases. One base is here and the other base is here (point to the ends). How many bases does a prism have? 2 bases (Rotate the prism so that the bases are in a different position, e.g. top and bottom. Point out that they are still the bases.) The bases determine the name of a prism, so this shape is called a triangular prism.

How many bases does the prism have? 2

Fill in the information in the booklet (p. 2). Trace the bases in red. Then draw all the faces (including the bases).

Now let’s build a rectangular prism. (Give each table group a model of a rectangular prism.) Tell students to look at the solid figure of the rectangular prism to give them an idea of what they are building. Have the students look at the shape and show you examples of edges, vertices, faces, and bases.

The students should build this shape using the Play-Doh and straws in a manner similar to that previously done with the triangular prism. While a square is a rectangle, do not use it for the base when building this rectangular prism.

Fill in the information in the booklet (pg 3). Dot the vertices and record the number.

How many toothpicks did we use for the rectangular prism? ___

Who can tell me about the edges on a rectangular prism?

A rectangular prism has 12 edges. (Students can verify it by counting the edges on the solid figure).

Fill in the information in the booklet (pg 3). Trace the edges (remember not to use red) and record the number.

Now let's count the faces. (Have students trace on paper or make an impression of each face of the model in Play-Doh.)

How many faces does a rectangular prism have? ____

What 2-dimensional shapes make up the faces of the rectangular prism? 6 rectangles

Now let’s look at the ends of this shape. What shapes do you see? 2 rectangles

Are they the same size? yes

Remember, the 2 identical faces at the opposite ends of a prism are the bases. One base is here and the other base is here (point to the ends). How many bases does a prism have? 2 bases (Rotate the prism so that the bases are in a different position, e.g. top and bottom. Point out that they are still the bases.) The bases are how this shape gets the name rectangular prism.

How many bases does the prism have? 2

Fill in the information in the booklet (p. 4). Trace the bases in red. Then draw all the faces (including the bases).

Square Prism & Cube

The students should build these shapes using the Play-Doh and straws in a similar manner as

previously done. When building the square prism, make sure the bases are squares by using

straws all the same size. Use longer straws to connect the two squares.

Once again, fill in the information in the booklet (pg 5). Dot the vertices and record the number.

How many toothpicks did we use for the square prism? ___

Who can tell me about the edges on a square prism?

A square prism has 12 edges. (Students can verify it by counting the edges on the solid figure).

Fill in the information in the booklet (pg5). Trace the edges (remember not to use red) and record the number.

Now let's count the faces. (Have students trace on paper or make an impression of each face of the model in Play-Doh.)

How many faces does a square prism have? ____

What 2-dimensional shapes make up the faces of the square prism? 4 rectangles and 2 squares which are “special rectangles”

Now let’s look at the ends of this shape. What shapes do you see? 2 squares

Are they the same size? yes

How many bases does the prism have? 2

Fill in the information in the booklet (pg 6). Trace the bases in red. Then draw all the faces (including the bases).

Have students build the cube and record the information about the number of vertices, edges, and faces in their booklet (p. 7-8). Proceed with the questioning as before.

How many toothpicks did we use for the cube? ___

Who can tell me about the edges on a cube?

A cube has 12 edges. (Students can verify it by counting the edges on the solid figure).

Now let's count the faces. (Have students trace on paper or make an impression of each face of the model in Play-Doh.)

How many faces does a cube have? ____

What 2-dimensional shapes make up the faces of the cube? 6 squares (“special rectangles”)

Now let’s look at the ends of this shape. What shapes do you see? 2 squares.

Are they the same size? yes

How many bases does the prism have? 2

The last two pages of the booklet maybe used as a mini scavenger hunt where the students move around the room to find examples of prisms in their classroom.

Pyramids

Now let’s build a pyramid. (Pass out a model of a pyramid to each table (they don’t have to be the same type it could be a square, rectangular, or triangular pyramid.)

Have students identify the base of their shape as either a square, triangle or rectangle. Have them first build the base using the straws and Play Doh.

How many bases does your pyramid have? 1

What 2-dimensional shapes make up the faces of your pyramid? Triangles

Allow students to complete their pyramid.

How are prisms different from pyramids? prisms have 2 bases; pyramids have 1 base; the faces are triangles and they come to a point.

Have each table or group name the pyramid they built. Remind students that like the prisms, pyramids get their name from the base.

Cone, Cylinder, & Sphere

What shapes have we not built? sphere, cone and cylinder

Can you build a sphere, cone or cylinder using the straws? (Let the skeptics try.)

Why not? They don’t have straight edges.

IMN ACTIVITY

Complete MATH_2_A_3D PRISM IMN ACTIVITY1 2014 with students and then paste it into their IMN on the right-hand side. Have students justify their thinking.

On the left-hand side, students should complete MATH_2_A_3D PRISM IMN ACTIVITY2 2014_RES.

Independent Practice

The students should complete 3-Dimensional Geometry Practice #1 (MATH_2_A_ 3D GEOMETRY IP1 2014_RES).

Part 7 Comparing A Cube, A Square Prism and a Rectangular Prism

1. Now that students have built the different types of prisms, draw their attention to their attributes. (Have them look in their Geometry booklet.) Ask them what they notice about the square prism, rectangular prism, and the cube.

If students don’t see it, ask leading questions to get them to recognize that the cube, the square

prism and the rectangular prism all have the same number of vertices, edges, and faces.

If they all have the same number of vertices, edges and faces why don’t they look the same?

Pass out the solids of the prisms so that students can re-examine them. Give students time to

discuss with their partner/table group.

Look at each solid or have students look at the drawings of the faces for each shape in their Geometry booklet. What do you notice about the faces of these shapes? They all have rectangles as faces.

What about the cube? The faces of the cube are all squares, and a square is a “special rectangle.”

Now let’s look at the bases of each shape. Remember a prism gets its name by its bases. (Students can either look at the red tracing of the bases in their Geometry booklet or examine the shapes.)

What polygon forms the bases of the rectangular prism? rectangles

What polygon forms the bases of the square prism? squares

What polygon forms the bases of the cube? squares (Since all faces are identical, any 2 opposite faces can be considered the bases.)

So if a prism gets its name from its bases, and a cube’s bases are squares, we can also call the cube a square prism.

We also learned that a square is a “special rectangle.” So that means that a square prism and a cube can also be called a rectangular prism.

Now return to your geometry booklet on p. 5-6 and add the name rectangular prism to the

Square Prism page. Then turn to p. 7 - 8 and add the names square prism and rectangular prism to the Cube pages. See picture on next page.

‘

2. Students can review the comparisons of prisms with the Smart Board Activity, MATH_2_A_COMPARING PRISMS1A 2014.RES. The directions for this activity are in the Smart Board slides. Students will need a piece of manila paper folded into six parts as shown below. They will paste the shapes found in MATH_2_A_COMPARING PRISMS1B 2014.RES in the proper boxes on the manila paper.

Mixed Practice

The students may now complete “3-D Geometry Mixed Practice 1” questions (MATH_2_A_3D GEOMETRY MIXED PRACT1 2014_RES).

Part 8 Composing 3-D Shapes

1. Identifying Faces on 3-D Shapes

The teacher should hold up a triangular prism. What plane shapes are used to make the faces of the triangular prism? triangles and rectangles

How many triangles are there? 2

How many rectangles? 3

Ask students to describe all the attributes (number of faces, edges and vertices).

Repeat the activity with rectangular prisms and cubes. You might wish to use different sizes, and some real life -objects such as a tissue box.

Pull out a cylinder. Ask the students what 2-D shapes are used to compose a cylinder. Students should be able to explain that there are circles on either end and that the curved surface connecting them is not a 2-D shape.

Repeat with a cone and a sphere.

Partner Practice

“Whose Faces are We?”- Students look at faces and determine the solid shape. (MATH_2_A_3D GEOMETRY5 2014_RES)

2. Discovering Nets

Prior to this lesson copy (on tag), cut and fold the net on page 65 to create a model of a square prism. (DO NOT TAPE TOGETHER).

We have just looked at the faces of different prisms. Now let’s take a closer look at the square prism found on page 6 in your geometry booklet. What shapes did you draw for the faces of the square prism? 4 rectangles and 2 squares

Hold up the paper model of the square prism. Then unfold the shape to show the net. Do you see the same faces you drew in your booklet in this net? Yes, there are 4 rectangles and 2 squares

What do you notice about the rectangles and the squares in the net? All the rectangles are touching the squares are on the end of one of the rectangles.

Why would the squares need to be on the ends? They are the bases of this prism.

Watch me as I refold the net. I now have a square prism again!

3. Guided Practice

Together read the Guided Practice Question 1 aloud. (p. 55) (A net is a pattern that you can cut and fold to make a model of a solid).

Begin the 4-Step process.

Main Idea: 3-D shape created

What polygons do you see on the net?. 2 triangles and 3 rectangles

Details/Known: 5 faces, 3 rectangles, 2 triangles

Which solid shape is composed of 2 triangles and 3 rectangles? (Allow students time to look at each shape, identify and label the faces of each shape. Then ask them to turn to a buddy and tell them which shape they think it is and why.)

Once students are through discussing, point to each answer choice and have the class show you their answer using “thumbs up” if they chose that answer and “thumbs down” if they did not.

Revisit the answer choices that were not chosen and ask students why they are not correct. Students should use the geometric solids to solve this question.

Strategy: Labeled shapes

How/Why: A triangular prism has 5 faces. 2 are triangles and 3 are rectangles.

Guided Practice Question 1

Which 3-D shape is created from the 2-D net below?

A. C.

B. D.

4. Using 3-D Figures to Make Other Solids

Ahead of time, build the object below using a cone and a cylinder.

Ask students which shapes were used to compose this figure. Give students a chance to explore and create their own solids using the geometric figures. After giving them a chance to build some on their own, tell them to use specific shapes, i.e. 2 cylinders and 2 rectangular prisms. Students may need to work in partners or table groups in order to have enough 3-D figures. Each table or group should explain which shapes they used to compose their new figure to the rest of the class.

5. Guided Practice Question 2 (p. 58).

,

Below is an example of what a completed 4-step process might look like.

Guided Practice Question 2

Which list of shapes make up this solid object?

A. 4 cylinders, 1 triangular pyramid, 1 rectangular prism

B. 1 triangular prism, 1 cube, 4 cylinders

C. 1 triangular prism, 4 cylinders, 1 rectangular prism

D. 2 rectangular prisms, 4 cylinders

6. Independent Practice

Students will complete the “3-D Geometry Mixed Practice 2 (MATH_2_A_3D GEOMETRY MIXED PRACT2 2014_RES).

Additional Resources

“True About Me” (3-D Shapes) - Students select which attributes apply to the shape.

Directions & Attribute Cards (MATH_2_A_3D GEOMETRY4A 2014_RES)

Garbage Cans (MATH_2_A_3D GEOMETRY4B 2014_RES)

Independent Questions (MATH_2_A_3D GEOMETRY4C 2014_RES)

“What am I?” Geometry Review PowerPoint - Students identify the geometric shape which matches an everyday object.

Powerpoint Game (MATH_2_A_3D GEOMETRY6A 2014_RES)

Student answer sheet (MATH_2_A_3D GEOMETRY6B 2014_RES)

3-Dimensional GT Extension Exploring Prisms (MATH_2_H_3D GEOMETRY 2014_ENR)

Teacher Vocabulary Reference Sheet (MATH_2_A_GEOMETRY1 2014_RES)

Part 9 Alternative Assessment

Guidelines

1. Pull 2 students to a quiet area to assess putting up a divider to make sure they cannot see each other’s work. See video for test management.

2. Give the student the following shapes: cylinder, sphere, cone, cube, square prism, rectangular prism, triangular prism.

3. Begin Task 1 of the assessment. The sorting of the shapes should be done in 5 minutes or less. If a student has difficulty getting started, give him/her two sheets of paper to help prompt the sorting of the shapes into two groups. (As students are sorting, you may take this opportunity to check on the rest of the class.) There is no time limit for the oral response to this task, as some students may have more to say than others.

4. Set up a timer for eight minutes. The remaining Tasks (2-5) should be completed within the 8 minutes. Record the shapes chosen, as well as their responses to the questions on the recording sheet.

5. A suggested word bank is provided if students need help with the math vocabulary.

Alternative Assessment

Place the following shapes on the table: cylinder, sphere, cone, cube, square prism, rectangular prism, triangular prism.

1. Begin the assessment by asking the student to sort the shapes into groups. (Do not give specifics on how to sort.) Once the student has completed this part of the task, ask him/her to tell you how the shapes were sorted. Listen for math vocabulary as the student describes the groups: edges, faces, vertices, quadrilaterals, polygons, bases, 2-dimensional, 2-D, 3-dimensional, 3-D, solids, etc.

Set your timer for 8 minutes. Now ask the student:

2. Can you find a shape with 4 faces all the same size and the same shape? (Allow time for student to examine each shape if necessary.)

What is the name of this shape? cube or square prism

3. Can you find a shape that has 6 vertices? (Allow time for student to examine each shape if necessary.)

What shapes make up the faces of this solid? 2 triangles and 3 rectangles

4. Can you find a shape that does not have straight edges? (Students may choose the cylinder, sphere or cone.)

What is the name of this shape? (Possible answers: cylinder or sphere or cone)

5. Can you find the cone? What shape does the base of the cone have? circle

Recording Sheet

Name: _____________________

|Task | |

| |Response |

| | |

|1 |4 |

| |3 |

| |2 |

| |1 |

| | |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with no teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with some teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| |Student was not able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| | |

| |4 |

| |3 |

|2 |2 |

| |1 |

| | |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with no teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with some teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| |Student was not able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| | |

| |Response |

| |Response |

| | |

| |4 |

|3 |3 |

| |2 |

| |1 |

| | |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with no teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with some teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| |Student was not able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| | |

| |Response |

|4 | |

| |4 |

| |3 |

| |2 |

| |1 |

| | |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with no teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with some teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| |Student was not able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| | |

| |Response |

|5 | |

| |4 |

| |3 |

| |2 |

| |1 |

| | |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with no teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with some teacher help. |

| |Student was able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| |Student was not able to complete the task using math vocabulary words in a meaningful and accurate way with the use of a word bank. |

| | |

|base |edge |quadrilateral |square prism |2-D |

|circle |face |rectangle |triangle |2-dimensional |

|cone |polygon |rectangular prism |triangular prism |3-D |

|cube |prism |solid |vertex |3-dimensional |

|cylinder |plane |sphere |vertices | |

| | | | | |

|base |edge |quadrilateral |square prism |2-D |

|circle |face |rectangle |triangle |2-dimensional |

|cone |polygon |rectangular prism |triangular prism |3-D |

|cube |prism |solid |vertex |3-dimensional |

|cylinder |plane |sphere |vertices | |

| | | | | |

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Polygon Sort Cards -

Teacher Set

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Polygon Sort Cards -

Teacher Set

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[pic]

Polygon Sort Cards -

Teacher Set

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Polygon Sort Cards -

Teacher Set

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[pic]

Polygon Sort Cards -

Teacher Set

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[pic]

Polygon Sort Cards -

Teacher Set

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[pic]

Polygon Sort Cards -

Teacher Set

Polygon Sort Cards -

Teacher Set

Polygon Sort Cards -

Teacher Set

Play-Doh

Play-Doh

or

Build two different pentagons. Draw the shapes you made.

Fill in the attributes.

_____ vertices _____ sides

Build two different hexagons. Draw the shapes you made.

Fill in the attributes.

_____ vertices _____ sides

Build two different octagons. Draw the shapes you made.

Fill in the attributes.

_____ vertices _____ sides

How is a hexagon different from an octagon?

____________________________________________________________

____________________________________________________________

____________________________________________________________

Build two different heptagons. Draw the shapes you made.

Fill in the attributes.

_____ vertices _____ sides

Build two different nonagons. Draw the shapes you made.

Fill in the attributes.

_____ vertices _____ sides

Build two different decagons. Draw the shapes you made.

Fill in the attributes.

_____ vertices _____ sides

Build two different shapes with 11 vertices. Draw the shapes you made.

Fill in the attributes.

_____ vertices _____ sides

Build two different shapes with 12 sides. Draw the shapes you made.

Fill in the attributes.

_____ vertices _____ sides

Jasper drew a polygon that had 3 sides. What polygon could he have drawn?

A. circle

B. triangle

C. square

D. pentagon

3 sides

polygon drawn

1

2

3

1

4 2

3

Point and trace the sides and count 1, 2, 3, 4.

1 2

5 3

4

Point and trace the sides and count 1, 2, 3, 4, and 5.

Square

Rectangle

Quadrilateral

Polygon

Tracy drew a hexagon.

If you cut the hexagon along the dotted lines, what new shapes would be made?

A. circles

B. rectangles

C. triangles

D. squares

1

2

3

These shapes have no straight edges and they can roll. (Let students roll them.)

Shapes that

Can Roll

These shapes all have triangular faces and come to a point. This point is a vertex.

Pyramids

The opposite ends of these shapes are identical faces. The other faces are rectangles. (Remember a square is a special type of rectangle.)

Prisms

Note to the Teacher: This lesson is focused on prisms, their attributes and how they get their name. Students will be exposed to pyramids and emphasis will be placed on identifying their attributes.

Note: Point out to students that the straws on this 2-D shape represent sides. Once they build a 3-D shape, the straws become edges.

The triangle has 3 sides.

cube

rectangular prism

square prism

This is an example of what a student booklet might look like. Remember that the drawings of the faces are approximations and do not have to be precise.

Prisms

Triangular Prisms

Rectangular Prisms

Square Prisms

Cubes

Name

An answer key is provided as a pull out tab on the last slide of the Smart Board Activity.

Which 3-D shape is created from the 2-D net below?

A. C.

B. D.

6 s

2 s

4 r

2 t

3 r

4 t

Which list of shapes make up this solid object? Triangular prism

Rectangular Prism

X cylinders

A. 4 cylinders, 1 triangular pyramid, 1 rectangular prism

X

B. 1 triangular prism, 1 cube, 4 cylinders

C. 1 triangular prism, 4 cylinders, 1 rectangular prism

X

D. 2 rectangular prisms, 4 cylinders

List of shapes

picture

Students should count and label the shapes. Then eliminate the answer choices.

Labeled and counted the shapes.

Total points __________

Word Bank

Word Bank

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