2-Dimensional Geometry - Pearson Schoolstorage.schoolnet.com/cfisd/MATH_2_A_1 2D GEOMETR… · Web viewMATH_2_A_1 2D GEOMETRY 2015_LES.docx. ... and learn about polygons that have

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Second GradeGeometry

Section 1: 2-Dimensional Shapes

Table of Contents Suggested Number of Days Page No.2-D Geometry Part 1 Polygons and Their Attributes Polygon Sort Cards Pentagon Recording Sheet 6 to 12-sided Polygons Recording Sheets Identifying Polygons Guided Practice Problems

Part 2 Quadrilaterals Labels

Part 3 Decomposing and Composing 2-D Shapes Guided Practice Problems

Part 4 Additional 2-D Resources

3 days (11/30 – 12/2)

1 day (11/3)

1 day (11/4)

1416172127

3033

3439

46

Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016

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2-Dimensional GeometryPlane 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 decompose 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, polygon, triangle, rectangle, square, special rectangle, quadrilateral, pentagon, hexagon, octagon, nonagon, decagon, heptagon, circle, 2-dimensional, 2-D, attribute, vertex, vertices

Teacher Background

Students will continue to investigate the attributes of 2-dimensional shapes (regular and irregular) and learn about polygons that have 7 ‒ 12 sides.

Student Background

Student have practiced naming, sorting, classifying and creating the following shapes: rectangles, squares (special rectangles), triangles, circles, hexagons and rhombi. Students traced the edges and dotted the vertices to identify the attributes. Students also composed shapes using Tangram pieces.

Part 1 Polygons and Their Attributes

Materials: “Gingerbread Man Attributes” PowerPoint(MATH_2_A_3 2D GEOMETRY 2015_RES)

Polygon sort activity - yarn or hoola hoops for circlesLabels (A, B, Not Polygons, Polygons)Polygon sort cards (pages 4 ‒ 12)

Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016 1

Note: Geometry Glossary – 2nd Grade Teacher Reference Document” (MATH_2_A_2 GEOMETRY 2015_RES) contains definitions. This is a teacher reference only and is not written in “kid-friendly” langage.

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posters of 2-D shapes (MATH_2_A_4 2D GEOMETRY 2015_RES)

Shape Construction – tiny Play-Doh balls, coffee stirrers or straws (different lengths depending on the shape being built) and student copies of pentagon recording sheet (page 16)

student copies of 6 to 12-sided polygons recording sheets (pages 17-20)

student copies of Identifying Polygons cards (pages 21-22)

“True About Me” materials – cards ‒ (MATH_2_A_6A 2D GEOMETRY 2015_RES)questions – (MATH_2_A_6B 2D GEOMETRY 2015_RES)garbage cans – (MATH_2_A_6C 2D GEOMETRY 2015_RES)

student copies of Guided Pactice Problems #1 and #2 (pages 27 ‒ 29)

student copies of 2-Dimensional Geometry Practice #1(MATH_2_A_7 2D GEOMETRY IP 2015_RES.doc)

IMN EntriesPolygon Activity ‒ (MATH_2_A_5 2D POLYGON IMN 2015_RES)Naming a 2-D Figure ‒ (MATH_2_A_8 2D POLYGON IMN 2015_RES)

What is a polygon?What are the attributes of 2-dimensional shapes and how do I use the attributes to name the shapes?

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 use the “Gingerbread Man Attributes” Powerpoint to develop an understanding of attributes (MATH_2_A_3 2D GEOMETRY 2015_RES).

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 4 ‒ 12 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 in which circle they think a particular shape will belong.


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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 attribute 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.

IMN Activities:

Discuss and complete the definition of a polygon.

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

This document can be found in MATH_2_A_5 2D POLYGON IMN 2015_RES.

Display cards used for the polygon sort for students to use when completeing the following activity:

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

This document can be found in MATH_2_A_5 2D POLYGON IMN 2015_RES.


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Polygon Sort Cards -Teacher Set

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3. Shape Construction (Play-Doh and straws)

To provide students with an opportunity to examine the attributes of a regular and irregular polygon, they will construct one using Play-Doh and coffee stirrers or straws.

Materials needed: Play-Doh balls and coffee stirrers or straws (Suggestion: Have one baggie with the same

length and one baggie with different lengths.) pictures of 2-D shapes pentagon recording sheet recording sheets labeled 6 ‒ 12 sided polygons

Display pictures of 2-D shapes. Explain to students that we call these shapes two-dimensional or 2-D shapes because they have no thickness — they are flat. The only two dimensions you can measure are the height and width.

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

Take a side and attach it to a vertex.

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

B. Ask the following questions:

How many stirrers/straws did we use for the pentagon? 5What do the stirrers/straws represent? sidesTherefore, 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? 5Play-Doh balls stand for ________? verticesSo, who can say that in a complete sentence? A pentagon has 5 vertices.

Is the pentagon a polygon? yesHow do you know it is a polygon? straight sides, 2-D, closed

Have students draw the shape they created in the top portion of the Pentagon recording sheet Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016

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Play-Doh

Play-Doh

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(p. 16). Tell students to check to make sure they drew the right shape by counting the sides and vertices and recording the number on the space provided. (Students should trace the sides with a marker or colored pencil and dot the vertices — a strategy learned in 1st grade.)

C. 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,

Have students draw their irregular pentagon on the bottom portion of the recording sheet.

Have a discussion about the similarities and differences of the two shapes and why they are both pentagons even though they look different.

Allow time for students to walk around to see the different pentagons created by their classmates.

4. Six to Twelve-sided Polygons

A. Students can continue building a few more regular and irregular shapes with the Play Doh and stirrers/straws or they can move on to creating these shapes on paper using the recording sheets for 6 to 12-sided polygons (pp. 17-20).

Now I want you to use what you have learned about polygons to draw a polygon that has 6 sides on the top half of the paper.

Before we begin, who can tell me what 2 attributes makes a shape a polygon? All polygons must have straight sides and be a closed shape.

As students finish drawing, have them check to make sure they drew the correct shape by counting the sides and vertices. Ask them to record this information on the lines beside the words.

Once completed, have students share their polygon and compare it with other polygons in the class. Tell students that you are going to reveal the name of the 6-sided shape they drew.


or

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Show the Hexagon poster and have the class read the name together.

These shapes may not look the same as your shapes, but they have 6 sides and6 veritices so they are hexagons just like your shapes.

Have students write Hexagon on the line of their paper.

Now ask students to draw a polygon with 7 sides on the bottom half of the paper. As before have students…

count and record the sides and the vertices on their sheet share and compare their shape with others in the class say and write the name of the shape on their paper when it is revealed by the

teacher

Continue in a similar manner for the rest of the shapes — octagon (8-sides), nonagon (9-sides), and the 10-sided, 11-sided and 12 sided polygons.

Students are not responsible for the names of the 10, 11 or 12-sided polygons.They are only responsible for creating the polygons and recognizing their attributes.

B. Practice classifying and sorting polygons up to 12 sides by their attributes using the Identifying Polygon cards on pages 21 and 22. The teacher calls out various attributes and students sort their shapes accordingly.

For example the teacher may say: polygons with 9 or more vertices shapes with 4 sides polygons with fewer than 5 vertices

Have students sort their figures into the category called and put the others in a group labeled NOT.

To save time, have students count and label the number of vertices and sides beforehand.


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Pentagon

_____ vertices _____ sides

Pentagon


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_____________________________________


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6 to 12-sided Polygons

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Identifying Polygons


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5. Partner Practice

Students determine which attributes describe specific shapes by doing the “True About Me” activity for 2-dimensional shapes (MATH_2_6A 2D GEOMETRY 2015_RES andMATH_2_A_6C 2D GEOMETRY 2015_RES.)

Five questions are available for students to answer after completing the above activity (MATH_2_A_6B 2D GEOMETRY 2015_RES).

6. Guided Practice

Together read Guided Practice Problem #1. Visualize, discuss and then insert the speed bumps.

Complete Steps 1 and 2 of the problem solving process.

Step 3: Strategy

Read, draw, and evaluate each answer choice before selecting an answer. (A copy of page 28 may be displayed for students to use as a reference.)

A. circle

Draw a circle in the air and then draw a circle beside the word on the answer choices.


3 sidespolygon drawn

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

A. circleB. triangleC. squareD. pentagon

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Refer back to the Play-Doh activity.

What did we use to represent the sides of a shape? strawsCan we make a circle with the straws? no Why?

(If necessary use straws to demonstrate.)

How many sides does a circle have? (Have students answer using the name of the shape and the number of sides in a complete sentence) A circle has zero sides.

Put a zero next to the drawing of the circle on the answer choices.

This is a good opportunity to reinforce the concept of a polygon. A circle is not a polygon.

B. triangle

Draw a triangle in the air and then draw a triangle beside the word on the answer choices.

Trace the sides and number them to find how many sides on a triangle.

How many sides does a triangle have? A triangle has 3 sides. Write a 3 next to the drawing of the triangle on the answer choices.

C. square

Draw a square in the air and then draw a square beside the word on the answer choices.Trace the sides and number them to find how many sides on a square.


1

4 2

3

1 2

3

Note: Please refrain from having students draw a hash mark to number the sides as this means congruent in the later grades.

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How many sides does a square have? A square has 4 sides. Write a 4 next to the drawing of the square on the answer choices.

D. pentagon

Draw a pentagon in the air and then draw a pentagon beside the word on the answer choices.

Trace the sides and number them to find how many sides on a pentagon.

How many sides does a pentagon have? A pentagon has 5 sides. Write a 5 next to the drawing of the pentagon on the answer choices.

Now direct students to go back and re-read the main idea and details.

How many sides did Jasper draw? 3What shape did he draw? triangle

Step 4: How/Why

Possible responses:I drew each shape.I traced and counted the sides.A triangle is a polygon and has 3 sides.

For Guided Practice Problem #2 have students dot and count the vertices on the shape before answering.

7. Independent Practice

Students will complete 2-Dimensional Geometry Practice #1(MATH_2_A_7 2D GEOMETRY IP 2015_RES).


1 2

5 3

4

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8. IMN Entry

Have students complete the IMN entry foumd in MATH_2_A_8 2D POLYGON IMN 2015_RES.

Jenny thinks this shape is a hexagon.

Is she right? Yes No

How do you know? ____________________________________________

_____________________________________________


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Guided Practice Problem #1

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

A. circleB. triangleC. squareD. pentagon

Shapes


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Guided Practice Problem #2Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016

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Allie made the following pentagon on her paper.

How many vertices are on this pentagon?

A. 3B. 4C. 5D. 6


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Part 2 Quadrilaterals

Materials: set of pattern blocks for each pair (2 squares, a hexagon, a trapezoid)

a large piece of construction paper for each student

SmartBoard Activity (MATH_2_A _9 2D GEOMETRY 2015_RES)

How do I know when a polygon is a quadrilateral?

1. Definition of a Quadrilateral

The teacher draws 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

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. The shapes in Group B do not have 4 sides and 4 vertices.

Replace the “Group A” label with the label “Quadrilaterals”. Replace the “Group B” label with the label “Not Quadrilaterals.”

What are the attributes of shapes that are quadrilaterals? (Refer to the shapes on the board.) 4 sides 4 vertices


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Let’s review the definition of a polygon. (Students may refer to their IMN.) 2-D straight sides closed shape

If students don’t notice, point out that all the shapes are polygons but only the polygons with 4 sides and 4 vertices are quadrilaterals.

All polygons with 4 sides are called quadrilaterals. (Have students repeat this statement and then turn to a partner and say it again.)

Write the statement on an anchor chart so students can refer to it often.

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, and identifying squares as special rectangles.

A. Have students fold a large piece of construction paper into four quadrants and then glue the labels Polygon, Quadrilateral, Rectangle and Square (page 33) as shown below.

Each student should have 4 shapes that can be traced---a square, a trapezoid, a hexagon, and a rectangle (one that is not a square). All of these shapes can be traced from pattern blocks , , except the non-square rectangle. Show students how tracing two squares side by side forms a non-square rectangle. To facilitate the tracing process students can work with a partner — one holds down the shape while the other traces.

B. Pull up the Smartboard (MATH_2_A _9 2D GEOMETRY 2015_RES) which lists the attributes of polygons, quadrilaterals, rectangles, and squares. For each shape, go through all four of these categories, 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.Hold up the hexagon.

What is the name of this shape? 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.)


Polygon Quadrilateral

Rectangle Square

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Is this hexagon a polygon? yesLet’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 opposite sides that are equal.)

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

(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 equal.)

The hexagon isn’t a square because ……

So which of these words can we use to describe a hexagon? only polygonLet’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 in a complete sentence. For example, “A square is a polygon, a quadrilateral, a rectangle and a square.”


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Quadrilateral

Polygon Square

Rectangle

Quadrilateral

Polygon Square

Rectangle

Quadrilateral

Polygon Square

Rectangle

Labels

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Part 3 Decomposing and Composing 2-D Shapes

Materials: rectangles p. 37 (several per student)

hexagons p. 38 (several per student)

student copy of Guided Practice Problems (pp. 39 ‒ 41) accompanying shapes (pp. 42 ‒ 45)

student copy of practice problems (MATH_2_A_10 2D GEOMETRY IP 2015_RES)

scissors

How do I cut apart a 2-dimensional shape to create more shapes? How do I make a new 2-dimensional shape using other shapes?

1. Exploration

The following activity has students decomposing a shape to create different shapes.

Pass out a rectangle (p. 37) to each student. Tell students to use the rectangle to create a new shape following the criteria below:

1) must only make one straight cut through the rectangle2) must create two new shapes with their cut 3) must be able to identify the attributes and name the shapes they created

Have a class discussion over the variety of shapes created.

Give students another rectangle and repeat the activity with different criteria:

1) must make 2 straight cuts through the rectangle2) must create 3 new shapes with their cuts3) must be able to identify the attributes and name the shapes they created

Now give each student a hexagon (p. 38) and apply criteria similar to the rectangle. The number of cuts and the number of shapes created may vary. Students should name the shape(s) created by first identifying their attributes.


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2. Guided Practice Problem #3 (p. 39)

Read the question and put in the speed bumps. Write down the main idea and the details/knownto begin the 4-step process.

Main Idea: new shapes made

Details/Known: hexagon

Strategy: (Nothing needs to be written here. Students cutting the shape is the strategy.)

Pass out the paper copy of the hexagon (p. 42) and the scissors. Each student needs only one hexagon to cut. The students 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: I cut the shapes.The new shapes are triangles.Triangles have 3 sides.


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Tracy drew a hexagon.

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

A. circlesB. rectanglesC. trianglesD. squares

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3. Guided Practice Problem #4 (p. 40)

Each student needs one square to cut apart (p. 43). Guide students through the 4-step process.

Main Idea: 2 new shapes made

Details/Known: square

Strategy: (Nothing needs to be written here. Cutting the shape is the strategy.)

How/Why: I cut the shapes.The new shapes are (non square) rectangles.Rectangles have 4 sides.

Guided Practice Problem #5 (p. 41)

Each student will need 4 triangles (p. 44) and 2 rectangles (p. 45). Begin the 4 step process by writing the main idea and the details/known. Allow time for students to check each answer choice by manipulating their shapes to try and create the shapes named. A visual of how to place the shapes for (D) the correct answer is shown below.

Main Idea: new shapes made

Details/Known: shapes put together

Strategy: (Nothing needs to be written here. Manipulating the shapes is the strategy.)

How/Why: checked each answer choice

4. Independent Practice

Students will complete 2-Dimensional Geometry Practice #2(MATH_2_A_10 2D GEOMETRY IP 2015_RES).


rectangle hexagon

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Tracy drew a hexagon.

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

A. circlesB. rectanglesC. trianglesD. squares


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Robert drew a square.

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

A. triangle and rectangleB. triangle and squareC. pentagon and rectangleD. rectangle and rectangle

Guided Practice Problem #5Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016

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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


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Part 4 Additional 2-D Resources

Mixed Practice (2-D Shapes)(MATH_2_A_2D GEOMETRY MIXED PRACT 2015_RES)

“Who Can Join Me?” and “Same Name Partner Search”These are activities which focus on the commoncharacteristics between shapes. In the first activity,the teacher holds up a word or a card, and studentsjoin him/her if their card meets the criterion. In thesecond activity, students wear a shape necklace andtry to find other students in the room who have the samename as they, e.g. “We are hexagons.”(MATH_2_A_2D GEOMETRY VOCAB ACT 2015_RES)

“Yarn Shapes”Students work together to create shapes with lengthsof yarn and “vertex crowns.”(MATH_2_A_2D GEOMETRY YARN 2015_RES)

2-Dimensional Geometry SmartboardThe class fills in the attributes of shapes and provides their name. (MATH_2_A_2D GEOMETRY 2015_RES)


Documents

2-Dimensional Geometry - Pearson Schoolstorage.schoolnet.com/cfisd/MATH_2_A_1 2D GEOMETR… · Web viewMATH_2_A_1 2D GEOMETRY 2015_LES.docx. ... and learn about polygons that have