MATH_2_A_1 2D GEOMETRY 2015_LES.docx
Second Grade
Geometry
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) / 1
4
16
17
21
27
30
33
34
39
46
2-Dimensional Geometry
Plane Figures
TEKS 2.8 Acreate two-dimensional shapes based on given attributes, including number of sides and vertices;
TEKS2.8 C classify and sort polygons with 12 or fewer sides according to attributes,
including indentifying the number of sides and vertices;
TEKS2.8 D compose two-dimensional shapes and three-dimensional solids with given
properties or attributes;
TEKS2.8 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 1Polygons and Their Attributes
Materials:“Gingerbread Man Attributes” PowerPoint
(MATH_2_A_3 2D GEOMETRY 2015_RES)
Polygon sort activity - yarn or hoola hoops for circles
Labels (A, B, Not Polygons, Polygons)
Polygon sort cards (pages 4‒12)
posters of 2-D shapes(MATH_2_A_4 2D GEOMETRY 2015_RES)
Shape Construction – tiny Play-Doh balls, coffeestirrers 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 (pages17-20)
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 2DGEOMETRY 2015_RES)
garbage cans – (MATH_2_A_6C 2D GEOMETRY 2015_RES)
student copies of Guided PacticeProblems #1 and #2(pages27 ‒ 29)
student copies of 2-Dimensional Geometry Practice #1
(MATH_2_A_7 2D GEOMETRYIP 2015_RES.doc)
IMN Entries
Polygon 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, theymust understand the meaning of the word attribute. The teacher may use the “Gingerbread Man Attributes”Powerpointto 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 pages4 ‒ 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.
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, “Oneattribute 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 whatattributes make it a polygon.
This document can be found in MATH_2_A_5 2D POLYGON IMN 2015_RES.
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 theseshapes 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-Dohball oneach end.
Take a side and attach it to a vertex.
Take more stirrers/straws and Play-Doh balls to createa regular pentagon.
B.Ask the following questions:
How many stirrers/straws did we use for the pentagon? 5
What do the stirrers/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
Have students draw the shape they created in the top portion of the Pentagon recording sheet
(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 (onein 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-sidedPolygons
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 sideson 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.
Show the Hexagon posterand have the class read the name together.
These shapes may not look the same as your shapes, but they have 6 sides and
6 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.
Identifying Polygons
5.Partner Practice
Students determine which attributes describe specific shapes by doing the “True AboutMe” activity for 2-dimensional shapes (MATH_2_6A 2D GEOMETRY 2015_RES and
MATH_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 28may 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.
Refer back to the Play-Doh activity.
What did we use to represent the sides of a shape? straws
Can 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 haszero sides.
Put a zero next to the drawing of thecircle 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.
How many sides does a square have? A square has 4 sides.
Write a4 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 a5 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? 3
What 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 GEOMETRYIP 2015_RES).
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? ______
______
Guided Practice Problem #1
Jasper drew a polygon that had 3 sides. What polygoncould he have drawn?
A.circle
B.triangle
C.square
D.pentagon
Shapes
Guided Practice Problem #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 2Quadrilaterals
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. Definitionof 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 sidesand 4 vertices. The shapes in Group B do not have 4 sides and 4 vertices.
Replace the “GroupA” 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
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.
Allpolygonswith 4 sides are calledquadrilaterals. (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 intofour quadrants and then glue the labelsPolygon, Quadrilateral,Rectangle and Square (page 33) as shown below.
Eachstudent 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 _92D GEOMETRY 2015_RES)which lists the attributes of polygons,quadrilaterals, rectangles, and squares. For each shape, go through all four of thesecategories, 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 hexagonmeets 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 hexagonmeets 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 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 equal.)
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 theshape 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 shouldstate what they have found in a complete sentence. Forexample, “A square is a polygon, a quadrilateral, a rectangle and a square.”