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## Three Sides

Pre-K-2
1

In this lesson, students compare and contrast shapes using attribute blocks. Because the equilateral triangle (a triangle with congruent sides and congruent angles) is the most common example used in textbooks and other reference materials, this is an important opportunity for you to help students realize that other triangles exist and that triangles can have angles of different measures. The lesson is designed to accommodate multiple learning styles and intelligences.

To begin this lesson, post four to six different shapes (including various “types” of triangles in nontraditional orientations) on the board. These shapes could include circles, squares, rhombi, rectangles, hearts, and stars, among others. Have students select the triangles from among the posted shapes and note which students recognize triangles and which do not. As students identify shapes which are or are not triangles, have them explain their reasoning.

Discuss with the class what a triangle looks like as well as what its properties are. It might be helpful to draw triangles in different orientations, label their properties, and place these on a chart for future reference.

Prepare one bag of attribute blocks for each pair of children to use for sorting. Give the students colored paper or felt squares for use as work mats. (The shapes placed in the bag should include some of those posted on the board. Viewing and touching the shapes enable students to make the transition from visual to concrete experiences with the properties of triangles.)

Ask students to sort the objects found in their bag into two groups – triangles and non-triangles. Have them tell how their objects are alike and different. Move among the students, posing questions (see Questions for Students section) and listening to the conversations they have with each other about the triangles and their orientation.

An easy way to assess students’ understanding is to ask them to hold a triangle in the air. This is good practice for the song activity which follows.

To close this lesson, ask each student to select a different shape and listen to the song “Shapes” by recording artists Greg and Steve. In this song, the students are asked to stand when the shapes they are holding are named. Repeat the song until the students readily recognize their shapes.

• Set of large shapes (i.e. circles, squares, rhombi, rectangles, triangles in different orientations)
• Attribute blocks
• Colored paper or felt squares
• The song “Shapes” by recording artists Greg and Steve (We All Live Together, volume 3)

Assessment Options

1. Use the teacher resource sheet Class Notes to record general comments about individual students’ understanding.
2. Use the teacher resource sheet Shape Recognition to document which shapes each student is able to identify. Write the date of your observation and a check if the student is able to identify the shape or an X if the student is not able to identify it.
 Shape Recognition Teacher Resource Sheet
3. Use the Sample Vocabulary Related to Geometry Teacher Resource Sheet to document students’ understanding of the geometry terms corner, angle, side, edge, and triangle.
 Sample Vocabulary Related to Geometry Teacher Resource Sheet

Extensions

1. Have students create a class book featuring triangles. Before the activity, you should create triangle-shaped book pages—individual three-holed punched sheets with students’ names across the top. To begin the activity, tell the students to cut triangle pictures from magazines, newspapers, catalogs, or other materials that you have provided. They should glue their pictures to their book page. It may be appropriate for some students to add “writing”; you or a volunteer may write a story dictated by the student. Then bind the hole-punched pages together with yarn and place the book in the classroom library for the children to check out overnight and read to their parents.
2. Move on to the next lesson, Tracing and Drawing.

Questions for Students

1. How many sides does every triangle have? Would you count the sides of one of your triangles for me?

[A triangle has 3 sides.]

2. Can you pick out a triangle from among the shapes on the board? How are the triangles like the other objects?

[All the shapes have corners and straight sides. All of the shapes are flat.]

3. How are the triangles different from the other objects?

[Only the triangles have three sides and three corners. Some of the shapes (circles, if included) do not have any corners.]

4. If my eyes were closed, how would you describe the triangle so that I would know what it looks like?

[It has three straight sides, three sharp corners. It is orange and flat. It looks like a slice of pizza.]

5. Would you count the number of sides of each of your shapes for me so we can see if they are triangles?

[Check to make sure students can do this for you.]

Teacher Reflection

• Did students have ample opportunity to discuss attributes of triangles?
• Did I model for students and encourage them to use proper geometric terms when describing the shapes?
• Did I provide closure by summarizing student learning?
• Did students meet lesson objectives? What evidence did I see to verify this?
• What additional adaptations are needed to support/challenge students

### Tracing and Drawing

Pre-K-2
In this lesson, students continue to discuss attributes of triangles. They  trace and draw triangles individually. Students recognize objects in their environment that are shaped like triangles and explain to the class how they recognized the shape.

### Geoboards

Pre-K-2
Students use appropriate vocabulary to describe shapes to their classmates. Students focus on the properties of shapes to develop mental images of objects from descriptors. They create multiple representations of triangles using geoboards, string, and crayons and paper.

### Making Virtual Triangles

Pre-K-2
In this lesson, students use virtual manipulatives to explore triangles. They create virtual representations of triangles on an electronic geoboard. They also identify shapes within shapes using tangrams. This activity is appropriate for a computer lab, so all students have access to the virtual manipulatives.

### Learning Objectives

Students will:

• Identify and describe triangles.
• Compare triangles and non-triangles.

### NCTM Standards and Expectations

• Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.
• Recognize and represent shapes from different perspectives.

### Common Core State Standards – Mathematics

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.A.1
Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.A.2
Correctly name shapes regardless of their orientations or overall size.

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.B.4
Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/''corners'') and other attributes (e.g., having sides of equal length).