## More Work with Shapes

3-5
1

Students continue to explore geometric concepts by modeling on the geoboard.  Communication is the Process Standard emphasized in this lesson.

To assess prior knowledge, view the KWL Chart from the previous lesson and ask students what amendments they would make to the chart today based upon yesterday’s lesson. This will give you a quick assessment of what students learned from the previous lesson and what you need to review before continuing with this lesson.

Alternatively, or as a lesson pre-assessment, students can work (either individually or in pairs) to review the basic geometric shapes (explored in this lesson) by using the Concentration interactive.

To do so, students should select the shapes under Levels, and either 1 or 2 players. In this activity, students match the names of common geometric shapes with picture representations.

The lesson then continues as described below.

On the Virtual Geoboard E-Example, have students create three-sided figures and compare them with those of a neighbor. Ask students to discuss the similarities and differences among the figures.

As a class, discuss the properties common to each figure. Encourage students to make connections among learning experiences to confirm their understanding of the properties of geometric shapes.

Students should work in pairs for this lesson. Have students create a four-sided figure and compare it with the one their partner made. Ask students to discuss the similarities and differences among the figures. As a class, discuss the properties common to each figure. Each figure has four sides.

Explain to students that they will experiment with other geometric properties important to understanding and working with figures. Also explain that you will give them time at the end of the lesson to explore other ideas they may have.

Tell students to use two rubber bands on the Virtual Geoboard E-Example to make a set of parallel line segments. As students work, pose the following questions.

• What is the important property of parallel lines? [They are two lines and they never touch.]
• How are parallel lines used in the environment and in art? [Examples might include railroad tracks, lines on a road, the sides of a bridge.]

Next, ask students to use two rubber bands on the Virtual Geoboard E-Example to make intersecting lines.

As students work, monitor their progress to check for understanding. Note which students demonstrate a complete level of understanding and those that need additional instruction and practice with the concepts of this lesson. The following questions will guide student’s attention to the similarities and differences between parallel and intersecting lines.

• What happens to the two intersecting lines? [They are touching each other (they meet.)]
• How do intersecting lines compare with parallel lines?

Have students use two rubber bands on the Virtual Geoboard E-Example to make perpendicular lines. Ask them to show a neighbor their example. Ask the following questions to direct students’ attention to the properties of perpendicular lines.

• What is special about perpendicular lines? [Perpendicular lines intersect to make a right angle (of 90 degrees.)]
• How are perpendicular lines and parallel lines different?
• Why is it important to know the properties of perpendicular and parallel lines as related to the previous lesson?

Tell students to make a quadrilateral with one set of parallel lines, two acute angles, and two obtuse angles. By asking the following questions, you can direct students’ attention to the properties of trapezoids. (Note: This is only one type of trapezoid.)

• What is name of your figure? [Trapezoid.]
• How do trapezoids differ from other quadrilaterals?
• Describe the properties of a trapezoid.

Ask students to make a quadrilateral that has two sets of parallel lines. Use the following questions to guide the discussion:

• What is the name of your shape? [Parallelogram.]
• Why is it important to know the properties of these figures compared with the figures in the previous lesson? [Not all quadrilaterals are rectangles.]
• Describe the properties of a parallelogram and explain how it differs from other quadrilaterals.

Have students make a shape that has five sides. Pose the following questions to help students see relationships between sides and angles.

• What is the name of this figure? [Pentagon.]
• How many vertices does it have? [5.]
• How does it compare with other figures we have made?
• Why is it important to know the properties of these figures compared with the figures studied previously?

Repeat with figures of six and eight sides. Ask the following questions to focus students’ attention on the properties of hexagons and octagons compared with other polygons.

• What is the name of this figure? [Hexagon or octagon.]
• How many vertices does it have? [6 or 8.]
• How does it compare with other figures we have made?
• Why is it important to know the properties of these figures compared with the figures studied previously?

Have one student volunteer to make each of the figures created in this lesson on the geoboard. Then have the student stand before the class so that others can visually compare the various shapes.

Invite students to discuss the similarities and differences. Focus attention on the discussion of parallel lines, perpendicular lines, and intersecting lines. Discuss the derivation of the names for each of the polygons.

To bring closure to the lesson, have students pair with a partner and take turns making shapes. Have the partner identify the vertices, numbers of sides, types of lines (parallel, perpendicular, intersecting), and angles.

Assessment Options

1. At this stage of the unit, students should know how to:
• Use geometric vocabulary
• Identify, compare, and analyze characteristics of geometric shapes
• Explore parallel, perpendicular, and intersecting lines
2. As students work, observe the knowledge they demonstrate and make notes about each student’s level of understanding for future reference and planning. When you pose questions to students, note the specific words and phrases they use. This will help you understand the meaning students make of the mathematics of this lesson.
3. The models on the geoboards serve as a good assessment of students’ knowledge of the objectives set for this lesson. Another assessment option is to ask students to respond in writing to a prompt such as “What did you learn from today’s lesson that you did not learn in the previous one?” or “Why is it important for you to know the meaning of parallel, perpendicular, and intersecting lines?” Writing allows students to process their knowledge in a different way so that it is internalized.
Extension
Move on to the next lesson, Finding Lines of Symmetry

Questions for Students

1. What different quadrilaterals did you make today? What are the characteristics of each?

[Rectangles, parallelograms, and trapezoids; Rectangles are parallelograms with right angles; Trapezoids have exactly one pair of opposite sides.]

2. What three types of lines did we make today? Can you draw an example of each?

[Parallel, intersecting, and perpendicular; student examples may vary.]

Teacher Reflection

• What challenges did students have who were less successful with creating the various figures?
• What kinds of questions did students ask once instructions were given for creating a figure? What did this tell me about their level of understanding?
• What strategies did I use to effectively assess and document each student’s understanding as he or she held up the geoboard? Which strategies were more natural to my working style? How can I engage students in helping me document their level of understanding?
• What experiences did I provide to challenge students who understood the lesson components?
• What changes should I make the next time I teach this lesson?

### Working with Shapes

3-5
Students review basic geometric terms related to triangles. They explore these terms and other geometric concepts by modeling them on the geoboard.

### Finding Lines of Symmetry

3-5
Students identify lines of symmetry and congruent figures. They explore these concepts with paper cutting and modeling on the geoboard.

### Who Was Wassily Kandinsky?

3-5
This lesson provides students with an exploration of the geometric figures Wassily Kandinsky used in his art. Students participate in a scavenger hunt to become familiar with Kandinsky’s works and the geometric figures used in his paintings.

### Seeing Geometry in Art

3-5
Students use paintings studied in the previous lesson to connect their knowledge of geometric shapes and terms with Kandinsky’s use of geometric figures.

### Mirroring Kandinsky

3-5
This lesson allows students to apply what they have learned in previous lessons by designing their own art. Students use Kandinsky’s style of art and their own creativity to make paintings that reflect their understanding of geometry.

### Learning Objectives

Students will:

• Use geometric vocabulary.
• Identify, compare, and analyze characteristics of geometric shapes.
• Explore parallel, perpendicular, and intersecting lines.

### NCTM Standards and Expectations

• Describe location and movement using common language and geometric vocabulary.
• Build and draw geometric objects.
• Create and describe mental images of objects, patterns, and paths.
• Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.