## Working with Shapes

- Lesson

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

To assess students' prior geometric knowledge, make a KWL Chart as a group. Record on the overhead projector or on a chart in the classroom. You and the students can refer to this chart in the future.

KWL Chart |

Direct students to the Virtual Geoboard, part of the NCTM E-Examples on the *Principles and Standards* Web site.

Virtual Geoboard E-Example |

Give students at least five minutes to make designs on their own using the geoboards. Tell them that this is the time to experiment and explore. Ask students to share what they learned from the activity. Then have them clear their boards.

Ask students to model geometric figures and discuss the online questions after creating each figure.

*Note:* It is important for students to process what they
are doing to create the various figures so that they will understand
the relationships among the figures. Talking helps students clarify and
extend their thinking. It also helps you understand what students are
learning.

Ask students to make a three-sided figure on their personal geoboards. Then, pose the following questions to guide students’ thinking about the properties of this three-sided figure.

- What is the name of this figure? [triangle]
- How many vertices does this figure have? [3]
- Show me an example of a vertex by holding your geoboard up and pointing to the vertex. Model this on the Virtual Geoboard E-Example.
- What is the relationship between the number of sides and the number of vertices?

Ask students to make a four-sided figure on their geoboards. Then ask the following questions to guide students’ thinking about the properties of this four-sided figure.

- What is the name of this figure? [quadrilateral]
- Why is it so named? Are the sides of your quadrilateral the same? Why or why not? This discussion helps focus on the equilateral quadrilateral.
- How many vertices does this figure have? [4]
- How do the four-sided figures compare with the three-sided figures? What are the primary similarities? What are the major differences?

Ask students to show you a right angle on the Virtual Geoboard E-Example using two rubber bands. Pose the following questions to guide their thinking about the properties of the right angle.

- How would you describe this shape to a partner who has never seen such a shape?
- What words can you use to describe the right angle? How is an understanding of these words important to an understanding of the shape you created?
- How is an understanding of these words important to an understanding of other shapes you might make?

Ask students to show you an acute angle on the Virtual Geoboard E-Example using two rubber bands.

- How would you describe this shape to a partner who has never seen such a shape?
- What words can you use to describe the acute angle?
- How does this activity compare with the previous ones?
- Why is it important to know the difference between acute and right angles?

Ask students to show you an obtuse angle on the Virtual Geoboard E-Example using two rubber bands. Ask a volunteer to model how to construct an obtuse angle using the virtual geoboard.

- How would you describe this shape to a partner who has never seen such a shape?
- What words can you use to describe the obtuse angle? How is an understanding of these words important to an understanding of the shape you created?
- Why is it important to know the difference between acute, right, and obtuse angles?
- What important knowledge is necessary for you to describe the difference among the three types of angles?

When students have made and discussed each of the figures, ask them to discuss the similarities among the figures. It may be helpful for students to display a sample of each figure or angle during this discussion.

Encourage students to consider the common properties that define each figure. Ask them to pose any questions they may have about each figure.

Bring closure to the lesson by having students write a brief summary of what they have learned and the questions they want to explore. Collect these work samples so that you can review and identify students’ knowledge and understanding to guide the next instructional activities.

**Assessments**

- At this stage of the unit, students should know how to:
- use geometric vocabulary correctly
- identify, compare, and analyze characteristics of geometric shapes
- recognize acute, obtuse, and right angles

- You may find it helpful to make notes about the models students create on the geoboards. This is a good assessment tool for determining which students have met the objectives for this lesson and which have not.
- You may also want to review and make notes about the written samples regarding student’s understanding and/or misunderstanding of the mathematical content of the lesson.

**Extensions**

- Pair students and have them take turns making shapes. Have each partner identify the vertices, numbers of sides, types of lines (parallel, perpendicular, intersecting), and types of angles.
- Students could also experiment with symmetrical shapes and have their partners identify lines of symmetry. Students can make a shape and their partners can make a similar and/or congruent shape. Shapes could be drawn on dot paper.

**Questions for Students**

1. What properties does a triangle have?

[3 sides, 3 angles, closed figure.]

2. Name all the different quadrilaterals and the characteristics they exhibit.

[Student responses may include parallelogram, rectangle, square, rhombus, and trapezoid.]

3. What are the three types of angles? Give examples of figures that have these types of angles.

[The types of angles are actue, right, obtuse; student examples may vary.]

4. Describe the three types of lines (parallel, intersecting, and perpendicular) and give examples of each.

[Parallel: lines never meet and are always the same distance apart; Intersecting: two or more lines that meet; Perpendicular: intersecting lines that meet at right angles; Student examples may vary.]

**Teacher Reflection**

- Which students were able to construct each of the different figures?
- What knowledge of lines and angles did students use to help them form specific shapes?
- How did modeling with the virtual geoboard help students understand the objectives of this lesson? What indicators did I have that students benefited from this modeling?
- What strategies did I use to effectively assess and document each student’s understanding as he or she held up the geoboard?
- What experiences did I provide to extend the assignment for students who understood the lesson components?

### More Work with Shapes

### Who Was Wassily Kandinsky?

### Seeing Geometry in Art

### Finding Lines of Symmetry

### Geometry in the World of Art: Mirroring Kandinsky

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
- Recognize acute, obtuse, and right angles

### Common Core State Standards – Mathematics

Grade 5, Geometry

- CCSS.Math.Content.5.G.B.4

Classify two-dimensional figures in a hierarchy based on properties.