Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (49 page)

5.
can be decomposed into
and another angle. The other angle is not on the “Angles” sheet. Find the measure of this missing angle.

Geometry: 4.G.1

“Draw and identify lines and angles, and classify shapes by properties of their lines and angles.”

1. “Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.”

Background

As they proceed in their study of geometry, students should be familiar with basic geometric terms, such as the following:

• Point:
  Represented by a dot, a point is an exact location in space. It is named by a capital letter.
  
• Line:
  Extending infinitely in both directions, a line is a straight path in space. It is named by two capital letters that represent points on the line.
  
• Line segment:
  A part of a line, a line segment is named by two capital letters, each one representing an endpoint of the segment.
  
• Ray:
  A part of a line, a ray has one endpoint and is designated by two capital letters, one representing the endpoint and the other representing a point on the ray.
  
• Angle:
  An angle is a figure formed by two rays that share a common endpoint, which is the vertex of the angle. One way an angle can be named is by a capital letter that represents a point on a ray, a capital letter that represents the vertex, and a capital letter that represents a point on the other ray. Another way to name an angle is by placing a number in the vertex. A third way is to label the vertex with a capital letter.
  
• Perpendicular lines:
  Two lines are perpendicular if they are in the same plane and intersect, forming right angles.
  
• Parallel lines:
  Two lines are parallel if they are in the same plane but do not intersect. The distance between the lines remains the same.
  

Activity 1: Drawing Geometric Figures

Students will draw points, line segments, lines, rays, angles (acute, right, and obtuse), and perpendicular and parallel lines.

Materials

Ruler; protractor; unlined paper; reproducible, “Drawing Geometric Figures,” for each student.

Procedure

1.
Explain that students will draw a variety of geometric figures. Briefly discuss the geometric figures presented in the Background and provide some examples.

2.
Hand out copies of the reproducible. Explain that it contains instructions for drawing basic figures, but it does not identify the figure.

3.
Tell your students to follow the instructions exactly, drawing all nine figures. They are to name and label the figures. They should use rulers and protractors to ensure accuracy.

Closure

Check students' figures. Review the features of each.

Answers

(1)
line
(2)
acute angle
(3)
parallel lines
(4)
obtuse angle
(5)
point
(6)
ray
(7)
right angle
(8)
perpendicular lines
(9)
line segment

Activity 2: Shapes and Structures

Working in small groups, students will create a collage illustrating points, line segments, angles, perpendicular lines, and parallel lines.

Materials

Scissors; glue sticks; markers; rulers; large construction paper; old magazines; newspapers. Optional: Computers with Internet access; printers.

Preparation

Prior to assigning this activity, ask students to bring in old magazines and newspapers in which they may find pictures of man-made objects and structures that provide examples of geometric figures.

Procedure

1.
Explain that students are to find examples of points, line segments, angles (acute, obtuse, and right), perpendicular lines, and parallel lines in pictures contained in magazines and newspapers. They should cut out the pictures and paste them onto construction paper, creating a collage. If your students have access to computers and the Internet, suggest that they go online to find and print examples of geometric figures.

2.
Instruct your students to label each of the pictures in their collage. They should write the geometric figure and the object or structure it was a part of. For example: “Perpendicular lines found on a bridge” or “Right angles on windows.”

3.
Encourage your students to be creative, neat, and thorough with their collages. Suggest that they include more than one example of each figure to make an interesting collage.

Closure

Have students share their collages with others. Display the collages.

Drawing Geometric Figures

Directions: Draw, label, and name each figure.

1.
Draw a line segment. Draw arrowheads at both ends of the segment. The arrowheads show that the figure extends in both directions.

2.
Draw a ray. Place the crosshatch of the protractor on the endpoint of the ray. Align the ray with the
line on the protractor. Mark a point near the scale of the protractor to make an angle less than
Draw a ray from the endpoint of the first ray through this point.

3.
Draw a line. Measure an inch below one of the points on the line. Mark a point. Mark another point an inch below another point on the line. Use your ruler to connect the two points you marked. Draw arrowheads on the ends of this line segment.

4.
Draw a ray. Place the crosshatch of the protractor on the endpoint of the ray. Align the ray with the
line on the protractor. Mark a point near the scale of the protractor to make an angle greater than
Draw a ray from the endpoint of the first ray through this point.

5.
Mark a dot.

6.
Draw a line segment. Draw an arrowhead at the end of one endpoint of the segment.

7.
Draw a ray. Place the crosshatch of the protractor on the endpoint of the ray. Align the ray with the
line on the protractor. Mark a point near the scale of the protractor to make an angle of
Draw a ray from the endpoint of the first ray through this point.