• Assess student comprehension levels based on performance on the Checklist (M-4-5-1_Checklist and KEY.docx) in Activity 2.
• Evaluate student vocabulary knowledge based on how well their drawings match their partner’s “requirements” in Activity 3.
• The Lesson 1 Exit Ticket (M-4-5-1_Lesson 1 Exit Ticket and KEY.docx) may be used to assess student mastery of geometry vocabulary words.

Activity 1

Make copies of some Arrowheads and Points (M-4-5-1_Arrowheads and Points.docx). These will be given to student volunteers throughout the activity.

Draw a point on the board – make it large so students can see it. “This dot, in geometry, when talking about shapes, is called a point. Lots of things in geometry deal with points. What does a point look like?” Students will probably note that a point is like a period or a dot. “A period, like at the end of a sentence, is the perfect way to think about a point—a very small dot.”

Select two volunteers to come to the front of the class and hold a piece of paper with a point. “[Student names] will be our points for a little while. So, imagine they are small dots. We’re going to use these lengths of rope and our points to show some things we can build using points.” Hand each point one end of the rope and have them stretch it out so it’s tight.

“This represents a line segment.” Write the term line segment on the board. “A line segment is part of a straight line, like the rope, that goes between two points, like our volunteers.” Draw a line segment on the board, making sure to clearly show the points at either end. Have the two volunteers each take one step closer to one another.

“Is this a line segment?” Discuss that it is not a line segment because the rope between the two points is not straight.

Ask students if any of them know the word segment. Discuss how the word segment means “part” or “part of.” “So, if this is a line segment, it’s really just part of a line. A line is straight, just like our line segment, but the difference is that a line keeps going forever and ever in both directions. It doesn’t end at any points along the way.” Hand each of the two volunteers an arrow and have them hold it over their respective ends of the rope.

Draw a line on the board and label it line, making sure to put arrows on either end. “We draw arrows on the end of a line to show that it keeps going in both directions.”

“So far, we have points and lines, which go on forever in both directions, and line segments which stop at both ends. What about something that goes on forever in only one direction?” Have one of the volunteers lower the arrowhead and replace it with a point. “We call this a ray.” Write the word ray on the board and draw a ray.

“What does the word ray mean or where have you heard the word ray before?” Guide the discussion toward rays from the sun and point out that they start at a specific point—the sun—and keep going forever through space (as long as they don’t run into anything along the way). Also, point out that rays from the sun are straight.

Hand the end of another piece of rope to the student who is representing the point of the ray. Then, have a (preferably taller) volunteer come up and hold the other end higher than the first ray to form an angle visible to the class. The second volunteer will need an arrowhead as well.

“So now we have two rays. They both start at the same point and make a ‘v’ shape where they meet. Does anyone know what we call this when we have two rays starting in the same place?” Discuss that it is called an angle. Write this on the board and draw a geometric interpretation of an angle. “There are angles all around us.” Point out angles at the corners of the room, patterns on shirts, and other objects around the class.

“Angles come in different shapes. The ones at the corner of the room are different than the one that our volunteers made out of rope. The angle our volunteers made is pretty skinny; the two rays are pretty close together. We call this kind of angle acute. The word acute just means, in general, that it’s a skinny angle, with the rays close to one another.” Write the word acute on the board and draw an example of a clearly acute angle.

To represent a right angle, you may have to take the end of the second ray, depending on the height of the third volunteer. Take the end and slowly increase the measure of the angle and have the class keep repeating the word acute as the size of the angle grows. When you are standing immediately behind the vertex of the two rays, have the class stop. “This is no longer an acute angle! It’s now a right angle. The two rays make a nice, square corner. Unlike acute angles, which can be any size of skinny angle, a right angle always looks exactly like a nice, square corner.”

Start to move beyond the vertex to make an obtuse angle. As soon as you move beyond the vertex, tell the class, “And when we have an angle that is wider or bigger than a right angle, we call it obtuse.”

Hand the second ray back to the volunteer and write and draw both right angle and obtuse angle on the board. Have the volunteer keep moving to make wider and wider obtuse angles until they get close to demonstrating a straight angle, at which point they can stop.

“So, an angle is just two rays that start at the same point and come in three types: acute, which are skinny; right, which make a square corner; and obtuse, which are bigger than right angles.”

Get four new volunteers. Make sure the first few volunteers get a chance to write down any material on the board before continuing.

Have two volunteers sit on the floor or kneel, each of them holding one end of a rope (with arrowheads) to make a line.

“What do we call this when it keeps going forever in each direction?” (a line)

Have the other two volunteers stand, each one behind one of the first two volunteers, and hold the second rope (with arrowheads) to make another line. Help them make it parallel to the first one by having them raise or lower the “ends” of the line.

“Now, we have two lines. Do these two lines cross one another?” (no) Remind students to consider that the two lines keep going forever in both directions, based on what the arrowheads indicate, so they have to use their imaginations. Students should still conclude that they won’t cross one another. “These lines are called parallel.” Write the word parallel on the board and draw two parallel lines. “Any lines that would never cross, no matter how long they are, are called parallel.”

Now, direct the two standing students. Have one kneel behind the lower of the two lines, and the other should hold the rope straight up. (Depending on the height, it may be necessary for you to hold the rope straight up.) “Are these lines parallel?” (no) “Why not?” (Because they cross one another.)

“When they cross, what kind of angles do we get?” Point out the two angles formed by the intersection of the two lines. “Do we get acute, right, or obtuse angles?” (right) “When two lines cross and they make right angles, we call the lines perpendicular.” Write the word and draw a diagram on the board.

Have the standing student “rotate” the upper line. It should still intersect the lower line but not at a right angle. “Are these lines parallel?” (no) “Why not?” (Because they cross one another.) “Are they perpendicular?” (no) “Why not?” (Because they don’t make right angles where they cross.)

Point out one of the angles and ask the class to describe it. Then have them describe the other angle.

Depending on class engagement and time, continue to manipulate the two lines to create different geometric figures and quiz students on what each model represents.

Activity 2

Give each student one copy of the Checklist (M-4-5-1_Checklist and KEY.docx).

“For this activity, I’m going to draw a figure on the board. Your job is to decide which geometric attributes make up each figure. We’ll do the first figure together.”

On the board, draw two perpendicular lines. Make the point at the intersection clear and make sure to include arrowheads on the ends of the lines. Label it Figure 1.

“Look at the row on your checklist for Figure 1. The first column for each figure is labeled Point (at the top of the page). So that first box is whether or not Figure 1 contains a point. Is there a point in Figure 1?” (yes) Indicate the point. “Then put the letter ‘Y’ in the box for ‘Yes.’ Is there a line?” (yes) “So you’ll put the letter ‘Y’ in the box to stand for ‘Yes.’”

“Is there a line segment?” (No, a line segment goes between 2 points, and there aren’t 2 points in the diagram.) Talk about why not; a line segment goes between two points and there aren’t two points in the diagram. “Then put the letter ‘N’ in the box for ‘No.’”

Work through the rest of the row. Note that there is a ray. Students may not recognize it at first but consider part of one of the lines in the figure from the point of intersection extending outward. (The first row should be: Y, Y, N, Y, N, Y, N, N, Y.)

Create a second figure that is a polygon. Write the word polygon on the board underneath the figure. “Figure 2 is an example of a polygon. A polygon is a figure that is closed. There are no holes or spaces in the sides, and all the sides are straight line segments. Everywhere the line segments meet, there is a point called a vertex.” Write the word vertex on the board, and then work through the checklist for Figure 2 with students.

Based on how students did on the first two figures, provide other figures. Figures can include sets of parallel lines, parallel and perpendicular lines, triangles, rectangles, and other plane geometry figures. The choice of figures should be done in relative increasing order of difficulty.

Activity 3

Have students work in pairs. Give each student a copy of the Student Checklist (M-4-5-1_Student Checklist.docx).

“First, each of you will draw your own Figure 1 on another sheet of paper without showing it to your partner. Then, you’ll fill in the row for Figure 1 based on the picture you just drew. Finally, you’ll give your checklist to your partner. They’ll be able to see, for example, that your figure contains a point, a line segment, and maybe a ray, and then they’ll have to draw a figure that has those things in it.”

Point out to students that they shouldn’t expect that their Figure 1, for example, and their partner’s Figure 1 will be identical. (You can let students figure this out as they go along, but many students may expect the figures to be identical and assume they’ve made an error when their drawings don’t match their partner’s.) Encourage students to start with simple figures until they get some practice, and then move on to figures with more things in them.

Depending on time, allow students to work through up to 9 figures.

Extension:

Use the following strategies to tailor the lesson to meet the needs of the students.

• Routine: Throughout the year, as students continue to learn about geometric shapes (triangles, squares, etc.), continue to use and stress proper terminology. For example, “A square is a shape made up of four points (vertices) connected by two sets of parallel line segments. There are four right angles.”

During the school year, when time allows, students may play the geometry vocabulary matching game at the following Web site:

http://www.learninggamesforkids.com/math_games/5th-grade-math/geometry-terms-5th/matchit-geometry-terms-5th.html

• Small Group: Students who may benefit from additional practice can be pulled into small groups. Have the students in each group work together to create a giant figure (on a piece of butcher paper, etc.), and then label all of the geometric parts used to make up the figure. The figures can be as creative and varied as students like.
• Expansion: Students who are ready to move beyond the requirements of the standard may study about estimating angle measures, congruence and similarity as well as learning the names of several geometric figures.

Students may practice a more advanced geometry vocabulary using the game at the following Web site:

http://www.aplusmath.com/cgi-bin/games/geopicture

Instructional and testing materials are available for individual student exploration at the following Web site:

http://www.geometry.uconn.edu/6th%20grade%20geometry/IrregularPolygons.htm