• Evaluate student drawings for labels to make sure that objects identified as point lines and planes are recognizable as such. Objects represented as points must indicate position, those identified as lines must indicate position and length, and those identified as planes must indicate location length and width. For the objects drawn, dimensions need not necessarily be expressed as measurements.

• In Lesson 1 Exit Ticket (M-G-1-1_Lesson 1 Exit Ticket.doc), students will demonstrate their understanding of basic geometric properties by indentifying one real-world example of a point, line, line segment, intersecting lines, and parallel lines.

Begin by asking students what they know about a point (e.g., What does it look like; what are its properties?) (Student responses might include: it has no definable dimensions of width, length, height; looks like a dot; etc.) [IS.6 - All Students] Explain to students that we will be using a penny as a representation of a point.

Give each student a supply of pennies (approximately 10 per student). [IS.7 - Struggling Learners] Each student should place two pennies on his/her desk to represent two points. Use the pennies sample for an idea of how the pennies should look once they are placed on the desk (M-G-1-1_Pennies Sample.doc).

Instruct students to use additional pennies to connect the original two points. Allow students to interpret the word connect in whatever way they like; they do not have to create a straight line of pennies connecting the two pennies. Discuss different student solutions and interpretations of the word connect.

Now, ask students to connect their two points using as few pennies as possible. Ask them to make observations about the arrangement of pennies on their desk. [IS.8 - All Students] Observations should include that the pennies form a straight line, that they used a minimal number of pennies, etc.

Identify the line of pennies connecting the two original points as a line segment. Ask students the following questions to further solidify the connection between points and line segments:

“What is your line segment made of?” (pennies/points)

“Is there another line segment you can make to connect the two points?” (no)

Lead into the idea of lines (as opposed to line segments) by using the following questions:

“How much longer could you make your line segment?”

“Could you make it extend forever if you had enough pennies?”

Identify a line as a line segment that continues forever, so it has no beginning and no end.

Ask students what they call a beam of light that comes from the sun (ray). Ask whether a sun’s ray has a beginning and an end if it keeps going into space. Use this idea to help define a ray as a line segment that continues forever from only one endpoint.

Label one penny as point A and the other as point B. On the board, list the notations for line segment AB (), line AB (), ray AB (), ray BA (), and measure of line segment AB (m(AB)). Ask students which of these most likely represents the line segment, which represents a line, which represents a ray. Ask students for opinions regarding the last notation (measure of line segment). Explain what it is and how it differs from the notation for line segment AB. (Possible answers: m stands for measure; it does not have arrows; there is no line over it.) Diagrams have been provided below for your reference.

Ask students to find the length of their line segments, in terms of pennies (e.g., My line segment is 10 pennies long).

Have students consider each of their line segments constructed of pennies. Ask students:

“Do any of these line segments intersect?” (no)

“Does this mean that they are parallel?” (no)

“Why not?” (Parallel means that they are the same distance apart along the entire path.)

“If each of these line segments were extended into lines, would they intersect?” (Yes, because they are not parallel.)

Choose two students and give them string to use to extend their penny lines so that they intersect.

Now draw the following: .

Distribute copies of the angle identification masters (M-G-1-1_Angles.doc) to the class and have students study the various angles. Explain to students that angles are formed when two rays intersect at a common starting point, and are measured based on how much rotation they cover. An angle that makes a full rotation around is 360 degrees. Demonstrate angle measurements using a protractor if desired. Explain to students that acute angles are any angles that are less than 90 degrees but more than 0 degrees. Also explain that obtuse angles are angles that have angle measurement between 90 and 180 degrees. Have students look at the various angles on the page and see what examples of each kind of angle look like.

Once students have looked at the angles, have them explore the room to identify the various angles of objects. [IS.9 - All Students] Most of the objects they find will be composed of ninety degree angles.

Point to one of the ninety degree angles students identify, and have them look at the point where the two rays that make up the angle meet. Explain to the class that this point is called the vertex of the angle.

Now draw a line on the board, but this time put three points on it. Tell the class that if three points all lie on the same straight line, the three points are said to be collinear. Not all sets of three points are collinear though (demonstrate by drawing three points in a triangle shape. No matter how hard you try, you cannot connect all three points by a straight line. Now have students draw three points at random and see if they can connect all three by the same straight line.

Pair students to draw various objects in the classroom that are composed of straight lines (e.g., black/white board, edges of walls, floor, ceiling, desks, doors). Encourage partners to draw at least three different objects and make sure to point out some objects that do not have parallel or perpendicular lines. Next, students should label each point of intersection with a different letter. Have them list each line segment in the drawing. Then have students identify any line segments that appear to be parallel. Finally, have students measure the length of each line segment (the actual line segment in the room, not the one drawn on the paper) and write the measurement of each line segment (M-G-1-1_Line Drawing Example.doc). [IS.10 - Struggling Learners]

Have a few students present their results. [IS.11 - All Students] Make sure to check for appropriate use of notation (ensure that students are distinguishing between the object and the measurement of the object). Discuss with students the existence of line segments in the real world. Also discuss the frequency of parallel lines: “Why are so many things in the world parallel or nearly parallel?” (aids in construction, creates solid structures, etc.). Encourage the audience to question each presenter for clarification or explanations of vertices, line segments, and parallel lines. [IS.12 - All Students]

As an exit activity, have students list on a piece of paper one real-world example of each: point, line, line segment, ray, intersection, parallel lines. [IS.13 - All Students] Alternatively, distribute Lesson 1 Exit Ticket (M-G-1-1_Lesson 1 Exit Ticket.doc) for students to complete and turn in as they leave class.

Extension:

• Ask students to visualize the hands of an analog clock with their position at 8: 45. [IS.14 - All Students] Leaving the hour hand unmoved in the same location, what is the angle measure between the minute hand an hour hand at 9:00? at 9:15? at 9: 30? [90 degrees, 180 degrees, 270 degrees]

• Point out to students that angles greater than 180 degrees are called reflex angles, and they can also be represented by subtraction from 360 degrees. For example, 270 degrees subtracted from 360 degrees is equal to 90 degrees, which is the angle measure between 9 and 6 on an analog clock.

• Find an equivalent angle measure for the following reflex angles.

• 1. 350 degrees [10 degrees]

• 2. 183 degrees [177 degrees]

• 3. 370 degrees [10 degrees]

• 4. 720 degrees [0 degrees]