Looking at things from different angles

This lesson will introduce students to angles using a resource of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop "Interactivate Your Bored Math Students."

A lesson plan for grade 6 Mathematics

By Beth Jorgensen

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Related topics

• Learn more about angles, hands-on, kinesthetic learners, mathematics, and transversals.

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Learning outcomes

Students will:

• define and give examples of alternate interior, alternate exterior, adjacent, and corresponding angles
• explain how to fill out the chart in the exploration questions
• discuss parallel and perpendicular lines
• define and show examples of right angles, obtuse angles, and acute angles

From http://www.shodor.org/

Teacher planning

Time required for lesson

105 Minutes

Materials/resources

• Graph Paper
• Pencil
• Linguine
• Protractor
• Beans: 4 for each student
• Popcorn Kernels: 4 for each student
• Angles Worksheet
• Ruler
• About 2 yds of string
• 2 yard sticks or meter sticks

Technology resources

Color monitor with access to the Internet for each student, either via a computer lab or a one computer classroom.

Pre-activities

Preceding this lesson student should be familiar with the following terms:

• acute angles
• obtuse angles
• right angles
• parallel lines
• perpendicular lines
• intersecting lines

Activities

I use 4 different activities that combine physical, visual, written and technological aspects to teach and reinforce this concept. Activities 1, 2 & 3 could be done in 1 hour. Activity 4 and the Assessment could be done in 45 minutes. The entire lesson would probably be best done over 2 days.

Activity 1

1. Each student will have 3 linguine noodles (any flat long noodles will work) and 2 different beans, 4 of each.
2. They will place 2 noodles on their desk parallel to each other. They will place the third noodle so that it intersects both the lines, but not perpendicular.
3. Instruct them to take 4 beans and place them in all the acute angles. Then take the 4 popcorn kernels and place them in all the obtuse angles.
4. They should now have 1 kernel/bean in each of the 8 angles.
5. This is the A-HA! moment; ask them to make some observations about what they can see.Hopefully they will notice that the acute angles are “vertical”, they may notice that outside top left and outside bottom right are the same bean/kernel (alternating exterior angles). At this point I am not overly concerned about terminology more about introducing the concept, although I would say the terms as they discover them. Keep prompting until all the concepts have been discovered. (It is up to your discretion what you do with the manipulatives, some students may want to eat them)

Activity 2

1. Students are still in seats, at desks. Choose 2 students to hold the string midway across the room. Then choose 4 students to form boundaries on both ends of the rope. What you want this to simulate is a volleyball court, the string being the net, and the rulers being the boundaries.
2. The net/string is the transversal and the sticks are the parallel lines. This is a good time to start reinforcing concepts. Lead them through a brief discussion about choosing sides for teams. “You go here, You go there…alternating.”
3. Once they have caught on ask where they think the interior part of the court is and where the exterior might be.
4. Finally place 2 students as alternating exterior people, continue until you have covered all possible combinations. They should remember that when they did the noodles those angles were equal.

Activity 3

Using the graph paper and rulers, each student will draw 2 parallel lines, and 1 transversal. They will label them 1 to 8. They will use the protractor and measure each angle and write the measurement in the angle. Along the side of the paper they will make a list of what they know about the relationships between different angles, such as:

• vertical angles: <1 = <4
• alternating interior angles
• alternating exterior angles
• adjacent angles
• corresponding angles
• supplementary angles (review)

They may ask the people in their group if they get stuck.

Activity 4

1. The student will need to have access to a computer for this activity. Go to Angles. Explain, model, and demonstrate the assignment to the students.
2. Have them go through this a number of times while you go around the room and check their scores, when you are convinced they have mastered the concepts, proceed to the assessment worksheet.

Assessment

• When students have shown that they understand the concepts to your satisfaction, hand out the Angle Worksheet.
• Students need to be aware that there are duplicates in some of the boxes. It would be beneficial to point some of these out before you begin.
• The most important part of this assessment is to find out if the student has grasped the major concepts: alternating interior angles, alternating exterior angles, vertical angles, & corresponding angles.
• There are a total of 216 entries on this sheet. I would be looking for mastery, competency, adequate (but lacking), and needs attention. Based on that I would assign students to groups and the following day start the lesson with a review that would allow the students to work together to fill in the gaps.
• 95-100% = mastery
• 75-95% = competency
• 50-75% = adequate (but lacking)
• less than 50% = needs attention

Because it is a chart it is fairly visible to tell what percentage of the chart is complete.

Supplemental information

Comments

At some point after activities 1 or 2 I would have a brief discussion about why this might be important to someone.