/ Math Learning Goals
· Construct acute, obtuse, right, and reflex angles.
· Estimate angle sizes and measure with a protractor.
· Bisect angles using a variety of methods, e.g., protractor, compass, paper folding, Mira. / Materials
· compasses
· protractors
· Miras
· BLM 6.1.1, 6.1.2, 6.1.3
Assessment
Opportunities
Minds On… / Whole Class à Demonstration
Develop four different ways to describe a straight angle using the headings: mathematical characteristics, everyday examples, diagram, and explanation. (See BLM 6.1.1 for sample responses.)
Groups of 4 à Exploring Angles
Post eight pieces of chart paper around the room. In groups of four, students focus on a specific angle, i.e., acute, right, obtuse, and reflex. Each angle is done twice. They define the angle and show examples, using available resources, books, Internet, etc.
Facilitate a class discussion using prompts such as:
· How did each group classify the angle? (by its degree range)
· Which angle(s) seems most common in the everyday world?
· Reflect on and explain why. (responses will variable) / Alternatively, use the Frayer model (BLM 5.1.1).
It is important that all four angles are represented.
Word Wall
· bisect
· acute angle
· obtuse angle
· right angle
· reflex angle
· estimate
Lesson may vary depending on what protractors are available (360° or 180°).
Copy protractors on overhead acetates and cut up for Home Activity.
Action! / Groups of 4 à Practice
Students complete Part A (BLM 6.1.2) and reflect after each measurement:
· Do we need to revise our estimates?
· Are our estimates within 10º?
Whole Class à Demonstration
Demonstrate how to bisect using a Mira, a compass, paper folding, and a protractor and mark equal angles using proper notation. Students complete each bisection, marking equal angles on BLM 6.1.2, Part B.
Individual à Reflection
Students reflect, using guiding questions:
· What happened to the original angle? (bisected)
· What does bisect mean? (divides angle into two equal parts)
· How does this method compare to the others, i.e., compass, Mira, paper folding, and protractor? (responses will variable)
Consolidate Debrief / Individual à Practice: Bisecting Angles
Students complete BLM 6.1.3, Part C.
Ask:
· What do you notice about the two new angles created after bisecting the original angle? (They are equal.)
· What conclusions can you draw? (Bisecting an angle divides it into two new equal angles.)
Curriculum Expectations/Observation/Mental Note: Assess students’ ability to bisect angles using at least two methods.
Demonstrate paper folding using a prepared angle on a piece of paper.
Practice / Home Activity or Further Classroom Consolidation
Using a protractor, a compass, and paper folding, complete the worksheet 6.1.3.
TIPS4RM: Grade 7: Geometry 22/09/2009 1
Unit 6: Day 1: Measuring and Bisecting Angles (A) / Grade 7/ Mathematical Process Goals
· Use a graphic organizer to reflect on knowledge of various types of angles.
· Consider the reasonableness of answers. / Materials
· compasses
· protractors
· BLM 6.1.2(A)
Assessment
Opportunities
Minds On… / Whole Class à Demonstration
Develop four different ways to describe a straight angle. (See TIPS4RM BLM6.1.1 Teacher for sample responses.) An alternative everyday example is a road sign that points in two opposing directions with the distance indicated for the two places.
Groups of 4 à Reflecting
Assign each group a different angle type. Each angle is completed twice. Students reflect on prior knowledge of acute, right, obtuse, and reflex angles (See TIPS4RM BLM 6.1.1 for sample answers.)
Whole Class à Discussion
Facilitate a class discussion using prompts such as:
· Which angle(s) seems most common in our everyday world?
· Why do you think that angle occurs most frequently?
· What angles are we most familiar with? Recall anchor angles of 90°, 45°,
and 180°. / / Mathematical Process Focus:
Reflecting
See TIPS4RM, Mathematical Processes package, Reflecting, p.5
Circulate among groups asking guiding questions:
After sharing within the group, students consider feedback and rewrite estimates.
Review the use of a protractor, particularly for reflex angles, as needed.
Action! / Individually à Estimating
Each student estimates the angles on BLM6.1.2(A) Part A.
Students reflect on the choice of strategy used to determine an estimate for the angle measure. Students do not measure the angle until after the sharing.
Groups of 3 à Sharing
Students share their estimates and their strategies for obtaining estimates with other group members.
They reflect on the input from group members to make any adjustments to their estimates.
Individually à Measuring
Using a protractor, students measure the angles on BLM6.1.2(A) Part A.
They reflect on the strategy they used and the reasonableness of their estimates using BLM6.1.2(A) Part B. Was your strategy effective? Why or why not?
Mathematical Process/Communicating/Checklist: Observe students as they communicate their reflections, noting the correct use of mathematical terminology.
Consolidate Debrief / Whole Class à Discussion
Pose the following questions:
· What is the relationship between the reflex angle and the acute angle in the diagrams?
· How does knowing this help you estimate a reflex angle?
Application
Practice / Home Activity or Further Classroom Consolidation
Identify two non-right angles in your environment and sketch a diagram of each, using a straight edge. Identify the type of angle, estimate, and determine the angle measure, using a protractor.
Unit 6: Measuring and Bisecting Angles (A) Jazz Day / Grade 7
/ Mathematical Process Goals
· Reflect on strategies for bisecting angles. / Materials
· compasses
· protractors
· Miras
· BLM6.1.3(A)
Assessment
Opportunities
Minds On… / Small Group à Sharing
Students present their two angles from previous day’s home activity. Students describe where the angle exists in their environment and what strategy they used to estimate the angle measure. / Mathematical Process Focus:
Reflecting
See TIPS4RM, Mathematical Processes package, Reflecting, p.5
Action! / Whole Classà Demonstration
Demonstrate how to bisect an angle using a Mira, a compass, paper folding, and a protractor. Mark equal angles using proper notation.
Individual à Bisecting Practice
Students use each of the strategies to bisect angles on BLM6.1.3(A). Students write down their reflections on page2 of the task.
Consolidate Debrief / Whole Class à Reflection
Pose the following questions orally:
· What do you notice about the two new angles created after bisecting the original angle? (They are equal.)
· What are the advantages and disadvantages of the different methods of bisecting an angle?
· Consider, if there are any situations where one method would work better than others.
Practice / Home Activity or Further Classroom Consolidation
Using a protractor, a compass, and paper folding, complete page3 of worksheet6.1.3A. / If there are Miras that students can take home, include this strategy in the Home Activity.
Grade 7 Unit 6 Adjusted Lesson: Mathematical Processes – Reflecting 22/09/2009 3
BLM6.1.2(A): Estimating and Measuring Angles
Part A
/ StrategyType of Angle: ______
Estimate: ÐABC ______° / Actual: ÐABC = ______°
/ Strategy
Type of Angle: ______
Estimate: ÐDEF ______° / Actual: ÐDEF = ______°
/ Strategy
Type of Angle: ______
Estimate: ÐGHJ ______° / Actual: ÐGHJ = ______°
BLM6.1.2(A): Estimating and Measuring Angles
Part B
Reflection
Compare your estimate with the actual measure for each of the angles.
1. For which angle was your estimate closest to the actual measure?
What strategy did you use to arrive at your estimate?
2. For which angle was your estimate furthest from the actual measure?
What strategy did you use?
What other strategy could you have used to make your estimate closer to the actual?
BLM6.1.3(A): Bisecting Angles
1. Bisect each angle using a different method (Mira, protractor, folding paper, compass).
2. Compare the methods you used for bisecting angles. Which do you prefer? Explain why.
Grade 7 Unit 2 Adjusted Lesson: Mathematical Processes – Representing 22/09/2009 6