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# Lesson 3: Measuring Angles • Lesson Title: Measuring Angles
• Lesson Length: Approximately 2 days
• NCTM Standard: Geometry Standard, Measurement Standard

#### Learning Objectives

1. The student will analyze and measure angles using a protractor.
2. The student will identify angles as right angle, acute angles, and obtuse angles.
3. The student will build and draw right, acute, and obtuse angles.

#### Connection to Bloom’s Taxonomy

• Analysis
• Application
• Comprehension
• Synthesis

## Lesson Materials

• Construction Paper
• Crayons or Colored Pencils
• Glue
• Index Cards
• Pencils
• Protractor
• Toothpicks
• Worksheets for lesson plan 3 (see sidebar)

## Making Connections

Angles are a very important concept in geometry though they are not often thought about in our daily lives. However, angles impact our lives in more ways than we think. Explain to students that we all use angles without even realizing. Ask students to brainstorm how angles are used in the world around us. Create a list from the brainstorming session.

Discuss the following questions:

1. How do people in various professions use angles to complete their work?
2. How do all people use angles in their everyday lives?
3. How do you ( as a child/student ) use angles?

Some possible ideas include the following:

• A baseball player moves across the field at various angles to catch a ball
• A football player throws a pass at the correct angle for a receiver to catch the ball
• When parking a car a driver uses the concept of angles to park in a particular space, especially when parallel parking
• A pilot maneuvers an airplane using a variety of angles to fly and land
• A contractor uses angles to build a house, a school, or any structure
• A cook holds a knife at various angles to chop and prepare foods
• A child uses angles to build a skateboard ramp or a bike jump
• A child skis or sleds at various angles to complete a downhill run
• A nurse adjusts a bed to create an angle that is comfortable for a patient
• A student places books on a shelf at a slight angle to prevent them from tipping over
• Umbrella’s can be tilted at an angel in order to stop rain or provide shade

## Exploring and Learning

1. Take the students on a walk around the school, both inside and outside. Have students work in pairs to identify and list angles they see in and around their school. The list may include the following: bike wheel spokes, pizza slices, clothing hangers, binders, hands of a clock, a playground slide, an open door, door stopper or wedge, chair, and even a pencil is held at an angle when used for writing.
2. Gather the class and ask each team to share two examples of angles. Create a class list of angles on the board, flipchart, or overhead:
3. Next, provide each student with a copy of the Angle Facts Worksheet (PDF). Guide students through each bullet on the worksheet. Draw examples of a straight line, right angle, acute angle and obtuse angle on the board or overhead.
4. Have students create vocabulary index cards with drawings and definitions for each of the bolded words on the worksheet; vertex, degrees, right angle, obtuse angel, and acute angle.
5. Direct student attention back to the class list generated in #2, above. Ask if there are any right angles on the list? Most likely students did not identify right angles. We tend to forget that a straight corner measuring 90 degrees is actually an angle. Instruct students to look around their classroom and identify at least five right angles. Items might include a television screen, computer monitor, calendar, book, window, and folder. This step can be repeated using acute angles and obtuse angles.
6. Present students with the following scenario:

RG and Hannie are working at the Raymond Geddes Elementary School Store. They are setting up a new sales display that includes several different math tools which includes rulers and protractors. RG and Hannie are not familiar with a protractor.

RG asked, “What is a protractor?"

Can you help RG and Hannie solve some problems using a protractor?

7. To help complete the scenario, ask students to define a protractor. Explain that a protractor is a tool used to measure angles. Ask the students if they have seen or used a protractor before.
8. Next, pair students together and provide each group with a protractor. Instruct students to make a list of observations based on the physical appearance of the protractor. Create a class list of observations by allowing each group to share 1 or 2 observations. The list may include the following:
• It is shaped like a semi circle (although some protractors can be a full circle)
• It looks like a ruler
• It has numbers labeled from 0 to 180
• There are two rows or scales of numbers
• The upper scale starts with 0 on the left side and increases to 180 on the right
• The lower scale starts with 180 on the left side and decreases to 0 on the right
• The upper scale measures angles with openings on the left
• The lower scale measures angles with openings on the right
• The protractor is clear so that the angle can be seen and measured accurately
9. Demonstrate how a protractor is used. Draw an angle on an overhead transparency or the board. Align the straight edge of the protractor along the bottom of the angle. Align the center of the protractor at the vertex of the angle. Use the scale to measure the angle accordingl.
10. Pair students together and provide them with a copy of Angle Worksheet. Instruct students to use a protractor in order to find the angle degree and the type of angle. Students can refer to the Angle Facts Worksheet for help in identifying the types of angles.
11. Additional measurement and angel identification can be done by having students create angles out of toothpicks. Angles can be created out of simple toothpicks and glued to construction paper creating a sheet of angles. Students can exchange angle sheets and then measure each angle with a protractor, record the measurement in degrees, and identify the angle.
12. Using the toothpick models, ask students to identify some objects that might resemble or contain each of the angles created. For example, a rectangle end table contains right angles at the corners, a recliner set back might resemble an obtuse angle, and the beak of bird may look acute.
13. Provide students with crayons or colored pencils to turn the toothpick models into images and drawings. Display the creative work of your students.

## Extended Learning and Practice

1. Discuss another measuring tool called the geometric compass. The school store might even have these for sale. Have students research who invented the geometric compass and its purpose. They will learn that the geometric compass was invented by Galileo and is a tool used to create a perfect circle.
2. Visit Mathisfun.com for additional information about angles and protractors. This site has an animated tutorial on how to use a protractor for measuring angle. Most angles can be defined as right, obtuse, or acute. Using the Mathisfun website, locate the name of an angle that is exactly 180 degrees (straight angle) and one that is greater than 180 degrees (reflex angle).

## Assessment

The lesson objectives can be assessed by evaluating the Angle Worksheet (PDF) with the Angle Worksheet Key (PDF). Use the Assessment of Student Progress (PDF) to assess students’ overall abilities to meet the lessons learning objectives which include identifying, drawing, and building various angles.

## Closure

Provide each student with an index card and have them answer the following questions on one side of the index card:

1. What are two new things that you have learned?