4th Grade Unit 10 Measuring Angles
Unit 10 Measuring Angles
Grade Level: 4th Grade / SubjectArea: MathematicsLesson Title: Measuring Angles / Lesson Length: 10 days
THE TEACHING PROCESS
Lesson OverviewThis unit bundles student expectations that address skills necessary to solve problems involving angles less than or equal to 180 degrees, including drawing and measuring angles with a protractor. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace. During this unit, students illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. They also illustrate degrees as the units used to measure an angle, where of any circle is one degree and an angle that "cuts" out of any circle whose center is at the angle's vertex has a measure of n degrees. Using a protractor, students determine the approximate measures of angles in degrees to the nearest whole number and also draw angles of a specified measure. Given one or both angle measures, students determine the measure of an unknown angle formed by two non-overlapping adjacent angles. The concepts of complementary and supplementary angles are embedded within the study of adjacent angles. Within this unit, all angle measures are limited to whole numbers.
Unit Objectives:
Students will be able to identify acute, right, obtuse, and straight angles. Students will be able to use academic vocabulary and calculate angles that are complimentary and supplementary. Using a protractor, students will be able to draw/measure angles and cut outs of a circle to the nearest degree.
Standards addressed:
TEKS:
4.1A: Apply mathematics to problems arising in everyday life, society, and the workplace.
4.1B: Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
4.1C: Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
4.1D: Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
4.1E: Create and use representations to organize, record, and communicate mathematical ideas.
4.1F: Analyze mathematical relationships to connect and communicate mathematical ideas.
4.1G: Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
4.7A Illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers.
4.7 B Illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers.
4.7 C Determine the approximate measures of angles in degrees to the nearest whole number using a protractor.
4.7 D Draw an angle with a given measure.
4.7 E Determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures.
ELPS:
ELPS.c.1A: use prior knowledge and experiences to understand meanings in English
ELPS.c.2D: monitor understanding of spoken language during classroom instruction and interactions and seekclarification as needed
ELPS.c.3B: expand and internalize initial English vocabulary by learning and using high-frequency English wordsnecessary for identifying and describing people, places, and objects, by retelling simple stories and basic informationrepresented or supported by pictures, and by learning and using routine language needed for classroomcommunication
ELPS.c.3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired
ELPS.c.4E: read linguistically accommodated content area material with a decreasing need for linguisticaccommodations as more English is learned
ELPS.c.4H: read silently with increasing ease and comprehension for longer periods
ELPS.c.5B: write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5F: write using a variety of grade-appropriate sentence lengths, patterns, and connecting words tocombine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired
ELPS.c.5G: narrate, describe, and explain with increasing specificity and detail to fulfill content area writingneeds as more English is acquired.
Misconceptions:
- Some students may think that the angle size is determined by the length of the rays rather than by the size of the turn.
- Some students may think that the orientation of the angle on a drawing will affect the measurement of the angle.
- Some students may not have made the connection between estimating the size of an angle before measuring and the appropriate scale on the protractor.
- Some students may think that degree measure for angles is read from only one side of a protractor (e.g.,An angle with a measure of 30° may be at the markings of 30° and 150° on the protractor).
- Some students may think that when measuring with a protractor, one of the two rays must always align with zero rather than recognizing thatan accurate measure is dependent upon the difference in the beginning and ending measure (e.g.,An angle with a measure of 30° can be determined by beginning at 0° and ending at 30° or by finding the difference between other ending and starting points, such as 180° – 150°, 100° – 70°, etc.).
Vocabulary:
- Acute – an angle that measures less than 90°
- Adjacent angles – angles that share a common vertex and side
- Angle – two rays with a common endpoint (the vertex)
- Angle congruency marks – angle marks indicating angles of the same measure
- Center of the circle – the point equidistant from all points on the circle
- Complementary angles – two angles whose sum of angle measures equals 90 degrees
- Congruent angles – angles whose angle measurements are equal
- Degree – the measure of an angle where each degree represents of a circle
- Obtuse – an angle that measures greater than 90° but less than 180°
- Protractor – a tool used to determine the measure of an angle
- Ray – part of a line that has one endpoint and continues without end in one direction
- Right – an angle (formed by perpendicular lines) that measures exactly 90°
- Straight – an angle that measures 180° (a straight line)
- Supplementary angles – two angles whose sum of angle measures equals 180 degrees
- Approximate
- Circle
- Congruent
- Cut out
- Interval
- Parallel
- Perpendicular
- Rotation
- Semi-circle
- Turn
- Unit
- Vertex
List of Materials:
Scissors
Bendable Brads (1 per student)
Geoboards
Dice
Dry erase boards
Two different colored paper plates
Dice (1-6 or 0-9)
Math Journals
Protractors
Notebook paper and 2 color map pencils
Manila Drawing Paper
Rulers
Complementary and Supplementary Angle Journal handout
Complementary Angle Measurements handout
Complementary Angles
Complementary Angle Partner Game handout
Measuring Complementary Angles handout
Complementary and Supplementary Angle Journal handout
Plato Angleo Directions and Recording Sheet
Measuring Supplementary Angles handout
Supplementary Angles
Supplementary Angle I Have Who Has Cards
Tic-Tac-Toe Cards
Measuring Supplementary Angles
Day 9- Circle and Angle Template
Day 9- Angles within Circles Practice
Day 10- Fractions and Angles within Circles
INSTRUCTIONAL SEQUENCE
Phase - Engage the Learner / Day 1
Activity: Finding the Measurement of an angle using a protractor
Pass out a protractor to each student.
ASK: (Allow for students to small group discuss their answers)
Does this tool resemble other mathematical tools that we have used in class before? (answers may vary, but students should come up with a ruler)
What is the purpose of a ruler? (To measure the length of an item)
What units of measurements are we familiar with in the fourth grade? (Inches and centimeters)
If a protractor resembles a ruler, then what is the purpose of the protractor in our math life? (To measure items.) We will use protractors to measure angles to the nearest degree.
Introduce protractors to students and have them watch the videos below to get a better understanding of how to use a protractor and to introduce the different concepts of angles.
- Brain Pop Video – Measuring Angles (This is a free video from Brain Pop)
- (This address is case sensitive.
Pose these questions:
How are we going to measure those angles? Students might say using a ruler. Guide students to identify the protactor.
Can we measure all angles?Yes, angles are measured with a protractor in degrees.
How would you identify an angle?Two rays that met at a vertex.
Journal entry: Angle rays handout
Instructions are in the picture…
Step 1- Cut out the angel rays figure 1. Glue the bottom ray to the paper and attach the top ray with a brass fastener. See third Picture.
Step 2. Cut out types of angles template. Fold into thirds along the dotted lines. Cut along the solid lines to make flaps on the top and bottom thirds. (figure 2)
Step 3. Fold into thirds again. On the outside flaps write each type of angel. Acute, Right, Obtuse and Straight.
Step 4. Open flaps back up. On the top third draw diagrams of the angle types on each flap. On the middle third write the definition for each angle. On the bottom third have students come up with examples from the classroom for each type of angle. (See picture 2)
Step 5. Color for visual appeal and glue into journal under angle tool.
Discuss each type of angle and have students show a model of each angle as you/together write their meaning. Explain what 90 degree angle is and practice showing what each look like.
I DO/YOU WATCH
- Draw an angle using a ruler (remember you are modeling) on the white board (smartboard/promethean/workspace).
- Demonstrate with your protractor how we could measure that angle.
Explain to students that each protractor shows what a 90 degree angle looks like and they can use it as a guide line. Talk through it while your students watch. They will observe you measuring the angles by following the line through the protractor and recording the degrees.
-You might say,
“You can see that the left RAY of the angle measures at 60 degrees and the right RAY of the angle measures at 116 degrees.
To find the measurement of my angle, I take those two numbers and find the difference between them.”
So, the measurement of the angle is 56 degrees. Be sure to show students the symbol for degrees and how to read the symbol.
WE DO
Give each student a copy ofMeasuring Angles
- Working problem 1 together.
- Put our protractors center on the vertex of our angle.
- Measure the left ray of our angle and write it down.
- Measure the right ray of the angle and write it down.
- If the Difference of the two numbers and show the answers.
YOU DO
Give each student a copy of
Have students work independently on the rest of the problems. Give the students about 10—15 minutes to work them and come back together for SHARE TIME. Teacher assists students that are struggling with the concepts.
Show students the Protractor Song at the end of the lesson and have them sing along. Discuss what they learned before they heard the song.
Protractor Song - (this link is case sensitive)
Use for a station later or for independent practice as a whole group.
What’s the teacher doing?
Monitoring student understanding, asking questions, explaining angles, modeling how to measure correctly / What are the students doing?
Measuring angles, asking questions, staying on task with table
Phase:Explore / Day 2
Activity: Drawing angles using a protractor.
Materials:
Protractor
Math journal
White board and markers
Drawing paper
Get students engaged by allowing them to sing the “Protractor Song” together.
Protractor Song - (This link is case sensitive.)
Journal entry: Steps to drawing an angle (have them write these in their journal)
- Draw a straight line with the straight edge of the protractor. This is your BASE.
- Place a dot at one end of the “arm” using the center hole in the protractor.
- Find the degree you want your angle to be and mark it with your pencil.
- Use the protractor, keeping the center at your dot and turn it to the straight edge side.
- Draw a line to your degree mark that you made.
With a protractor you will draw a straight light with the straight edge of the protractor like it is a ruler. Then, you will tell the students it is extremely important that you place your pencil in the center of the protractor where the tiny “center hole” is and make a mark. This is how we create the vertex.
“We will be making a 110 degree angle. If an angle measures 110˚, What classification is the angle? Obtuse
Watch how I draw the angle and how I use the protractor to help with my measurement of degrees.”
Go through the steps from the journal and bring them to life for the students. Make them watch closely how you go through every step.
WE DO
Every student will be creating an angle that measures 120 degrees with you. Go through the steps of creating an angle.
Show your work on the smartboard or promethean while students are drawing theirs on a white board and a marker.
YOU DO/I WATCH
Students will be interactively playing these practice problems on the smartboard (you could even do this in small groups on laptops, Ipads, or Samsung Tablets).
Use the following link Drawing Angles – for homework or exit tickets -
What’s the teacher doing?
Modeling how to draw angles, using academic vocabulary, monitoring student understanding / What are the student’s doing?
Being involved in drawing angles, cooperating with peers during protractor practice game, writing notes about “steps to draw angles”
Phase - Elaborate the concept / Day 3
Day 3 Activity
Topic: Introduction to complementary angles
Materials:
Geoboards
Dry erase boards
Complementary and Supplementary Angle Journal handout
Math Journals
Protractors
Complementary Angle Measurements handout
Complementary Angles
What are angles? (Two rays with a common endpoint or vertex.)
Let’s review the angles that we have learned about the past several days.
The students can use the Geoboard App on the IPads, Samsung Tablets or you can have the students draw the angles on their dry erase boards.
As a class you can use an interactive geoboard at the following link.
Model an acute angle. The students should draw or display the following angle.
How do you know this is an acute angle? (It measures less than 90.)
Model a right angle. The students should draw or display the following angle.
How do you know this is a right angle? (It measures 90 or it forms the corner of a square)
Model an obtuse angle. The students should draw or display the following angle.
How do you know this is an obtuse angle? (It measures greater than 90 or the angle is large and OPEN)
Do you think I can have more than two angles total 90?( Maybe)
Go to the Math Is Fun Website
The students will discover that complementary angles are two angles that add up to 90. For example a 40 and a 50 angle would be complementary angles. The angles can be together for a 90 angle or they can be apart. They complement each other because they total 90. For example 25 + 65 = 90
The students can also move the angles to discover the measurements of complementary angles and that they must total 90.
Have the students practice finding the complement for a given angle. They can work the problems on their dry erase boards.
Angle / Complement
30
28
85
50
47