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4th Grade Unit 10 Measuring Angles

Unit 10 Measuring Angles

Grade Level: 4th Grade Subject Area: MathematicsLesson Title: Measuring Angles Lesson Length: 10 days

THE TEACHING PROCESS

Lesson Overview This 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.

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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 EnglishELPS.c.2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as neededELPS.c.3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communicationELPS.c.3H: narrate, describe, and explain with increasing specificity and detail as more English is acquiredELPS.c.4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learnedELPS.c.4H: read silently with increasing ease and comprehension for longer periodsELPS.c.5B: write using newly acquired basic vocabulary and content-based grade-level vocabularyELPS.c.5F: write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquiredELPS.c.5G: narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs 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 that an 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.).

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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:ScissorsBendable Brads (1 per student)GeoboardsDiceDry erase boardsTwo different colored paper platesDice (1-6 or 0-9)Math JournalsProtractorsNotebook paper and 2 color map pencilsManila Drawing PaperRulersComplementary and Supplementary Angle Journal handoutComplementary Angle Measurements handoutComplementary AnglesComplementary Angle Partner Game handoutMeasuring Complementary Angles handoutComplementary and Supplementary Angle Journal handoutPlato Angleo Directions and Recording SheetMeasuring Supplementary Angles handoutSupplementary Angles

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Supplementary Angle I Have Who Has CardsTic-Tac-Toe CardsMeasuring Supplementary AnglesDay 9- Circle and Angle TemplateDay 9- Angles within Circles PracticeDay 10- Fractions and Angles within Circles

INSTRUCTIONAL SEQUENCEPhase - 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)

http://youtu.be/SFvtQN3LMWE (This address is case sensitive.

After video, explain that angles are everywhere. Take a moment and point out some angles you see around the room. Be sure to use the examples provided in the videos.

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)

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http://youtu.be/SFvtQN3LMWE


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

1. Draw an angle using a ruler (remember you are modeling) on the white board (smartboard/promethean/workspace).

2. Demonstrate with your protractor how we could measure that angle.-put the center of the protractor at the VERTEX (intersection) of the angle and follow each

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line to the nearest degree.

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 DOGive each student a copy of Measuring Angles http://www.mathworksheets4kids.com/angles/measuring/standard-type1-easy1.pdf

1. Working problem 1 together.2. Put our protractors center on the vertex of our angle.3. Measure the left ray of our angle and write it down.4. Measure the right ray of the angle and write it down.5. If the Difference of the two numbers and show the answers.

REPEAT the “We Do” step 2 more times for extra guided practice.

YOU DO6

http://www.mathworksheets4kids.com/angles/measuring/standard-type1-easy1.pdf


Give each student a copy of http://www.mathworksheets4kids.com/angles/measuring/standard-type1-easy1.pdf

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 - http://youtu.be/KtAYV2FqdBE (this link is case sensitive)

http://www.mathplayground.com/measuringangles.htmlUse 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 2Activity: Drawing angles using a protractor.Materials:ProtractorMath journalWhite board and markersDrawing paper

Get students engaged by allowing them to sing the “Protractor Song” together.

Protractor Song - http://youtu.be/KtAYV2FqdBE (This link is case sensitive.)

Journal entry: Steps to drawing an angle (have them write these in their journal)

1. Draw a straight line with the straight edge of the protractor. This is your BASE.2. Place a dot at one end of the “arm” using the center hole in the protractor.3. Find the degree you want your angle to be and mark it with your pencil.4. Use the protractor, keeping the center at your dot and turn it to the straight edge side.5. Draw a line to your degree mark that you made.

I DO/YOU WATCH

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.

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http://youtu.be/KtAYV2FqdBE

http://www.mathplayground.com/measuringangles.html

http://youtu.be/KtAYV2FqdBE




“We will be making a 110 degree angle. If an angle measures 110˚, What classification is the angle? ObtuseWatch 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

http://www.studyzone.org/mtestprep/math8/f/protractor5l.cfm

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 - http://www.gscdn.org/library/cms/71/13771.pdf

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 ActivityTopic: Introduction to complementary anglesMaterials:GeoboardsDry erase boardsComplementary and Supplementary Angle Journal handoutMath JournalsProtractorsComplementary Angle Measurements handoutComplementary Angles

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http://www.gscdn.org/library/cms/71/13771.pdf

http://www.studyzone.org/mtestprep/math8/f/protractor5l.cfm


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.http://goo.gl/VCaSC

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 http://goo.gl/IFvsk

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 9

http://goo.gl/IFvsk


on their dry erase boards.

Angle Complement30°28°85°50°47°

90° - 30° = 60°90° - 28° = 62°90° - 85° = 5°90° - 50° = 40°90° - 47° = 43

As the students are working the problem discuss reasonable answers. Remind them that half of a right angle is 45°. If the angle is greater than one half it will measure greater than 45°. If the angle is less than one half it will measure less than 45°.

The students will glue the Complementary and Supplementary Angle Journalhandout into their journal. They will write the definition of a complementary angle on top of the flap.

Definition - Complementary angles – two angles whose sum of angle measures equals 90 degrees

The students can use a protractor to draw complementary angles under the flap. They can draw an example of one with the two angles connected and one with the angles apart. You will have to model this on the board.

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Exit Ticket – The students will complete the Complementary Angle Measurements handout.

Homework Complementary Angles – The students will need protractors to draw the angles. You may need to send them home with the students or allow them to draw the angles at school.What’s the teacher doing?

Check and monitor as the students review the angles acute, obtuse, and right on the IPads or on the website.

Monitor as students calculate complement angles.

Monitor as the students glue the Complementary and Supplementary Angle Journal handout into their journals.

Assist the students as they use a protractor to draw complementary angles which are together and apart.


Constructing acute, obtuse, and right angles on the Ipads or on the website.

Interact with the Math is Fun activity.

Calculate to determine the complement angles on dry erase boards.

Glue Complementary and Supplementary Angle Journalhandout into their journals and write the definitions of a complementary angle.

Use a protractor to draw complementary angles which are connected and apart.

Complete the Exit Ticket - Complementary Angle Measurements handout.

Phase – Elaborate/Explain Day 4

Day 4 ActivityTopic: Review and measure complementary anglesMaterials:Complementary Angle Partner Game handoutDieProtractors

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Measuring Complementary Angles handout

Yesterday we discovered complementary angles. What is a complementary angle? (A complementary angle is two angles whose sum of the angle measures equals 90 degrees.)

Use the website XP Math games http://goo.gl/rWzKfS to match angles which total 90°.

Today the students will calculate the measure of complementary angles.

Use Visnos Basic Angles Activity to practice measuring angles with a protractor and reading the protractor. (You will need to practice with this website and learn how to use it before class.) http://goo.gl/gATpuo

After practicing with the protractor the students will now play Complementary Angle Partner Game. The students can select a partner or the teacher can assign partners.

Go over the following rules with the class.

Player 1 draws a line through the vertex of one of the right angles. (The two angles should not be equal.)

Player 1 measures the two angles with a protractor and names one of the angles as A. The other angle will be the complement of A.

Player 1 rolls the die and uses the chart at the bottom of the game board to score points. Players switch roles and play again.

To score points the students will roll a die.

Roll

1 You score the complement of A.2 Opponent scores A, you score the complement of A.3 You score smallest, opponent score largest.4 You score A, opponent scores complement of A.5 Your score A.6 You score largest, opponent scores the smallest.

The students will keep their score.

The handout can be run front and back so the students can play 8 times today or they can play the game on the back another day. You can adapt the game by having the player divide the angle into three parts. They can label the angles A, B, and C with the measure of angle C never used. The rules for each roll would remain the same.

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http://goo.gl/gATpuo

http://goo.gl/rWzKfS


Exit Ticket – The students will complete Measuring Complementary Angles handout.


Monitor the students as they match the complementary angles for the game website.

Assist the students with calculating the complementary angle.

Monitor and assist the students as they use a protractor.

Monitor and assist the students as they play Complementary Angle Partner Game with a partner.


Actively participating in the matching game for complementary angles. Calculating the angle if necessary on a dry erase board or paper.

Use a protractor to measure angles. The students will read the protractor to determine the degree of the angles.

Play Complementary Angle Partner Game with a partner.

Use a protractor to measure the angles in the game. Add the measure of the angles to keep their score.

Complete Exit Ticket – Measuring Complementary Angles handout

Phase Elaborate/Explain Day 5

Day 5 ActivityTopic: Introduction to supplementary anglesMaterials:Dry erase boardComplementary and Supplementary Angle Journal handoutProtractorPlato Angleo Directions and Recording SheetTwo different colored paper platesDice (1-6 or 0-9)Measuring Supplementary Angles handoutSupplementary Angles

What is a complementary angle? (two or more angles whose sum of the angle measures equals 90°)

Today we will learn about supplementary angles.What is a supplementary angle? (two angles whose sum of angle measures equals 180 degrees)

We will now watch a video which reviews complementary angles and introduces supplementary 13


angles. http://goo.gl/D848r2

After the video go to the Math Is Fun Website http://goo.gl/SSgGC

The students will discover that supplementary angles are two angles that add up to 180°. For example a 60° and a 120° angle would be supplementary angles. The angles can be together for a 180° angle or they can be apart. They supplement each other because they total 180°. For example 85° + 95° = 180°

The students can also move the angles to discover the measurements of supplementary angles and that they must total 180°.

Have the students practice finding the supplement for a given angle. They can work the problems on their dry erase boards.

Angle Supplement115°55°

120°75°

100°

180° - 115° = 65°180° - 55° = 125°180° - 120° = 60°180° - 75° = 105°180° - 100° = 80°

The students will refer back to the Complementary and Supplementary Angle Journal handout. The students will write the definition of a supplementary angle on top of the flap.

Definition – Supplementary angles – two angles whose sum of angle measures equals 180 degrees.

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http://goo.gl/D848r2


The students can use a protractor to draw supplementary angles under the flap. They can draw an example of one with the two angles connected and one with the angles apart. You will have to model this on the board.

Play Plato Angleo with a partner. Prior to playing get two different colored paper plates and slit to the middle and interlock the plates.

Each pair of students will need a pair of dice, (a regular pair of dice or a pair of deca dice (0-9), a set of paper plates, a protractor, and a recording sheet.

The students will work with a partner. You can partner the students or let them select a partner.

1. The partners determine who will be Player A and Player B.

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2. Player A, roll a pair of dice and this will determine the first angle in degrees. If the player rolls a 5 and a 9 you can say 59° or 95°. Player A will record the measure on the recording sheet.

3. Player B will then use the interlocking paper plates to determine the supplement. They will twist the plates until they generate the angle. Check by using the protractor to measure the angle to make sure it is accurate. Record the angle measure on the recording sheet and sketch the supplementary angles.

4. Alternate turns as you complete the activity.

Example – Student A rolled 72° so student B will have a supplement angle of 108°.Player B will use a protractor to measure the angle. Player A can check the angle.

Exit Ticket – The students will complete Measuring Supplementary Angles handout.

Homework – Supplementary Angles - The students will need protractors to draw the angles. You may need to send them home with the students or allow them to draw the angles at school.


Monitor the students as they watch the angle video.

Monitor the students as they calculate supplement angles.

Assist the students as they write the definition of supplementary angle in their journal.

Monitor and assist the students as they use protractors to draw supplementary angles in their journals.


Actively watch the angle video.

Interact with the supplementary angle website.

Calculate supplement angles.

Write the definition of supplementary angle on the Complementary and Supplementary Angle Journal handout.

Use a protractor to draw supplementary angles below the flap.

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Partner the students for Plato Angelo activity.

Assist the students as they draw supplementary angles for Plato Angelo activity.

Monitor as the students complete the Exit Ticket Measuring Supplementary Angles.

Complete Plato Angelo activity with a partner.

Complete the Exit Ticket - Measuring Supplementary Angles.

Phase – Elaborate/Explain Day 6

Day 6 ActivityTopic: Practice with supplementary anglesMaterials:dry erase boardsSupplementary Angle I Have Who Has CardsNotebook paper and 2 color map pencilsTic-Tac-Toe CardsMeasuring Supplementary Angles

What are supplementary angles? (two or more angles whose sum of the angle measures equals 90°)

If I have and angle which measures 100° what is its supplement? (80°)45°? (135°)

Let’s watch the following video to remind us how to measure supplementary angles. http://goo.gl/vnYJX4

Use the following interactive activity to find supplement angles. You can also measure complementary angles or both complementary and supplementary angles.http://goo.gl/VYkfVn

The students can use their dry erase board to find the supplement angle by working subtraction problems.

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http://goo.gl/VYkfVn

http://goo.gl/vnYJX4


Pass out Supplementary Angle I Have Who Has Cards to the students. They will start with the card with a star on it. The students will read Who Has…. and the student that has the answer will respond. The game will continue around the room until your get back to the card with a star on it.

As a whole class you can now review by playing a Tic-Tac-Toe game. Partner the students and have them draw a Tic-Tac-Toe board on their paper. The students will use two different color map pencils to write the answers on their game board.

Use the Tic-Tac-Toe Cards for the clues. The students will take turns solving the problems on their dry erase boards. If the student is correct he will write the number on the board using his map pencil. The first person to tic-tac-toe wins.

The answers for the game are 100° 180° 60° 135° 118° 30° 140° 95° 125°

After one round a student can call out the clues and the students can rotate partners.

This game can be put in a center for practice later.

Exit Ticket – The students will complete Measuring Supplementary Angles.

What is the teacher doing?

Monitor as the students watch the video. Question the students about how they calculate to find the supplement angle.

Assist and monitor the students as they calculate the supplement angles for the interactive game.

Assist the students if they do not know how to find the measure of the angles.

Pass out the cards for Supplementary Angle I Have Who Has.

Monitor and assist the students as they calculate the answers.

The teacher will read the clues as the students play Tic-Tac-Toe.

Monitor and assist the students as they complete the Exit Ticket Measuring Supplementary Angles


Actively watching the video and participating in the class discussion.

The students will interactive with the game on the website. The students will calculate the supplement and they can go to the computer and type in the measure of the angle.

The students will play Supplementary Angle I Have Who Has.

The students may need to use the dry erase board to calculate the answers.

The students will work with a partner to play Tic-Tac-Toe. The students will need to calculate the answers.

Complete Exit Ticket Measuring Supplementary Angles

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Phase – Elaborate/Explore/Evaluate Day 7

Activity: Students will extend their knowledge during Station time.

Clearly state the routines and procedures of the stations. Be sure to monitor procedures to ensure meaningful use of time and activities. Be sure to have centers that students have prior experience with therefore you are not teaching 5 new stations at a time.

Each group will have a knowledge folder at that travels with them from group to group. This is where the students will turn in all of the record sheets, player’s cards, and any other product of their stations.

Station 1 – Measuring Angles See handout for directions Students use protractors to measure the degree of the angle. 4 sets of Angle Task Cards (copied on card stock, cut apart, and laminated) Angle Task Card Record Sheet 4-5 Protractors.

Station 2 – Supplementary Memory See handout for directions Supplementary Memory (copied on card stock, cut apart, and laminated) Scratch paper Pencils

Station 3 – Complementary Angle Partner Game.Review the following rules with the class.

Player 1 draws a line through the vertex of one of the right angles. (The two angles should not be equal.)

Player 1 measures the two angles with a protractor and names one of the angles as A. The other angle will be the complement of A.

Player 1 rolls the die and uses the chart at the bottom of the game board to score points. Players switch roles and play again.

To score points the students will roll a die.

Roll

You score the complement of A. Opponent scores A, you score the complement of A. You score smallest, opponent score largest. You score A, opponent scores complement of A. Your score A. You score largest, opponent scores the smallest.

The students will keep their score.The handout can be run front and back so the students can play 8 times today or they can play the

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game on the back another day. You can adapt the game by having the player divide the angle into three parts. They can label the angles A, B, and C with the measure of angle C never used. The rules for each roll would remain the same.

Station 4 – Teacher’s discretion This station should include skills previously taught but not quite mastered.

Station 5 - Teacher Station Students will rotate through the teacher to work on underdeveloped skills, critical thinking

skills, and extension activities. These activities need to be identified through the use of DATA and teacher observation These skills should be differentiated for each student.


The teacher is monitoring for accuracy and working with targeted students during small group instruction.

Differentiating instruction to target weaknesses students have through the use of teacher observation and DATA.


The student is extending their knowledge during center time by completing centers record sheet and turning in a final product.

Students are to work collaboratively through the stations together.

Phase – Evaluate the learning Day 8

Activity – Problem Solving Gallery Walk

MaterialsComplimentary and Supplementary Angles – Handout.

Prior to this lesson, post each of the eight problem solving questions around the room.

Students will travel in groups of 2-3 to work each angle problem that is displayed around the room. (The teachers should travel with a group of struggling students to provide small group instruction).

Students will work collaboratively to solve each problem. Students will record their answers on the front and back of manila drawing paper that is

folded into 4ths.

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(Just because they do not have a word problem in front of them, does not mean they do not need to work out, explain, or justify their answers.)

Students are given 3-4 minutes per problem and then rotate to the next displayed problem.

Following the Gallery Walk –Project the Complimentary and Supplementary Angles handout with the document camera.

Review each problem with the students to ensure accuracy and problem solving ability. (The teacher models appropriate problem solving strategies for each problem. Focusing on the vocabulary for the new unit.)


Assist struggling students with solving problems in the gallery walk.

Teacher models the problem solving method using angles.

What are students?

Participate when questions are being asked.

Work in collaborative groups to solve problems in their gallery walk.

Producing an individual answer sheet on manila paper.

Phase – Engage the learner/Explore the concept

Day 9

Activity – Measuring the cut out of an circleGive the students a protractor and ask them to explain to you what shape a protractor is. (a half-circle) Ask them how many total degrees are in the protractor (180°). Then, give them another protractor and ask them to make a circle out of the 2 protractors. Ask them how many degrees this makes. (360°). Explain to students that a full circle always has a total of 360°.

For today’s activity, give the students the handout “Day 9-Circle and Angle Template”. Have the students cut out the circle and the rays that are on the two pages. Also, give the students a single

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brad. Have students remind you what the term “vertex” means. Ask them where they think the vertex is on a circle, since it has no sides to connect in order to make a vertex. Instruct them that it is the center of the circle. Then, have the students put the brad through the white dots on the rays they previously cut out. Next, have them put the brad through the vertex of the circle. The end result should look like a clock with moveable hands.

Show the students how to measure an angle on the circle using a protractor and their circle with attached rays. When the students seem to fully understand the concept, give them the handout “Day 9-Angles within Circles Practice”.

What is the teacher doing?First, the teacher gives every 1-2 students 2 protractors.

Teacher says: “What is the exact shape of a protractor?” “Look around the top of the protractor.

How many total degrees does the protractor measure?”

“Exactly! If I trace around the top circle part of the protractor, I see that it measures 180°. Now, use your other protractor to make a full circle. Do you see how if I put the 2 protractors back to back I will make a circle? How many degrees are in this circle?”

“Correct! If I found the total degrees in one full circle, it would measure 360°. Next, we are going to talk about how to cut out smaller angles out of a circle.”

The teacher should then pass out the handout “Day 9- Circle and Angle Template”. The teacher should monitor to make sure that the students are cutting correctly and are staying on task.

Next, the teacher should ask the students to review the term “Vertex”.

“In the past, we have talked about the vocabulary term ‘vertex’. Who can tell me what a ‘vertex’ is?”

“Do you think a circle has a vertex?”

“Based on your definition, you’re right. A circle can not have a vertex. However, a circle actually does have a vertex. The


Student’s answers will vary, but the correct answer is a “half-circle”.

“It measures 180° in all.”

The students should be talking amongst themselves and their partner to first, create a circle with their 2 protractors, then, determining how many degrees are in a full circle.

Students should say, “If there are 180° in one half circle and I have a full circle now, there should be 2 sets of 180°, which means there is 360° in one full circle.”

The students should be cutting out the circle and the rays, and then will wait for further instructions.

Students answers will vary, but they should say something like, “A vertex is the corner that is made when two sides meet on a geometric figure.”

“A circle doesn’t have any edges or corners, so it can’t have a vertex.”

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vertex of a circle is located directly in the middle. Do you see the dot in the center of the circle that you just cut out? That is the circle’s vertex.”

The teacher should then instruct the students to insert the brad that the teacher has given them into the circle on each ray, then through the vertex of the circle, in order to create a type of clock with moveable hands.

“Using your circle that we just created and your protractor, show me how you would measure a 90° that is in this circle.”

Students should make their circle look like the one below.

Repeat this several times until students understand the concept of creating angles within circles. Try to stay away from going past 180° until the students have a general understanding of the concept. When they do go past 180°, explain how you can just add 180 to whatever other degree to create the larger angle.

When students understand the concept, have students complete the handout “Day 9-Angles within Circles Practice”. They may work on this individually or with a partner.

The students should be actively engaged and creating the circle with moveable hands, in order to understand how to cut out and measure angles in a circle.

Students should be actively engaged and following along throughout the practice in order to fully understand the concept.

When ready, students should complete the handout individually or with a partner.

Phase - Explore/Elaborate on the concept Day 10

Activity – Using the fraction1/360 to find the degree of the cutout of a circle

First, review the activity from yesterday. Students will have to understand this in order to move on

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to the next portion of this topic.

Next, introduce to the students how we will create a fraction out of an angle that has been cut out of a circle. First, explain to the students that 360 is the total number of degrees in a circle; therefore, it will be our denominator since it is the total. Then, show the students a what the circle looks like when I cut a 90° angle out of the circle with the moveable rays that we used yesterday. Explain to the students that this angle is 90° out of 360°, so the fraction that this angle represents

is 90

360 . However, if I look at this angle on the circle, I can clearly see that it is actually 14 of the

circle. If I was to simplify 90

360 , this is what it would look like:

90360

÷ 9090 =

14

Next, on the circle with the moveable rays, create a 180° angle cut out. Ask the students what fraction they think this angle will create within the circle, then show them how you would simplify it

to see that it is, in fact, 12. Repeat the same steps with a 270°, since it represents the benchmark

fraction 34 .

When the students are ready, give them the handout “Day 10-Fractions and Angles within circles”.

What is the teacher doing?To begin the lesson, the teacher will review the lesson from the day before. To introduce the next portion of this topic, try to follow the following script:

“Yesterday we measured angles within circles. Today, let’s imagine that those angles that we measured yesterday were actually cut out of the circle. We can create a fraction out of this cutout also. For example, what are the total amount of degrees in a full circle?”

“Right. So, if the total is 360°, will that be our fractions numerator or denominator?”

“On my circle with moveable rays that I created yesterday, let me show you a 90° angle. If I was to cut out this amount from this circle, what fraction of the circle did I cut out?”

“You’re right. It does look like 14 and it is


“There are 360 degrees in the whole circle.”

“It will be our denominator, since the denominator is the total.”

“It looks like you cut out 14 of the circle.”

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14 . However, it is also

90360 . We already

talked about the fact that 360 is our denominator, since it is the total amount of degrees in the circle. Ninety is our numerator, since it is the amount of degrees being represented. If I look at these two fractions even closer, I will see that even though these I found these two

fractions two different ways- 14 by looking

at the cutout of the fraction and 90

360 by

measuring the angle- these fractions are

equivalent. If I simplify 90

360 by dividing

both the numerator and the denominator

by 90, I will get 14 .”

Repeat this with several other fractions until the students understand the concept. When students seem to understand the concept, pass out the hand out “Day 10-Fractions and Angles within circles”. Students can work on this individually or with a partner. It is important to actively monitor the students to ensure that they are fully understanding the concept.

While working on the handout, the students should be actively engaged and using their prior knowledge on fractions and measuring angles to help them to fully understand the topic.

Phase – Evaluate the learning Day 11

Activity – Performance Assessment

Provide students with a protractor.

Analyze the situation(s) described below. Organize and record your work for each of the following tasks. Using precise mathematical language, justify and explain each mathematical process.

The town of Pineville is building a new sports park that will be circular in shape. The three main sections of the park will contain a football field, a tennis court, and a skate park.

1) The fourth grade students at Pine Elementary are looking at a diagram of the plans for the park. They notice that the circular shape that outlines the park has a football field in one of the sections.

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a) Determine the measure of the angle represented by the “cut-out” or section of the circle where the football field is located. Describe how the measure of an angle can be illustrated as a part of a circle using the terms turn, center, vertex, rays, and angle.

b) Identify the angle the football field section represents as a portion of a circle in terms of .

2) The diagram shown below illustrates how the park will be divided. The largest section will contain a skate park and the smallest section will have equipment and apparel shops.

a) Given the angle measure of the section for the equipment and apparel shops, determine the measure of the angle for the section for the skate park.

3) City officials are looking for entries of designs of skateboard kicker ramps that will be used in the skateboard park. Kyle and Terry both built a ramp using this design

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a) Kyle built his kicker ramp as shown below. Determine the approximate measure of the angle of incline on the kicker ramp in degrees to the nearest whole number.

b) Terry wanted to design a kicker ramp with a 12° angle of incline. Use a protractor to draw a kicker ramp diagram of Terry’s design with the given angle measure.

c) Describe the incline of Terry’s kicker ramp as being steeper, as steep as, or less steep than Kyle’s kicker ramp.

What is the teacher doingWhile the students are working on the Performance Assessment, the teacher will be actively monitoring and evaluating the student’s understanding of all of the concepts within the unit.

What are the students doing?The students will rely on their previous knowledge to accurately answer the questions given on the Performance Assessment.

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