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3 rd Grade Geometry: Angles and Triangles Taught at Moffitt Elementary

Jessica GeorgeElementary [email protected]

AbstractThis curriculum unit includes six lessons on angles and triangles. The first lesson

involves students making acute, obtuse, right, and straight angles by throwing a beanbag attached to string. The second lesson in the unit involves students constructing the different types of angles on a geoboard and geoboard paper. Lesson three has students build an astrolabe to introduce them to measuring angles. The fourth lesson has students classify triangles by their sides. During this lesson students construct triangles out of straws and complete a problem solving worksheet. Lesson five has students classify triangles by their angles. The lesson has the students use geoboards and geoboard paper to make the different types of triangles. The last lesson in the unit has students discover the sum of the interior angles in a triangle through an activity. Materials needed for the unit include: beanbag, string, geoboards, rubber bands, geoboard paper, washers, straws, astrolabe pattern, construction paper, ruler, marker, butcher paper, tape, scissors, worksheets, whiteboard, dry erase marker, and document camera.

In this unit, you will find: Standards, benchmarks, and objectives Calendar and schedule A pre and post assessment Six lesson plans

Standards and Benchmarks

Common Curriculum Goal I:3.3 Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters.

Benchmark: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute).

Objectives:1) After a lesson on obtuse, right, straight and acute angles students will be able to

accurately describe an obtuse, right, straight, and acute angle with 3 out of 3 correct.2) After a review of obtuse, right, and acute angles students will be able to make and draw

the three different types of angles on a geoboard and geoboard paper with 3 out of 3 correct.

3) After a lesson on making an astrolabe, students will be able to make a mariner’s astrolabe and go around the room measuring the angle of different objects in the classroom by at least measuring 5 angles.

mailto:[email protected]

Common Curriculum Goal I: 3.3 Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters.

Benchmark: 3.3.2 Identify, describe, compare analyze, and informally classify triangles by their sides and angles.

Objectives:1) After a lesson on isosceles, scalene, and equilateral triangles students will be able to

construct and label the three different types of triangles with 3 out of 3 correct.2) After a lesson on isosceles, scalene, and equilateral triangles students will be able to solve

story problems using isosceles, scalene, and equilateral triangles on a worksheet with 7 out of 9 correct.

3) After a lesson on acute, right, and obtuse triangles students will be able to make and draw the three types of triangles on a geoboard and geoboard paper with 3 out of 3 correct.

Common Curriculum Goal II: 8.3 Geometry and Measurement: Analyze two- and three-dimensional spaces and figures by using distance and angle.

Benchmark: 8.3.2 Use models to show that the sum of the angles of any triangle is 180 degrees and apply this fact to find unknown angles.

Objectives:1) After an activity on the sum of the interior angles of a triangle students will be able to

model that the sum of the interior angles of any triangle is 180 degrees by completing the activity with 3 angles of a triangle glued on a straight line.

Calendar and Schedule

Lesson Date: Lesson Activities and ObjectivesWeek 1Monday

Instructional Strategy: Whole group activity making angles by throwing a beanbag with a string attached.Math: Identifying anglesActivity: BeanbagGoal: 3.3 Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters.Benchmark: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute).Objective: After a lesson on obtuse, right, and acute angles students will be able to describe an obtuse, a right, and an acute angle with 100% accuracy.

Week 1 Instructional Strategy: Whole group activity making angles on a geoboard

Tuesday and drawing angles on geoboard paper.Math: Constructing obtuse, acute, and right anglesActivity: Making obtuse, acute, and right angles on geoboards and geoboard paper.Goal: 3.3 Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters.Benchmark: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute).Objective: After a review of obtuse, right, and acute angles students will be able to make and draw the three different types of angles on a geoboard and geoboard paper with 3 out of 3 correct.

Week 1Wednesday

Instructional Strategy: Independent activity measuring the angles of objects in the classroom using an astrolabe.Math: Measuring anglesActivity: Mariner’s AstrolabeGoal: 3.3 Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters.Benchmark: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute).Objective: After a lesson on making a mariner’s astrolabe students will be able to make an astrolabe and go around the room measuring the angle of different objects in the classroom by at least measuring 5 angles.

Week 1Thursday

Instructional Strategy: Independently make scalene, isosceles, and equilateral triangles using straws and independently complete a worksheet.Math: Making and Identifying different types of trianglesActivity: Straw construction and worksheet.Goal: 3.3 Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters.Benchmark: 3.3.2 Identify, describe, compare analyze, and informally classify triangles by their sides and angles.Objectives: 1) After a lesson on isosceles, scalene, and equilateral triangles students will be able to make and label the three different types of triangles with 3 out of 3 correct.2) After a lesson on isosceles, scalene, and equilateral triangles students will be able to solve word problems on a worksheet with 7 out of 9 correct.

Week 1Friday

Instructional Strategy: Whole group making right, obtuse, and acute triangles on a geoboard and geoboard paper.Math: Constructing right, obtuse, and acute trianglesActivity: Geoboard trianglesGoal: 3.3 Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters.

Benchmark: 3.3.2 Identify, describe, compare analyze, and informally classify triangles by their sides and angles.Objective: After a lesson on acute, right, and obtuse triangles students will be able to make and draw the three types of triangles on a geoboard and geoboard paper with 3 out of 3 correct.

Week 2Monday

Instructional Strategy: Whole group activity modeling that the interior angles of any triangle adds up to 180 degrees.Math: Sum of interior angles of any triangleActivity: Triangle angles on a straight angleGoal: 8.3 Geometry and Measurement: Analyze two- and three-dimensional spaces and figures by using distance and angle.Benchmark: 8.3.2 Use models to show that the sum of the angles of any triangle is 180 degrees and apply this fact to find unknown angles.Objective: After an activity on the sum of the interior angles of a triangle students will be able to model that the sum of the interior angles of any triangle is 180 degrees by completing the activity with 3 angles of a triangle glued on a straight line.

Lesson Plan: Week 1, Day 1

Descriptive Data: 3rd Grade; Angles and Review of Lines and Line Segments; Total Time of 50 minutes; 9:00-9:50am

Goal: 3.3 Geometry and Measurement: Describe and analyze properties of two dimensional shapes, including perimeter.


Objective: After a lesson on obtuse, right, and acute angles students will be able to describe an obtuse, right, straight and acute angle with 100% accuracy.

Materials:Teacher:

Beanbag String (6m) Whiteboard Dry erase marker Paper Marker Butcher paper

Student: Paper Pencil Worksheet

Adaptations:Early Finishers: Students who finish early will walk around the classroom identifying and drawing right, obtuse, and acute angles. This is sort of like an angle scavenger hunt. SPED: Check in with J often. While we are doing the beanbag activity, make sure he is passed the beanbag a few times. This will hopefully keep him engaged in the lesson. This will also help me determine if he understands the material, or if he will need some individual instruction.Behavioral: Make sure X has his spot card at the beginning of the lesson. When X is on task give him a spot on his card. Check on D often also. Make sure she gets to catch the beanbag at least once. If she does not she will probably get frustrated and have a breakdown. For I, remind him of his chance to earn a coupon at the beginning of the lesson. ELL: For these students make sure to draw and label pictures of lines, rays, line segments, acute angles, right angles, and obtuse angles clearly. This will help provide them, and all the students, with comprehensible input.

Procedure:Activate Prior Knowledge: Ask the students if they can remember the types of lines (lines, rays, line segments) we talked about two weeks ago. Students who remember can go up to the board and draw them. Point out key features like the arrows and the end points. Make sure to define the different types of lines to the students. This can be done either by the students or by the teacher if need be.Introduction: Tell students that when lines, rays, and line segments connect they form angles. There are three types of angles that we are going to learn about today: acute, right, straight, and obtuse. Instruction:

Take the beanbag and drawing out a line of string, toss it to a student in my direct line of sight (make it so that it is J). Have J stand before tossing him the beanbag. Discuss with the students what we have made.Questions:

1. What have we made?2. Is this a line, ray, or line segment?3. Why do you think this is a…

Have J pass the beanbag to M, keeping a 180-degree angle. Discuss with the students what is made now.Questions:

1. What do we have now? Explain to the students that we don’t have just one line segment anymore. Now we have

two line segments. Line segments have a start and an end point. Name the line segments. We have line segment Miss J-J and line segment J-M. Retrieve the beanbag. Go to the whiteboard and draw what we made. Write the names of the line segments on

the board. Discuss with the students the names of line segments.Questions:

1. Is J-Miss J the same as Miss J-J?2. Is J-M the same as M-J?3. Is there another name for the line segment Miss J-J?

Tell students that when two lines meet but go in different directions they form an angle. Explain that the meeting point of two lines has a special name. It is called the vertex. Write the word on the board.

Have D stand up. Toss her the beanbag. Then ask her who she would like to toss the beanbag to. Have that student stand up. Then, have D toss the beanbag.

Discuss the vertex.Questions:

1. Who is the vertex? Continue making angles by having students choose who they want to pass the beanbag to,

having that person stand up, and then passing them the beanbag. Name all the people who are vertices.

Retrieve the beanbag and go to the board. Underneath the written word “vertices” draw a picture of an angle and an arrow pointing to the vertex.

Give the bag to J. Have him stand up. Ask students who have not had a chance to catch the beanbag raise their hand. Ask him to choose one of those students with their hands raised to pass the beanbag to. Once he chooses, have that student stand up and toss the beanbag.

Have a volunteer name the line segment. Have the holder of the beanbag toss it to another student who has not had a turn. Ask someone to name the vertex and another to name the line segments. Explain that angles are formed by lines meeting at a vertex. Point out the angle that was

just made. Continue explaining that angles have names based on their size. Show students the different types of angles using my arms.

Have the students take part in a TPR activity. Say one of the types of angles and have the students show the angle with their arms.

Next, toss the beanbag around the classroom making different angles. Have the students identify each one as acute, right, obtuse, and straight.

Finish by drawing the angles on the piece of butcher paper, which will be hung up in the classroom.

Guided Practice: Guided practice is included in the instruction portion of the lesson.Independent Practice: Have the students work independently on their worksheet for 5 minutes. After 5 minutes the students can, if they want, discuss their answers with the person sitting next to them. Students who finish early and are working on the challenge activity can discuss with others in the class.

Closure: Ask students what they learned today. Ask students if they have any questions that need to be clarified. Students who finished early can share what angles they found in the classroom.

Assessment: Collect the worksheet

Reflection:

Name: _______________________________________________________

Acute Right Obtuse


Descriptive Data: 3rd Grade; Angles; Total Time of 50 minutes; 9:00-9:50am



Objective: After a review of obtuse, right, straight and acute angles students will be able to make and draw the four different types of angles on a geoboard and geoboard paper with 3 out of 3 correct.

Materials:Teacher:

Geoboard Rubber bands Angles butcher paper (from previous lesson) Geoboard paper Document camera

Student: Pencil Geoboard paper Geoboard Rubber bands

Adaptations:TAG: The TAG students who understand this concept quickly will walk around the classroom assisting students who need extra help. Teaching other students requires a deeper understanding of the material.SPED: Check in with J often. While we are making the different types of angles on our geoboards and geoboard paper see if he is on task. When he gets confused he tends to sit confused rather than raising his hand. If he is having a lot of difficulty with the activity he and N can work together.Behavioral: Make sure X has his spot card at the beginning of the lesson. When X is on task give him a spot on his card. Check on D often also. Make sure she is making angles on her geoboard and not putting the rubber bands on the geoboard to make a picture. For I, remind him of his chance to earn a coupon at the beginning of the lesson. Go over expectations with him continuously throughout the lesson.ELL: For these students make sure to remind them of the butcher paper we made. This will help them because it will remind them to refer to their resources around the classroom if they need assistance. Also, make sure to show them an example of an acute, obtuse, and right angle on the geoboard. This will help them see what they are supposed to do.

Procedure:

Activate Prior Knowledge: Discuss with students what we did yesterday. Go over the angles butcher paper. Once students have refreshed their memories of the different types of angles we covered yesterday, do the same TPR activity as yesterday. The teacher says acute, right, straight, or obtuse and the students show the angle using their arms.Introduction: Tell students that today we are going to make these four different types of angles on a geoboard and on geoboard paper. Ask the students if they have ever used a geoboard before.Instruction:

Explain and show students that a geoboard is a five by five array of pegs that you wrap rubber bands around to make different images. Tell students they can be used in many different ways.

Tell students that today we are going to be using the geoboards to make acute, obtuse, and right angles.

Explain that along with geoboards, we have geoboard paper. Show students the geoboard paper and explain to the students that the black dots

represent the pegs on the geoboard. Point out to the students that the geoboard paper is also in five by five arrays.

Ask students what it should look like and sound like when we are using the geoboards, rubber bands, and geoboard paper.

o Make sure students understand that they should not shoot the rubber bands. Ask students what they think should happen if the teacher catches a student shooting rubber bands.

They will get their geoboard taken away and will only be able to use the geoboard paper.

Tell students that the teacher is going to start looking for students who are ready to go and get their geoboard and their geoboard paper.

o Start dismissing students. Once students have gotten their geoboards make a right angle on the geoboard. Display

the angle on the document camera. Questions:

1. What type of angle is this?2. What is the measurement of this angle?3. How do you know that this is a right angle?

Have students make this exact angle on their geoboard. Walk around the classroom to make sure the students are on task.

Get the classes attention and make the angle on the geoboard paper under the document camera using the “think-aloud” technique so that students will be able to make it on their own geoboard paper.Questions:

1. Is the angle I have on my geoboard the same as the angle on my geoboard paper?2. What type of angle is on my geoboard paper?

Have students make the angle on their geoboard paper. Ask volunteers to come up to the front and show their geoboard paper.

Have the students make their own right angle on their geoboard. Then, have them copy the angle on their geoboard paper.

Ask for volunteers to come up and show their angle on their geoboard and their geoboard paper.Questions:

1. Is this a right angle?2. Does his/her angle on the geoboard match the one on the paper?3. How do you know this is a right angle?

Repeat the same process for acute, straight, and obtuse angles. First, the teacher models and the students do what the teacher did. Second, the students make their own. Third, the students show their angles to the rest of the class using the document camera.

Guided Practice: The guided practice portion of the lesson is included in the instruction portion of the lesson.Independent Practice: Students are given time to independently practice the concepts during the instruction portion of the lesson. However, the students will make a “quiz” for their neighbor. First, the students will make an acute, obtuse, straight, and a right angle on their geoboard and geoboard paper. On the geoboard paper they will label the different angles. Second, students will switch their geoboard with the person next to them. Their neighbor will then have to draw their partner’s angles on their geoboard paper and label them. Lastly, when the students are finished they will compare their geoboard papers. Did they label the angles the same?

Closure: Ask students what they learned today. Ask students if they have any questions that need to be clarified.

Assessment: Collect the geoboard paper.

Reflection:

Small Geoboards (twelve)


Descriptive Data: 3rd Grade; Mariner’s Astrolabe; Total Time of 50 minutes; 9:00-9:50am



Objective: After a lesson on making a mariner’s astrolabe students will be able to make an astrolabe and go around the room measuring the angle of different objects in the classroom by at least correctly measuring 5 angles.

Materials:Teacher:

Astrolabe pattern Straw Scissors Tape Fishing sinker (or some other weight i.e. washer) 6 in. long piece of string Pencil Astrolabe worksheet Whiteboard Dry erase marker Globe

Student: Astrolabe pattern Straw Scissors Tape Fishing sinker (or some other weight i.e. washer) 6 in. long piece of string Pencil Astrolabe worksheet

Adaptations:TAG: Students will be given a protractor and try to figure out how to measure angles using the protractor by comparing it to the astrolabe. SPED: J should be able to take part in this activity fairly independently. However, have the EA sit with him when we are making the astrolabe. This will help ensure that he has made the astrolabe correctly.Behavioral: Make sure X has his spot card at the beginning of the lesson. When X is on task give him a spot on his card. Throughout the activity make sure X is doing the activity appropriately. Check on D often also. Make sure she is making and using the astrolabe the right

way. When she is feeling frustrated make sure to go over to her and help calm her down. Otherwise she may walk out of the classroom. For I, remind him of his chance to earn a coupon at the beginning of the lesson. Make sure he is actually doing the activity. ELL: For these students make sure to talk through the steps for making an astrolabe very clearly in order to make the input comprehensible. Also, show the steps using the document camera using the “think-aloud” technique.

Procedure:Activate Prior Knowledge: Ask students about what we have been working with in math. Also, ask them what the last reading theme was (Voyagers).Introduction: Tell students that today we are going be combining math concepts and the theme from the last reading unit. Instruction:

Ask students how the characters in the Voyagers theme travelled from place to place. Questions:

1. How did the characters in “The Island below the Stars” find the island?2. How did the characters in “Trapped by the Ice” navigate?3. How did the characters in “Racing Danger” navigate?4. What objects in the sky did they use?

Tell students that a mariner’s astrolabe was used to determine the latitude of a ship at sea by measuring the altitude, or angle, of the sun or a star. Tell students that these tools were made about A.D. 400.

o Explain to students what latitude is using a globe and how long ago A.D. 400 was. Tell students that today we are going to make these astrolabes. Show students the astrolabe pattern.

Questions:1. What do you notice about the pattern?2. Why does the astrolabe pattern only have numbers 0-90 degrees?3. Does the pattern remind you of anything?

Point out to students why the pattern only has numbers 0-90 degrees.o Because if the explorers wanted to know the angle of a star behind them, rather

than bending backwards, they would simply turn around to measure the object.Guided Practice:

Call on students who are ready to get their supplies. They will go to the back table and get one of each of the materials.

Once all the students have gotten their supplies and are back at their desks make the astrolabe.

o The steps are on the pattern. Explain to students that when using an astrolabe they have to choose an object that is

between their line of sight and straight up through their head.o Draw a picture on the whiteboard.

Have the president come up to the front. Ask the president what object they want to measure in the classroom.Questions:

1. Is it possible to measure this object?2. Is this object between your line of sight and the top of your head?

Demonstrate for the students how to use the astrolabe. Have the entire class take part in measuring the object. Have the class president pass out the worksheet. Explain to the students how to use the worksheet.

o In the column on the left write the object they are measuring. In the column on the right write the measurement in degrees.

As a class, use the object we just measured to fill out the worksheet. Have another student come up to the front and choose an object. Have the class measure the angle of this object using their astrolabe.

Independent Practice: Have the students walk around the classroom measuring the angle of different objects in the classroom. Have the students fill out the worksheet too.

Closure: Ask students what they liked about the activity.

Assessment: Collect the astrolabe worksheet.

Reflection:

Name: ________________________________________________________________________

Object Measurement


Descriptive Data: 3rd Grade; Classifying Triangles by Sides; Total Time of 50 minutes; 9:00-9:50am


Benchmark: 3.3.1 Identify, describe, compare, analyze, and informally classify triangles by their sides and angles.

Objectives: 1) After a lesson on isosceles, scalene, and equilateral triangles students will be able to make and label the three different types of triangles with 3 out of 3 correct.2) After a lesson on isosceles, scalene, and equilateral triangles students will be able to solve word problems on a worksheet with 7 out of 9 correct.

Materials:Teacher:

Straws Triangles worksheet Scissors Construction paper Marker Tape Butcher paper

Student: Straws Triangles worksheet Scissors Construction paper Marker Tape Pencil

Adaptations:Early Finishers: Students who finish early will identify isosceles, scalene, and equilateral triangles in our classroom. Students who finish early may also walk around the classroom assisting students who need help with either the worksheet or constructing triangles. SPED: Check in with J often. While on the carpet have him sit in the front so that I will be able to see whether or not he is focusing on the lesson. After dividing the students in half and sending them to their designated activity, immediately go check in with J to make sure he understands what he is supposed to be doing. Have the EA sit with him and help him with both the worksheet and constructing isosceles, scalene, and equilateral triangles.

Behavioral: Make sure X has his spot card at the beginning of the lesson. When X is on task give him a spot on his card. Check on D often also. Remind her of the opportunity to earn points for math. For I, remind him of his chance to earn a coupon at the beginning of the lesson. ELL: For these students make sure to draw and label pictures of isosceles, scalene, and equilateral triangles on butcher paper at the beginning of the lesson. This will help them, and all the students, keep the information clear. They will also be able to refer to the butcher paper while they are working on the tasks.

Procedure:Activate Prior Knowledge: Draw a picture of a triangle on the whiteboard. Ask students what this is a picture of. Then, tell students that just like there are different types of angles, there are also different types of triangles. Draw an isosceles, equilateral, and a scalene triangle on the whiteboard. Ask students what they notice about the different triangles. Introduction: Tell students that today we are going to talk about how to categorize triangles by their different sides. Instruction:

Tell students that there are three different types of triangles that are classified by the length of the sides of a triangle.

Tell students that the first type of triangle we are going to talk about is a triangle where all sides are the same length, called an equilateral. Write the word on the board and draw a picture of an equilateral triangle.

Write triangles on the top of the butcher paper. Then, below write equilateral. Ask the students what an equilateral triangle is. Write the definition next to the word. Ask a student to volunteer to draw an equilateral triangle on the butcher paper. Next, get the students’ input on what the other triangles might look like.

Questions:1. I drew a triangle where all sides are the same length what is another possibility

for the length of the sides of the triangle?2. What might another triangle look like?3. How might a triangle be different than the one I drew?

Have a student come up to the whiteboard and draw another triangle. Whatever the student’s triangle is, isosceles or scalene, tell the students what type of

triangle it is and write the name on the butcher paper. Ask another student to come up and draw the triangle on the butcher paper. Again, get the students’ input on what the other triangle might look like.

Questions:1. This triangle has sides that are _________________?2. What might another triangle look like?3. How might a triangle be different than the one “name” drew?

Have a student come up to the whiteboard and draw the last triangle. Whatever the student’s triangle is, isosceles or scalene, tell the students what type of

triangle it is and write the name on the butcher paper. Ask another student to come up and draw the triangle on the butcher paper. Tell students that we are going to start the activity for today and look for students who

are ready to go back to their desks.Guided Practice:

Tell students that I am going to divide them in half. One half of the students are going to be making isosceles, scalene, and equilateral

triangles out of straws. The other half of the students are going to be completing a worksheet on the different types of triangles. Then, the two halves will switch.

Tell the students that first we are going to be making one triangle together, as a class.o Get a straw.o Ask the students how we can make a triangle out of one straw.o Make an equilateral triangle using the “thing-aloud” method.o Tape the sides on a piece of construction paper and label the triangle.

Questions:1. How will I make the other two triangles?2. What type of triangle have I made?3. How do you know this is an equilateral triangle?

Next, go over the worksheet with the students.o Complete 1-2 questions depending on the students’ understanding.

Questions:1. What are some strategies I can use to solve these problems?2. Would it be helpful to draw a picture?

Independent Practice: Students will be given time to work on their straw triangles and their worksheets independently or with a partner.

Closure: Bring students back to the carpet and ask them if they have any questions. Also, ask students what they liked and what they did not like about the activity.

Assessment: Collect the worksheet and the construction paper with the triangles made of straws.

Reflection:

Name: ______________________

Which Triangle am I?Tell whether each triangle is isosceles, scalene or equilateral. Then explainyour thinking (for example, write “because two sides are equal”)

1. My sides measure 3 cm, 5 cm and 3 cm. What type of triangle am I?



4. My sides measure 12 in, 15 in and 15 in. What type of triangle am I?

5. My sides measure 200 in, 300 in and 400 in. What type of triangle amI?

6. Two of my sides measure 14 cm and 17 cm. All my sides add up to 45cm. What type of triangle am I?

Name: ______________________

Triangle Fun!Solve the word problems below.

1. Jim has a pool in the shape of a triangle. If the sum of the sides ofthe pool is 100 ft. One of the sides of the pool measures 30 ft andanother measures 40 ft. What type of triangle is the pool shaped like?Hint: Draw a picture!

2. If the sum of the sides of an equilateral triangle is 45 centimeters,what does each side measure?

3. If one side of an isosceles triangle measures 4 meters and anotherside measures 6 meters, what could the remaining side measure? (Giveall possible answers!)

Extra Credit/Optional:Write your own word problem about different types of triangles! Thensolve your problem!


Descriptive Data: 3rd Grade; Classifying Triangles by Angles; Total Time of 50 minutes; 9:00-9:50am


Benchmark: 3.3.1 Identify, describe, compare, analyze, and informally classify triangles by their sides and angles.

Objective: After a lesson on acute, right, and obtuse triangles students will be able to make and draw the three types of triangles on a geoboard and geoboard paper with 3 out of 3 correct.

Materials:Teacher:

Geoboard Rubber bands Geoboard paper Large clock Marker Blank butcher paper Triangles by sides butcher paper (previous lesson) Angles butcher paper (previous lesson) Whiteboard Dry erase marker

Student: Geoboard Geoboard paper Rubber bands Pencil

Adaptations:TAG: Students who understand the concepts can start by making triangles that include a specific side classification and an angle classification. SPED: Check in with J often. While on the carpet have him sit in the front so that I will be able to see whether or not he is focusing on the lesson. At the end of our time on the carpet check in with J to make sure he is prepared to do the activity on the geoboard. Also, have the EA sit with J to help him make the different types of triangles during the lesson.Behavioral: Make sure X has his spot card at the beginning of the lesson. When X is on task give him a spot on his card. Check on D often also. Make sure she also has her spot card at the beginning of the lesson. Also, make sure she is participating in the activity not just making a picture on the geoboard. For I, remind him of his chance to earn a coupon at the beginning of the lesson. Remind all students of the behavioral expectation. If students are seen shooting rubber bands they will no longer be able to make triangles on their geoboard. They will only be able to make triangles on their geoboard paper.ELL: For these students make sure to draw and label the pictures of acute, obtuse, and right triangles. This will help them, and all the students, keep the information clear. The students will also be able to refer to this piece of butcher paper for the entire lesson, which will help them, and all students, have a permanent example.

Procedure:Activate Prior Knowledge: Ask the students if they can remember the types of triangles we learned about yesterday (equilateral, isosceles, and scalene). Have students define the different triangles. Introduction: Tell students that yesterday we discussed classifying triangles by their sides. Tell them that today we are going to be talking about a different way to categorize triangles. Have students make predictions about what the categories will be based on today. Tell them that we are going to categorize triangles according to their angles. Instruction:

Review the different types of angles with students.Questions:

4. Who can name one type of angle?5. What is an acute angle?6. What is an obtuse angle?7. What is a right angle?

Ask students:o If we are going to classify triangles by angles what do think will be some of the

names of the different triangles? After posing the question see if the students can come up with the types on their own:

acute triangle, obtuse triangle, and right triangle. Go over acute triangles.

Questions:1. What do you think an acute triangle will look like?2. How many acute angles will an acute triangle have? Why?

Write triangles at the top of the butcher paper and write acute triangles underneath. Define an acute triangle as a triangle that has three acute angles. Have a student come up to the whiteboard and draw what they believe is an acute

triangle.o Tell the student whether their drawing was correct or not. Make sure to give the

student credit for attempting to do something that they did not necessarily know how to do.

Next, ask a student to come up and draw an acute triangle on the butcher paper. Write right triangle on the butcher paper. Define a right triangle as a triangle that has one right angle. Have a student come up to the whiteboard and draw what they believe is a right triangle.

o Tell the student whether their drawing was correct or not. Make sure to give the student credit for attempting to do something that they did not necessarily know how to do.

Repeat the same process for an obtuse triangle. An obtuse triangle is defined as a triangle with one obtuse angle.

When students are ready, send them to get their geoboards and geoboard paper. Have the students go back to their desks.

Guided Practice: Once students are back at their desk, make an acute triangle on the teacher’s geoboard. Place the geoboard under the document camera. Have the students make the same acute triangle on their geoboards.

Review how to make the triangle on geoboard paper by having the students draw it on their geoboard paper too.

Next, have the students make their own acute triangles on both their geoboard and their geoboard paper.

Have students come up to the document camera and show their triangles.Questions:

1. What type of triangle did you make?2. Why is this an acute triangle?

Repeat the same steps with the obtuse triangle and the right triangle. Pose the following questions to the students:

Questions:1. Is it possible to make a triangle with two obtuse angles?2. Is it possible to make a triangle with two right angles?

Ask these questions one-by-one. Have the students work on their geoboards to try to answer these questions.

o Students may work with their neighbor. However, remind them of their voice level, which should be at a level 3.

Discuss students’ answers with the whole class. Have students put away their geoboards and pick up their rubber bands. If there is time continue the dice recording sheet.

o Call a student up and have them roll three dice. Next, have the students try to build the triangle using the straws that correspond to the numbers rolled on each die. Continue filling out the chart. Lead students to the realization that the two shortest sides of the triangle must add up to be equal or greater than the third side.

Independent Practice: Making their own types of triangles and investigating whether or not a triangle can have two right angles or two obtuse angles.

Closure: Ask students if they have any questions about what was covered today. Ask students what they liked and did not like about the activity.

Assessment: Collect the geoboard paper. Check to see if the students drew the three types of triangles: acute, obtuse, and right.

Reflection:

Small Geoboards (twelve)


Descriptive Data: 3rd Grade; Sum of Interior Angles of a Triangle; Total Time of 50 minutes; 9:00-9:50am

Goal: 8.3 Geometry and Measurement: Analyze two- and three-dimensional spaces and figures by using distance and angle.

Benchmark: 8.3.2 Use models to show that the sum of the angles of any triangle is 180 degrees and apply this fact to find unknown angles.

Objectives: After an activity on the sum of the interior angles of a triangle students will be able to model that the sum of the interior angles of any triangle is 180 degrees by completing the activity with 3 angles of a triangle glued on a straight line.

Materials:Teacher:

Construction paper Blank computer paper Marker Scissors Glue Ruler Whiteboard Dry erase marker Worksheet Document Camera

Student: Construction paper Blank computer paper Marker Scissors Glue Ruler Worksheet (TAG)

Adaptations:TAG: This should be a new concept for these students since it is an 8th grade standard. Therefore, these students should also be engaged and learning in the lesson. SPED: Check in with J often. While on the carpet have him sit in the front so that I will be able to see whether or not he is focusing on the lesson. At the end of our time on the carpet check in with J to make sure he is prepared to do the activity. Also, have the EA sit with J to help him during the activity.Behavioral: Make sure X has his spot card at the beginning of the lesson. When X is on task give him a spot on his card. Make sure he is participating in the activity. He may get frustrated and give up. Check on D often. Make sure she also has her spot card at the beginning of the

lesson. If she is getting frustrated, make sure to go over and assist her. Otherwise she might try to leave the classroom. For I, remind him of his chance to earn a coupon at the beginning of the lesson. ELL: For these students the hands-on explorative nature of the lesson should help these students understand the concept. At the end of the lesson make sure to re-cap what concept was learned. This will help piece the activity together if the students did not understand.

Procedure:Activate Prior Knowledge: Ask students how many angles are in a triangle. Review with the students the types of triangles we covered yesterday: acute, obtuse, and right.Introduction: Tell students that yesterday we discussed classifying triangles by their angles. Tell them that today we are going to learn what all the angles in a triangle add up to equal. Instruction:

Draw a triangle on the whiteboard. Have students make predictions about the sum of the interior angles in a triangle.

Questions:1. What do you think all the angles in this triangle add up to be?2. Why do you think they add up to equal that number?

Write students’ predictions on the board. After many of the students have gotten the opportunity to say their predictions, give the

students a hint about what the sum adds up to equal.o Ex. 100-200

Again have the students make predictions about the sum of the interior angles of a triangle.Questions:

1. Now that you know that the sum is between 100 and 200 what do you predict is the answer?

2. Is that number between 100 and 200?3. Why do you think they add up to equal that number?

Circle the number that is closest and tell the students that this is the closest number to the correct answer.

o Do not tell the students the answer yet. Draw a different triangle on the whiteboard that looks very different from the first.

o Ex. If you drew an acute scalene triangle the first time, draw an obtuse isosceles triangle this time.

Ask students to make predictions about the sum of the interior angles of this triangle.Questions:

1. What do you think all the angles in this triangle add up to equal?2. Do the angles in this triangle add up to equal something greater than, less than, or

equal to the angles of the first triangle?3. Why do you think the angles of this triangle add up to equal that number?

Once most of the students have had the opportunity to make their predictions, tell the students that the angles in this triangle add up to exactly the same number as the angles in the first triangle.

Tell students that now we are going to do an activity that will tell us what the angles add up to equal.

Guided Practice: Dismiss students who are ready to get their supplies. Have them sit at their desks. Do these tasks with the students to model for them what each step looks like.

o Using a ruler draw any triangle on the blank piece of computer paper with a marker.

o Identify the angles with an arc and label them with any letters.o Tear the angles off of the triangle.o Make a point on the construction paper.o Place the point in the middle of the cut sides (angle of the triangle) on the point.

They should match up to form a straight line. Students may need assistance.

o Once the angles are lined up correctly, glue them on the construction paper. Discuss with the students what this activity tells us about the sum of the angles in a

triangle.Questions:

1. What type of angle do these angles make when they are lined up on a line?2. How many degrees are in a straight angle?3. If all the angles of a triangle make a straight angle, what do we know about the

measurement of the sum of the angles in a triangle?Independent Practice: N/A

Closure: Ask what the sum of the interior angles of a triangle is. Ask the students how this activity helps prove this concept.

Assessment: Collect the construction paper with the angles glued on.

Reflection:

Pre-assessment: Angles

Name: ________________________________________________________________________

1) Which of the following is a right angle?

A)

B)

C)

2) Which of the following is an obtuse angle?

A)

B)

C)

3) Which of the following is an acute angle?

A)

B)

C)

4) What is the measure of the following angle?

Write your answer here:





Pre-assessment: Triangles

Name: ________________________________________________________________________

1. Color the isosceles triangle blue, the scalene triangle red, and the equilateral triangle yellow.

2. Color the acute triangle purple, the obtuse triangle green, and the right triangle orange.

Post Assessment: Angles and Triangles

Name: ________________________________________________________________________

Direction: Complete the sentence

1) This is a ____________ angle. 4) This is a ________________ angle.

2) This is a _______________ angle. 5) This is a _________________ angle.

3) This is a _____________ angle. 6) This is a ___________________ angle.

Directions: Circle the number that is CLOSEST to the measurement of each angle

7) 90° OR 10° 10) 78° OR 170°

8) 110° OR 20° 11) 13° OR 80°

9) 180° OR 90° 12) 168° OR 93°

13) What do you use to measure an angle?

Directions: Questions 13- are two part questions. Make sure you answer both parts. For the first part make sure you write both the angle classification and the side classification.

EX. Obtuse Scalene (angle) (side)

14) a) What type of triangle is this?

b) How do you know this is that type of triangle?







20) What number do all the angles in a triangle add up to equal?

References

Astrolabe Pattern. Retrieved from http://www.astro.washington.edu/users/solontoi/astro101/CelNav/astrolabe.pdf

Blackline Masters. Small Geoboards (twelve). Retrieved from http://lrt.ednet.ns.ca/PD/BLM/pdf_files/geoboards/small_geoboards4.pdf

Mankus, M.L. (1998). What is the sum of my angles. Retrieved from http://mason.gmu.edu/~mmankus/tripoly/tri.htm

Math Extensions. (2006). Beanbag. Retrieved from http://www.saskschools.ca/curr_content/byersjmath/geometry/teachers/angles/teachfac.html

Super Teacher Worksheets. (2010). Types of Angles. Retrieved from http://www.superteacherworksheets.com/geometry/angles.pdf

Willemsen-Goode, R.L. Geometry: A three week unit plan. Retrieved from http://www.swarthmore.edu/SocSci/Education/Portfolios/rwillem1/3WeekLessonPlan.html

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http://www.google.com/imgres?imgurl=http://www.basic-mathematics.com/images/geometric-figures8.gif&imgrefurl=http://www.basic-mathematics.com/geometry-test.html&usg=__1r6RFStnthXagLFAmwxp8w2ivj8=&h=243&w=399&sz=3&hl=en&start=0&tbnid=BFsbbz1FBZom6M:&tbnh=114&tbnw=187&prev=/images%3Fq%3Dacute,%2Bobtuse,%2Band%2Bright%2Btriangle%26um%3D1%26hl%3Den%26safe%3Dactive%26biw%3D1264%26bih%3D601%26tbs%3Disch:10%2C155&um=1&itbs=1&iact=hc&vpx=675&vpy=261&dur=1106&hovh=175&hovw=288&tx=108&ty=106&ei=vktSTNWZKuSLnAeV15z5Ag&page=1&ndsp=17&ved=1t:429,r:14,s:0&biw=1264&bih=601

http://rchsbowman.wordpress.com/2009/09/30/geometry-notes-isosceles-triangles/

http://rchsbowman.wordpress.com/2009/09/30/geometry-notes-isosceles-triangles/




http://www.google.com/imgres?imgurl=http://www.eduplace.com/math/mw/background/6/09/graphics/ts_6_9_wi-4.gif&imgrefurl=http://www.eduplace.com/math/mw/background/6/09/te_6_09_overview.html&usg=__x7eHXFdcGBbIDEMTWP9-oZ5oKZk=&h=302&w=431&sz=4&hl=en&start=0&tbnid=Rl-Qjso93QPA7M:&tbnh=142&tbnw=202&prev=/images%3Fq%3DIsosceles%2Btriangle%26um%3D1%26hl%3Den%26safe%3Dactive%26sa%3DN%26biw%3D1264%26bih%3D601%26tbs%3Disch:10%2C168&um=1&itbs=1&iact=hc&vpx=143&vpy=247&dur=783&hovh=142&hovw=202&tx=172&ty=148&ei=jkpSTIDSOZSInQfXvYWMAw&page=1&ndsp=20&ved=1t:429,r:13,s:0&biw=1264&bih=601n



http://www.swarthmore.edu/SocSci/Education/Portfolios/rwillem1/3WeekLessonPlan.html

http://www.swarthmore.edu/SocSci/Education/Portfolios/rwillem1/3WeekLessonPlan.html

http://www.superteacherworksheets.com/geometry/angles.pdf

http://www.saskschools.ca/curr_content/byersjmath/geometry/teachers/angles/teachfac.html

http://www.saskschools.ca/curr_content/byersjmath/geometry/teachers/angles/teachfac.html

http://mason.gmu.edu/~mmankus/tripoly/tri.htm

http://lrt.ednet.ns.ca/PD/BLM/pdf_files/geoboards/small_geoboards4.pdf

http://www.astro.washington.edu/users/solontoi/astro101/CelNav/astrolabe.pdf

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