step 1 lesson plan · web view2018. 10. 17. · ccss.math.content.hsg-co.b.6 use geometric...

UKanTeach 5E Lesson Plan

Author (s):Team Members:Ole Hansen & Mackenzie Justis

Title of Lesson:

Congruent TrianglesLesson #2Date lesson will be taught: 11/22 and 11/25Grade level: 9

Lesson Source (kit, lesson): Lesson Plan Title: Congruent Triangles— Is This Enough Information? http://www.learningpt.org/pdfs/mscLessonPlans/dotson.pdf

Concepts/Main Idea – in paragraph form give a broad, global statement about the concepts and vocabulary you want students to understand as a result of doing this activity:

Students will learn about congruent triangles and other congruent figures, the features that allow us to call them congruent, and distinguish between similarity and congruency.

Objective/s- Be specific; prioritize; include higher-order objectives; be sure they are measurable. Write objectives in SWBAT form…The Students Will Be Able To:

EvaluationIn the space below, explain the type(s) of evaluation that will provide evidence that students have learned the objectives of the lesson (formative and summative). You will provide student copies at the end of the lesson.

• Determine whether two triangles are congruent and provide the correct reason as to why the triangles are congruent.• Name congruent triangles and provide the correct reasoning for the triangles being congruent.• Use the fact that all of the corresponding parts are congruent to solve new problems.

Questioning: Students responses to questions will give an indication whether students understand the material or not.

Observations: Observing students’ task word as well as their body languages throughout the lesson will help show their level of understanding of the material.

Discussion: Giving open-ended questions that will trigger the students’ creative and critical thinking skills in a discussion with other students and as a class.

Summative: Collection of the students’ answers to the Bell Work exercises, their guided notes, and the “Discovering Congruent Triangles Activity” worksheet.

• State the information that is required in order for the triangles to be congruent.

NGSS and Common Core Standards

Math Lessons:

1. Common Core Math Practice Standard

CO-B.6. Understand congruence in terms of rigid motions.

2. Common Core Math Content Standard

CCSS.Math.Content.HSG-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

3. Currently tested indicator

G.G.28Determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles

4. NGSS Science and Engineering Practice

M1. Make sense of problems and persevere in solving them.

Materials list (BE SPECIFIC about quantities) for Whole Class:

per pair of students: - 1 yardstick

- 1 protractor

per Student: - 1 “ With the Drop of a Pencil” worksheet

- 1 “Geometry Notes- Similarity and Triangle Congruence” sheet (guided notes).

Advance preparation:

Include handouts at the end of this lesson plan document (blank page provided)

Accommodations: Include a general statement and any specific student needs

Students will follow the classrooms guidelines and respect the rules. The teachers will walk around the room to make sure that students stay on task and understand. If a student has ADHD, they will be kept entertained with the constant transitions of activities.

Safety: Include a general statement and any specific safety concerns

If there is the least perception of misuse of the yardsticks during the experiment, they will be taken away from those students performing bad behavior with the equipment. Students will know that they are working and learning in a safe zone.

Engagement: Estimated Time: __________

What the teacher does AND how will the teacher direct students: (Directions)

Probing Questions: Critical questions that will connect prior knowledge and create a “Need to know”

Expected Student Responses AND Misconceptions - think like a student to consider student responses INCLUDING misconceptions:

Have the students individually work on the Bell Work exercise by answering the questions for first 2 minutes.

Bring the students back as a whole for a class discussion

Have the students pair-and-share for one minute.

Have the students pair-and-share this probing question for one minute.

Have the students pair-and-share about what they think ‘congruency’ is.

Bring the students back to a whole class discussion.

Raise your hand if you think 1 is congruent”.“Raise your hand if you think 1 is similar”.“Raise your hand if you think 1 is equal”.Do what you did for 1 with 2, 3, and 4.

Talk to your partner about whether the Starbucks cups in 1 are congruent or not”.Have the students pair- and- share for one minute.

“Why are the t-shirt and the angle not congruent?”

“Talk to your partner about the angle and the t-shirt in 2. Are they congruent?”

“Don’t they have the same number?”

“Why are the iPhones in 3 similar?”

Some students raise their hands.Most students raise their hands.Few or no students raise their hands.

“They are not congruent”.

“They don’t look the same”

“Yes, but I can’t see where the math comes in”.

“They have the same shape”.

“They burn”, “They have the same meaning”, “They are the same objects”.

“Yes, and they have different colors, so they are not the same”.

“Yes, I think they are synonyms to each other”.

Have the students write down what they think is the difference between ‘similarity’ and ‘congruency’ on their own piece of paper.Collect their papers after one minute.

“What can we say about the candles in 4?”

“One of them is a sphere and one of them is a cube, right?”

“Some of you think that ‘congruent’ means the same as equal, right?”

Teacher Decision Point Assessment: Everyone has to turn in their thoughts on a piece of paper. Allow 2 min on

their own.

Exploration: Estimated Time: __________

What the teacher does AND what the teacher will direct students to do: (Directions)

Probing Questions: Critical questions that will guide students to a “Common set of Experiences”


Give the students the solutions to the Bell Work exercise.Have the students talk to their partner about what thoughts they had and what was confusing to them in the Bell Work.

Have them also share with each other which one was the hardest to figure out. Talk about it as a class.

The students have used many words related to figuring out what can be said about the different objects. Factors include: ‘size’, ‘shape’, ‘numbers’, ‘logos’, ‘object’, and ‘color’. Write these visually to everyone on the board. Have the students decide which factors go with each object on their own piece of paper.

Have the students talk to their partner about what they think the definition of ‘similarity’ is.

Teacher says: “Raise your hand if you feel confident in your definition of ‘similarity’.

Pass out a marker to the students who raised their hands, and have them write their definition on the board.Restate their own definitions orally, so everyone

“Talk to whom is next to you if this is what you got and what might have been confusing that made it difficult for you”

“What if you don’t pay as much attention to the actual objects, but the numbers instead?”

“So, the iPhones are congruent. What makes them congruent?”

“Okay so we can say quantity matters to us, (record on the board) what were some other factors that you considered or used to help you decide?”

“Number 2 was the hardest one”.

“The objects are not related to each other but the numbers are the same”, “I don’t see how they can be equal”.

“They are both 25”.

“They are the same objects”.

“Measure, color, object”

can hear what some of their fellow students think ‘similarity’ means.

Teacher Decision Point Assessment:

Explanation: Estimated Time: __________


Clarifying Questions: Critical questions that will help students “Clarify their Understanding” and introduce information related to the lesson concepts & vocabulary – check for understanding (formative assessment)


Hand out the guided notes. Start on the slide titled “How do we know any two figures are SIMILAR?”, lecture it, and relate it the Starbucks cups.

Go to the slide titled “Similar Figures…” with the definition of similar figures and restate orally what it is.

Have the students talk to their partner about what a proportion is and what some real-world examples involving proportions are.

Teacher says: “Raise your hand if you think a proportion is a ratio”.

Have a couple students share what their definitions of proportion are.

Go to the slide titled ‘Proportions’. Restate orally the definition of a proportion. Have the students work in their pairs to find the x-values on this slide.

Have a student share with the rest of the class how they went about solving the proportions.

“What was similar about the Starbucks cups?”

“What are two things that must be corresponding in similar figures?”

“The shapes”, “The logos”.

“Sides”, “their shapes”

“Fraction equals fraction, I think I heard, or is that something else?”, “when something is proportional”.

Make sure that everyone understands the way proportions in exercises like these are solved by asking “who didn’t understand how to solve proportions?” and then go through an example in a lecture-based fashion.

Teacher Decision Point Assessment: When everyone seems confident about how to solve proportions.

Elaboration: Estimated Time: __________


Probing Questions: Critical questions that will help students “Extend or Apply” their newly acquired concepts/skills in new situations


Go to the “Experiment Time!” slide. Tell them to follow the directions that are on this slide. Have one student from each pair of students come up to teacher to pick up one protractor, one yardstick, and two “With the Drop of a Pencil” worksheets.

Circulate the classroom, observe students, and help students who are off task or who have any questions.

When students seem to be finished with the activity, collect the material.Draw the focus of attention back to the class as whole and lead a class discussion on their findings.

“How could you have measured the distance from the leg of a desk to the pen(cil) differently?”

“What point on the pencil did you measure the distance from? Does it matter where this point on the pen is located?”

“What did you use the protractor for?”

“What was different in the measurement from the pen to the desk and the person to the desk?”

“What else could you possibly figure out in this experiment?”

“By measuring from a different leg on the same desk”, “by measuring from another height on the leg of the desk”.

“The closest point”, “The end with the ink”, “It doesn’t matter where the point is”, “It depends on the way the pen ends up lying on the floor”.

“To measure angles”, “We measured the angle the top of the desk to the pen made with the floor”.

“The second measurement required more yardsticks”.

“Proportion”, “Different angles”, “Triangles”, “.

Teacher Decision Point Assessment: You want someone to mention ‘similar triangles’ in asking the final question

Evaluation: Estimated Time: __________Critical questions that ask students to demonstrate their understanding of the lesson’s performance objectives.Formative Assessment(s): In addition to the final assessment (bell ringer or exit slips), how will you determine students’ learning within this lesson: (observations, student responses/elaborations, white boards, student questions, etc.)?

The students will turn in a piece of paper at the end of class as an exit slip.They will have been asked to write in their own words what they think similarity, and congruence mean. They can relate it to the bell work or triangles. They are also told to write any questions they have, we want to see their thought process.

These responses will be addressed the next day.

Summative Assessment: Provide a student copy of the final assessment/exit slips or other summative assessments you use in the lesson

Materials list (BE SPECIFIC about quantities) for Whole Class:

per pair of students: - Bag of triangles to sort

- Straw experiment worksheet

- 6 straws and paper clips

- 1 protractor- ruler

per Student

- 1 “Geometry Notes- Similarity and Triangle Congruence” sheet (guided notes).

Advance preparation: Create Power point and guided notes

Include handouts at the end of this lesson plan document (blank page provided)

Accommodations: Include a general statement and any specific student needs

Students will follow the classrooms guidelines and respect the rules. The teachers will walk around the room to make sure that students stay on task and understand. If a student has ADHD, they will be kept entertained with the constant transitions of activities.

Safety: Include a general statement and any specific safety concerns

Students will be instructed and expected to use the classroom tools appropriately. Students will know that they are working and learning in a safe zone.

Engagement: Estimated Time: __________

What the teacher does AND how will the teacher direct students: (Directions)

Probing Questions: Critical questions that will connect prior knowledge and create a “Need to know”


Display the Bell Work on the board for the students as they walk in the door.

Pick up the bell work.

Allow discussion on bell work & pass out baggies of triangles.

Next slide, Triangle activity.

Walk around, listen to their responses.

Discuss their results.

Introduce translations

Discuss

“If we extend the lines of an angle to make the sides bigger, what happens to the angle?”

“Turn to the closet person to you and share your thoughts about this question. “

Slide: With who is next to you, group the triangles you were given.“Discuss:

1. How or why can we move a figure so that it is still congruent to the original shape?

2. How did you decide to group your triangles?”

“Decide how to group the triangles you were given.”

“Raise your hands and show me how many groups you made with your fingers.”

“How did you determine how to categorize the triangles?”

Slide: Ways to move a figure so it is still congruent to the original shape.Translation (slide) Reflection (flip) Rotation (turn)

Discuss: Why do these transformations allow us to call the figures congruent still?

Students will work individually on their bell work.

“I think the angle grows too, because the whole thing is the angle and it gets bigger.”

“I think these are all isosceles triangles and these are equilaterals. “

Students raise their hands and put 3 fingers up *or however many groups they made.

“Some had the same angle measurements.”“Isosceles, equilateral, scalene”“They were the exact same or scaled.”

“When you turn the triangle, nothing about it changes.”

Students show work on Document Camera

Back to Notes

“Someone show on the Web Cam their reasoning.”

“Did anyone else do something similar to this with different triangles? Or did anyone see something different with these two triangles?”

“Go ahead and write this down because it’s pretty important.Slide: “Because after any of the transformations…The shape still has the same size, area, angles and line length.”

Students display on the cam to the class how they turned their triangles.

“We did that with triangles 4 & 5.”“We used reflection with the triangles she used because you can flip your paper over and it would be the same thing. Only you can’t really see through the paper, which makes it harder. “

Write their notes.

Exploration/Explanation: Estimated Time: ____40______


Probing Questions: Critical questions that will guide students to a “Common set of Experiences”


Explain Straw Activity

Demonstrate how to connect the straws with the paperclips.

Walk around the classroom; watch they each get the same triangle.

Once the triangles are created, have the students compare triangles with their teams.

Ask if everyone created exactly the same triangle? (Yes.)

Choose two students’ triangles to share with the class and compare.

Lay one triangle on top of the other, showing that all of the parts are exactly the same measure.

Display on board this slide:Begin part one of the packet and answer the questions that follow.Each pair has:

6 paper clips bag of straws with the following

lengths: 2 straws 8 centimeters in length, 2 straws 11 centimeters in length, 2 straws 5 centimeters in length

“Why do each of you have the same triangle.. someone cheating? Common lets be serious for a minute..”

“Well someone show me how to make a different triangle.”

“Okay lets keep this thought in mind.If we have all three different side lengths but you and I have the same three kinds of pieces, is my triangle going to be similar or congruent to yours? Think to yourself for a second.”“Please show us your triangles.Walk towards each other, can we consider this to be a transformation of some sort?”

“How do you connect the straws?”

Students will begin to look through their packets instructions and get their materials in order.

“We aren’t cheating!”

“We have to use one of each length, so we can’t make another triangle.. since there are only three pieces there’s only one way we can do it.”

“I think they are congruent because it’s the same thing but just turned..”

Students will watch the two volunteers.

Discuss with the class that the triangles are congruent: all of the parts are the same or congruent.

Note to the class to get their notes out this is important!

Repeat these steps.

“Think about this: what can be determined about the angles within the triangle?”

“Go ahead and get your notes out and write this down!”

“we didn’t even pay any attention to the angles and they “took care of themselves.”

This is called SSS (Side-Side-Side) Congruence —all one has to have is the sides congruent on two triangles and the triangles are congruent because only one triangle can be formed from the given information.

“They are all the same!”

Students will takes notes on SSS then return back to their packets for part 2 and repeat.

Explanation: Estimated Time: __________


Clarifying Questions: Critical questions that will help students “Clarify their Understanding” and introduce information related to the lesson concepts & vocabulary – check for understanding (formative assessment)


See above, with explore.

Elaboration/Evaluation: Estimated Time: ____5 minutes______


Probing Questions: Critical questions that will help students “Extend or Apply” their newly acquired concepts/skills in new situations


Yacht Question:Prior to the start of a yacht race, you (the judging official) must certify that all of the sails are the same size. Without unrigging the triangular sails from their masts, how can the official (you) determine if the sails oneach of the boats are the same size?

Allow students to answer in small groups discussing how they came up with the solution.

A spokesperson for each group will present the team’s solution if there is time.

“How could the official make sure that the sails are the exactly the same? “

The official could use SSS Congruence —make sure all of the sides are congruent.

“I would need to bring it down!”

“Just ask long the boards are and the lengths of the sail. It would be hard to get a huge protractor out!”

Evaluation: Estimated Time: __________Critical questions that ask students to demonstrate their understanding of the lesson’s performance objectives.Formative Assessment(s): In addition to the final assessment (bell ringer or exit slips), how will you determine students’ learning within this lesson: (observations, student responses/elaborations, white boards, student questions, etc.)?

They will pass in their answers at the end of the class as an exit slip.

Summative Assessment: Provide a student copy of the final assessment/exit slips or other summative assessments you use in the lesson

The yacht problem is a summative evaluation and informal which is comforting.

Geometry Notes- Similarity and Triangle Congruence

Objectives: 1) Student will be able to recognize congruent figures and their corresponding parts.2) Students will be able to distinguish between similar and congruent triangles.

Bell Work: Are these objects congruent, similar or equal?

A) Starbucks Cups

B) An angle and a T-Shirt

C) The new IPhone

D) Candles

Concept of Similar vs Congruent Figures

Similar Figures:

Similar figures have the same BUT

________________________________________________________.

Proportions:

EX 1: Practice finding X: a) (4/X) = (8/10) b) (6/3) = (X/2)

Congruent Figures:

Congruent figures have all ________________________________ AND all

___________________________________.

Question 1: How many ways are there to move a figure so that it is still congruent to the original shape? What are they?

Question 2: Why do these transformations allow us to call the figures congruent?

THEOREM: If you have ________________ of corresponding angles congruent of two triangles the, the 3rd pair is also ________________.

EX 1: List the following information of these two triangles.Congruent Triangles:Corresponding Congruent Angles:Corresponding Congruent Sides:

Focus on Similar Triangles

How to Prove Triangles are Similar:

Note: How much of that information is necessary to concludetwo triangles are similar?

Focus on Congruent Triangles

Side-Side- Side PostulateIf the ___________ of one triangle are congruent to the sides of a second triangle, then the triangles are ___________________.Abbreviation:

Side- Angle- Side Postulate

If two sides and the included ____________ of one triangle are congruent to two ___________ and the included angle of another triangle, then the triangles are __________________.Abbreviation:Example #1: Write a proof.Given: , , and G is the midpoint of both and .Prove:

Angle- Side- Angle PostulateIf two _____________ and the included _________ of one triangle are congruent to two angles and the included side of another triangle, then the triangles are _____________________.Abbreviation:

FHEI HIFE EI FH

HIGFEG

Angle- Angle- Side PostulateIf two angles and a non-included side of one triangle are congruent to the corresponding two ______________ and a side of a second triangle, then the two triangles are ____________________.Abbreviation:

Example #2: Write a proof.Given:

Prove:

Discovering Congruent Triangles Activity (Edit and take answers off this page!)

Objective: Understanding congruent triangle postulates and theorems using inductive reasoning.

Materials needed: straws, protractor, ruler, and construction paper or cardstock

Groups: small groups from 2 to 4 students

Have students cut straws into the following lengths:

2 straws 8 centimeters in length2 straws 11 centimeters in length2 straws 5 centimeters in length

Part 1

1. Have students put the 3 straws of different lengths together to form a triangle as shown.

2. Form another triangle with the other set of straws.

3. Measure the angles of both triangles using a protractor.

Questions:

1. What are the measures of the 3 angles in the first triangle?

2. What are the measures of the 3 angles in the second triangle?

3. What is the relationship between the angles of each triangle?

4. Are the triangles congruent?

5. Can the straws be rearranged to form a triangle with different angles?

Part 2

1. Take 2 of the straws, place them on a piece of paper, and form a 60 degree angle between them.

2. Take the 2 straws of the same length and also form a 60 degree angle between them.

3. Draw a line to represent the 3rd side. Repeat the process for the 2nd triangle.

4. Measure the length of the 3rd side and the two remaining angles for each triangle.

Questions:

1. What is the length of the 3rd side?

2. What are the measures of the remaining angles?

3. Are the two triangles congruent?

4. Use any two straws and any angle of your choice. Do you get the same result? Will you always get the same result?

Part 3

1. Measure three angles measuring 80, 60, and 40 degrees on the corners of 2 pieces of construction paper or cardstock, cut them out, and label them.

2. On a piece of paper, take one of the straws, and place two of the cut-out angles on each end as shown. Repeat the process for the 2 nd triangle.

3. Using a ruler, draw a segment along each of the angle. The two segments should intersect forming the last angle. Repeat the process for the 2 nd triangle.

4. Measure the 3rd angle and the lengths of the 2 sides in each triangle.

Questions:

1. What is the measure of the 3rd angle for each triangle?

2. What are the measures of the remaining 2 sides for each triangle?


4. What if you used the 5cm straw? The 8cm straw? A straw with a different length?

Part 4

1. Use two of the angles used in the example above. 2. Use one of the straws and place one of the angles alongside it as shown. Draw a long segment like the dashed one in the drawing. Repeat the process

for the 2nd triangle.

3. Place the second angle along this segment so that when a 2nd segment is drawn, it will connect with the end of the straw.

4. Measure the 3rd angle and the two remaining sides.

Questions:

1. What is the measure of the 3rd angle for each triangle?

2. What are the measures of the remaining 2 sides for each triangle?


Part 5

1. Place two of the straws together forming an angle of any degree for one triangle, and repeat the process for the 2nd triangle.

11 cm

8 cm

40°

2. Use one of the pre-cut angles and place alongside the longer of the sides but not as the included angle.

3. Draw a segment to connect the 3rd side to the other two sides.

4. Swing the 8cm straw so that it hits the 3rd side at a different spot in the 2nd triangle as in the first.

5. Measure the 3rd side and the remaining 2 angles in each triangle.Questions

1. What is the measure of the 3rd side for each triangle?

2. What are the measures of the remaining 2 angles for each triangle?


4. Do you think that you would get different results if you used a different angle?

Part 6

1. Place the 3 angles so that they can form a triangle without measuring the sides initially. Draw segments connecting the angles. Repeat the process for the second triangle.

2. Measure the 3 sides for each triangle.

Questions

1. What are the measures of the 3 sides for each triangle?


4. Draw two triangles for each part, and using the correct marks, show which sides and angles are congruent. Match the correct shortcut for each set of triangles from the following choices, and tell whether or not the shortcut is valid for proving triangles congruent. SSS, SAS, AAS, AAA, ASA, SSA

S means that the corresponding sides of the triangles are congruent. A means that the corresponding angles of the triangles are congruent.

Name: ______________________Date: _______________________

With the Drop of a Pencil!

Task:1. Casually drop a pencil next to a desk.2. Find the distance from the pencil to a leg of the desk.3. Find the height of a desk.4. Record the information discovered:

Question: What else do you think we can possibly determine with the data found? Try finding it.

Continue:5. Now, one person picks a random spot in the room to stand. 6. Mark that spot and find the distance from it to the desk.7. Record the information discovered:

Question: What else can you possibly say with the data you have found so far?

8. Draw your experiment in the space provided:

Question: If you had repeated this experiment again would you get the same results? Why do you think this?

step 1 lesson plan · web view2018. 10. 17. · ccss.math.content.hsg-co.b.6 use geometric...

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