Download Step 1 Lesson Plan

UKanTeach 5E Lesson Plan
Author (s):
Team Members:
Ole Hansen & Mackenzie Justis
Title of Lesson:
Lesson #2
Date lesson will be taught: 11/22 and 11/25
Grade level: 9
Lesson Source (kit, lesson):
Congruent Triangles
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 Evaluation
sure they are measurable. Write objectives in SWBAT form…
The Students Will Be Able To:
In 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.
Questioning: Students responses to questions will give an indication whether
students understand the material or not.
•
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.
•
State the information that is required in order
for the triangles to be congruent.
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.
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)
Accommodations: Include a general statement and any
for Whole Class:
specific student needs
per pair of students:
per Student:
-
1 yardstick
-
1 protractor
-
1 “ With the Drop of a Pencil” worksheet
-
1 “Geometry Notes- Similarity and Triangle Congruence”
sheet (guided notes).
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.
Advance preparation:
Include handouts at the end of this lesson plan document (blank page provided)
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:
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.
Some students raise their hands.
Most students raise their hands.
Few or no students raise their hands.
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.
Talk to your partner about whether the
Starbucks cups in 1 are congruent or not”.
Have the students pair- and- share for one
minute.
“They are not congruent”.
“Why are the t-shirt and the angle not
congruent?”
“Yes, but I can’t see where the math comes in”.
“They don’t look the same”
“They have the same shape”.
“They burn”, “They have the same meaning”, “They
are the same objects”.
“Talk to your partner about the angle and
the t-shirt in 2. Are they congruent?”
Have the students pair-and-share about what they
think ‘congruency’ is.
Bring the students back to a whole class
discussion.
“Yes, and they have different colors, so they are not
the same”.
“Don’t they have the same number?”
“Why are the iPhones in 3 similar?”
“Yes, I think they are synonyms to each other”.
“What can we say about the candles in 4?”
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.
“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”
Expected Student Responses AND Misconceptions think like a student to consider student responses
INCLUDING misconceptions:
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.
“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”
“Number 2 was the hardest one”.
Have them also share with each other which one
was the hardest to figure out. Talk about it as a
class.
“What if you don’t pay as much attention to
the actual objects, but the numbers
instead?”
“The objects are not related to each other but the
numbers are the same”, “I don’t see how they can be
equal”.
“So, the iPhones are congruent. What
makes them congruent?”
“They are both 25”.
“They are the same objects”.
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
“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?”
“Measure, color, object”
can hear what some of their fellow students
think ‘similarity’ means.
Teacher Decision Point Assessment:
Explanation: Estimated Time: __________
What the teacher does AND what the teacher
will direct students to do: (Directions)
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.
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)
“What was similar about the Starbucks
cups?”
“What are two things that must be
corresponding in similar figures?”
Expected Student Responses AND Misconceptions think like a student to consider student responses
INCLUDING misconceptions:
“The shapes”, “The logos”.
“Sides”, “their shapes”
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.
“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: __________
What the teacher does AND what the teacher
will direct students to do: (Directions)
Probing Questions: Critical questions that
will help students “Extend or Apply” their
newly acquired concepts/skills in new
Expected Student Responses AND Misconceptions think like a student to consider student responses
INCLUDING misconceptions:
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?”
“By measuring from a different leg on the same desk”,
“by measuring from another height on the leg of the
desk”.
“What point on the pencil did you measure
the distance from? Does it matter where
this point on the pen is located?”
“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”.
“What did you use the protractor for?”
“To measure angles”, “We measured the angle the
top of the desk to the pen made with the floor”.
“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?”
“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)
Accommodations: Include a general statement and any
for Whole Class:
specific student needs
per pair of students:
-
Bag of triangles to sort
-
Straw experiment worksheet
-
6 straws and paper clips
-
1 protractor
ruler
-
1 “Geometry Notes- Similarity and Triangle Congruence”
sheet (guided notes).
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.
per Student
Advance preparation: Create Power point and guided notes
Include handouts at the end of this lesson plan document (blank page provided)
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”
“If we extend the lines of an angle to make
the sides bigger, what happens to the
angle?”
Expected Student Responses AND Misconceptions think like a student to consider student responses
INCLUDING misconceptions:
Students will work individually on their bell work.
Allow discussion on bell work & pass out
baggies of triangles.
“Turn to the closet person to you and share
your thoughts about this question. “
“I think the angle grows too, because the whole
thing is the angle and it gets bigger.”
Next slide, Triangle activity.
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?”
Display the Bell Work on the board for the
students as they walk in the door.
Pick up the bell work.
“I think these are all isosceles triangles and these
are equilaterals. “
Walk around, listen to their responses.
“Decide how to group the triangles you
were given.”
Discuss their results.
“Raise your hands and show me how many
groups you made with your fingers.”
Students raise their hands and put 3 fingers up *or
however many groups they made.
“How did you determine how to categorize
the triangles?”
“Some had the same angle measurements.”
“Isosceles, equilateral, scalene”
“They were the exact same or scaled.”
Introduce translations
Slide: Ways to move a figure so it is still
congruent to the original shape.
Translation (slide) Reflection (flip) Rotation
(turn)
Discuss
Discuss: Why do these transformations
allow us to call the figures congruent still?
“When you turn the triangle, nothing about it
changes.”
“Someone show on the Web Cam their
reasoning.”
Students display on the cam to the class how they
turned their triangles.
“Did anyone else do something similar to
this with different triangles? Or did anyone
see something different with these two
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. “
“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.”
Write their notes.
Students show work on Document Camera
Back to Notes
Exploration/Explanation: Estimated Time: ____40______
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”
Expected Student Responses AND Misconceptions think like a student to consider student responses
INCLUDING misconceptions:
Explain Straw Activity
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
“How do you connect the straws?”
Walk around the classroom; watch they each
get the same triangle.
“Why do each of you have the same
triangle.. someone cheating? Common lets
be serious for a minute..”
“We aren’t cheating!”
Once the triangles are created, have the
students compare triangles with their teams.
“Well someone show me how to make a
different triangle.”
“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.”
“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?”
“I think they are congruent because it’s the same
thing but just turned..”
Demonstrate how to connect the straws with the
paperclips.
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.
Students will begin to look through their packets
instructions and get their materials in order.
Students will watch the two volunteers.
Discuss with the class that the triangles are
congruent: all of the parts are the same or
congruent.
“Think about this: what can be determined
about the angles within the triangle?”
“They are all the same!”
Note to the class to get their notes out this is
important!
“Go ahead and get your notes out and write
this down!”
Students will takes notes on SSS then return back to
their packets for part 2 and repeat.
Repeat these steps.
“we didn’t even pay any attention to the
angles and they “took care of
themselves.”
This is called SSS (Side-SideSide) 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.
Explanation: Estimated Time: __________
What the teacher does AND what the teacher
will direct students to do: (Directions)
See above, with explore.
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)
Expected Student Responses AND Misconceptions think like a student to consider student responses
INCLUDING misconceptions:
Elaboration/Evaluation: Estimated Time: ____5 minutes______
What the teacher does AND what the teacher
will direct students to do: (Directions)
Probing Questions: Critical questions that
will help students “Extend or Apply” their
newly acquired concepts/skills in new
Expected Student Responses AND Misconceptions think like a student to consider student responses
INCLUDING misconceptions:
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 on
each 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? “
“I would need to bring it down!”
The official could use SSS Congruence —
make sure all of the sides are congruent.
“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.
Name:
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 3 rd 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 conclude
two triangles are similar?
Focus on Congruent Triangles
Side-Side- Side Postulate
If 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: EI  FH , FE  HI , and G is the midpoint of both EI and FH .
Prove: FEG  HIG
Angle- Side- Angle Postulate
If two _____________ and the included _________ of one triangle are
congruent to two angles and the included side of another triangle, then
the
triangles
_____________________.
Abbreviation:
are
Angle- Angle- Side Postulate
If 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: V  S
TV  QS
Prove: VR  SR
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 length
2 straws 11 centimeters in length
2 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 2nd 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 2nd
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?
3. Are the triangles congruent?
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?
3. Are the triangles congruent?
Part 5
1. Place two of the straws together forming an angle of any degree for one triangle, and repeat the process for the 2 nd triangle.
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.
8 cm
40°
11 cm
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?
3. Are the two triangles congruent?
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?
2. Are the two triangles congruent?
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.
2.
3.
4.
Casually drop a pencil next to a desk.
Find the distance from the pencil to a leg of the desk.
Find the height of a desk.
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?