Differentiated Instruction Teaching/Learning Plan:

Subject: Grade 10 Academic MathematicsCourse Title: Principles of MathematicsCourse Code: MPM 2DLesson Title: Congruent & Similar TrianglesDuration: 75 minute periods

Outcome/Outcomes Targeted by the Lesson:Overall Expectation(s):By the end of the course, students will:

o Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity

Specific Expectation(s):Solving Problems Involving Similar Triangles By the end of the course, students will:

o Verify, through investigation (e.g., using dynamic geometry software, concrete materials), the properties of similar triangles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides)

o Describe and compare the concepts of similarity and congruence

Learning Goal(s):By the end of the lesson, students will be able to:

o Explain what a congruent triangle iso Explain what a similar triangle iso Explain what a scale factor iso Describe the conditions for Congruencyo Describe the conditions for Similarityo Recognize that if 2 pairs of corresponding angles are equal, then the two triangles are similaro Recognize that if 2 corresponding sides in 2 triangles are equal, then the triangles are congruento Demonstrate tat a triangle is congruent and/or similar to anothero Determine unknown measures using their knowledge of congruent and/or similar triangles

Success Criteria:o Identify whether or not the triangle is congruent by using the ‘conditions for Congruency’

- SSS (Side, Side, Side)- SAS (Side, Angle, Side)- ASA (Angle, Side, Angle)

o Identify whether or not the triangle is similar by using the ‘conditions for Similarity’

- SAS ~ (Side, Angle, Side)- AA ~ (Angle, Angle)- SSS ~ (Side, Side, Side)

o Use the proportionality statement to find the scale factor and determine the missing side lengths of the triangle

Expectations of Prior KnowledgeDiagnostic Assessment:(The diagnostic assessment will be done the day before this lesson. The purpose of the diagnostic assessment is to determine prior knowledge/skills and discover student interests as well as to identify which students require additional support and enriched material during this lesson).

Before teaching this lesson, it is essential that students become familiar with the following vocabulary and/or skills/knowledge:

o Obtuse Angleo Acute Angleo Isosceles Triangleo Equilateral Triangleo Scalene Triangleo Right-Angled Triangleo Solving missing angles using parallel lines (transversal, alternate, corresponding angles)o Opposite Angleso Pythagorean Theorem: a2 + b2 = c2 (knowing when and how to use the formula)o Properties of a triangles (all angles within a triangle add up to 180o)o Complementary Angles (two angles are complementary if they add up to 900 – a right angle)o Supplementary Angles (two angles are supplementary if they add up to 180o – straight line)

Therefore, a diagnostic assessment will take place a day before this lesson to ensure that students know the required vocabulary needed for this unit. Students will have already been taught this vocabulary and/or skills/knowledge in previous mathematics classes, however, some students may not remember the vocabulary and so, this diagnostic activity will serve as a review for most students. This will be quite helpful for students in reviewing important concepts and vocabulary. On the day prior to this lesson, students will receive a handout with questions regarding all of the above-mentioned concepts. (See ‘Formative Assessment’ for more details on the diagnostic assessment as well as ‘Appendix A: Diagnostic Assessment’ to view the actual handout).

Classroom Routines:

As students walk into class, they are expected to go straight to their assigned seats and take out a piece of paper and a pen. The ‘minds on activity’ will already be on the SMARTBoard or white board and students are expected to start the word problem right away. It usually involves a mathematical word problem, brainteaser, word puzzle, joke or small activity that connects to the material that is being taught in the lesson. For this given lesson, the ‘minds on activity’ is a brainteaser. Instructions will be written on the whiteboard or typed on the SMARTBoard. In addition to written instructions, the teacher will also explain

what to do orally, to appeal to both the visual and auditory learners. Students are allowed to work in partners (usually with the student sitting next to them), however, they are not to be disruptive and/or too loud as others may need silence in order to solve the problem. After around five minutes or so, the students raise their hands when they have an answer and wait patiently to share their thoughts until the teacher calls on them.

After the ‘minds on activity’ is completed, the teacher moves onto the actual lesson. Before the lesson is taught, the teacher explains the learning goals and success criteria for the day’s lesson. The learning goals are written on the whiteboard and are also included on the SMARTBoard page. In addition, the teacher will orally explain the learning goals and success criteria to appeal to both the auditory and visual learners.

Participation in the classroom is always welcomed and the students will often ask questions whenever they need extra clarification.

For the students who are deaf and/or hard of hearing, they will be positioned strategically in the class. They will be sitting in the front of the class, with the good ear facing the teacher. The teacher will never turn his/her back on the students, as lip reading is very beneficial to these students. The teacher will enunciate his/her words in a normal speaking tone.

ACCOMMODATIONS1. Group work: For the minds on activity, students are allowed to work in pairs to solve the brain -teaser. This is very beneficial for students who are deaf and/or hard of hearing as it is easier for them to understand what is going and they are better able to solve the task.

2. Handouts: SMARTBoard lessons will have a corresponding handout.

3. SMARTBoard lessons: These lessons will help students who are deaf and/or hard of hearing as they have a visual to look at as the teaching is talking. Anything that the teacher says will be visually represented through the SMARTBoard. Vocabulary, formulas, answers will be colour coded and bolded to emphasize importance.

4. Classroom desk set-up: The students’ desk will be structures in groups. This way, if the class has group discussions or co-operative learning activities, these students are better able to participate.

5. Encourage participation: Teachers will be patient, repeat instruction as often as necessary, and motivate the students to keep trying.

6. Assistive technology: If assistive technology is necessary, it will be used such as the FM Radio Band Technology System.

7. Word Wall: Any new terminology that is discussed in the lesson will be posted in the word wall on the bulletin board in the classroom. This way, the student knows that this is an important word that he/she needs to become familiar with.

PART 1: MINDS ON ACTIVITY

(The goal is to establish a positive learning environment, connect the topic to prior learning and/or experiences, setting the context for learning and completing the diagnostic assessment)

Description: 1. How many triangles? (7 minutes)This brainteaser is called “How many triangles can you find?” and it was found on the website ‘kissfm969.com.’ This brainteaser asks students to determine the number of triangles they see in the visual. Since this is the beginning of the Trigonometry unit, students will be working with and seeing triangles quite often. Thus, this activity is very appropriate to use as it involves the use of triangles. It is a good activity to use as it allows students to start thinking about triangles. These types of brainteasers are really good for helping students practice their logical reasoning, creative thinking and problem solving skills. It helps students go beyond the obvious answer, which in this case would be to just simply count the number of individual triangles they see. This activity will expose students to questions that require one to ‘think outside the box’ in order to successfully answer a question.

(For students who are deaf and/or hard of hearing, this is a great activity to get them engaged and to participate in class).

(This brainteaser can be found at this link: http://kissfm969.com/how-many-triangles-can-you-find/?trackback=tsmclip)

Given Visual:

Solution:The correct answer is 92 triangles. In order to solve this brainteaser, you have to recognize that the big square can be divided into 4 small squares. Then, you have to count the number of triangles in one square, and then do the same by combining two squares, three squares and finally all four squares.

Number of triangles in one square:- 8 (non-overlapping triangles) - 8 (overlapping triangles with diagonal a part of one of the sides)- 3 (diagonal is perpendicular to one of the sides of the triangle) By using one square, there are 76 triangles (8 + 8 + 3 = 19 x 4 = 76)Number of triangles in two squares:- 3 (common side of square is perpendicular)

By using two squares, there are 12 triangles (3 x 4 = 12)

Number of triangles in three squares:- 1 (all squares should be a part of the triangle)By using three squares, there are 4 triangles (1 x 4 = 4)

Number of triangles in four squares:By using four squares, there are no triangles

Final Answer:Therefore, when adding up all answers together, the final is 92 triangles (76 + 12 + 4 = 92)

Role of the Teacher:

In regards to the brainteaser, the problem will already be posted on either the white board or the SMARTBoard. Instructions will be delivered visually and orally; the instructions will be presented on the whiteboard and/or the SMARTBoard and the teacher will also explain the instructions with a clear, loud voice. The goal of this brainteaser is to encourage critical thinking and to set the tone for learning. Although this brainteaser is difficult to answer, the teacher will motivate students who are feeling discouraged by developing their confidence and reinforcing the fact that they have the capabilities to solve the problem. Teachers will also encourage students to ask reflective questions, which will bring out student opinions’ and will provide immediate and positive feedback. After the teacher has explained the instructions and finished doing his/her attendance, he/she will observe the student’s progress in completing the assigned task in a notebook. The notes he/she will record consists of: the level of engagement from the students, how quickly students were able to answer the problem, the level of student motivation, students behaviour (were they talking to their peers beside them or were they focused on completing the assigned task?), the level of difficulty, and the conversations that are occurring amongst students. After about 5 minutes, the teacher will call the class’ attention and ask if anyone would like to volunteer in answering the question. At this point, the teacher is giving other students the opportunity to teach the class and express their thought process in answering the question. If for whatever reason the student has not answered the brainteaser properly, the teacher will step in and provide the correct answer to the class.

(With respect to the students who are deaf and/or hard of hearing, the teacher will constantly be checking in with these students to make sure that they are doing okay and understanding what needs to be done).

(An example of an observational note by the teacher will be shown in greater detail under the section ‘Formative Assessment’)

Role of the StudentAt this time, students will work independently on trying to solve the brainteaser. Once a student has finished solving the brainteaser, he/she will wait quietly at his/her desk for the teacher’s next instruction.(Students will be allowed to work in groups, therefore, for students who are deaf and/or hard of hearing, they will be able to work in pairs and practice conversing with their peers).

Supplies Needed:

o SMARTBoard, Computero SMARTBoard page showing the ‘How many triangles do you see?’ brainteaser

(including the given visual and the solution)

PART 2: ACTION(Consider the diagnostic data and the results of the Minds On Activity when planning learning activities. In this section, introduce new learnings or extend/reinforce prior learning)

Description:

1. Diagnostic Activity Take-up (10 minutes) – See Appendix A(It is important to note that this activity was found on the commoncore.aetn.org website titled, “Identifying Similar Triangles” by the Mathematics Assessment Resource Service University of Nottingham & UC Berkeley in 2012. It has been re-designed, modified and adjusted to fit the needs and expectations of this Grade Ten Academic Lesson).

Before teaching the lesson, the teacher will quickly review/take-up the diagnostic assessment with the students. The teacher asks students to switch papers with the student next to them and mark their peers work. This is to be used as a formative assessment tool. Although the mark will not count toward the student’s grade, it will help the teacher determine who is struggling and who understands the material. Thus, if a student received a low mark on the diagnostic assessment, this will indicate that the student needs more help understanding the mathematical concept. (See ‘Formative Assessment’ for more detail)

The review lesson will consist of reviewing the following concepts:o Solving missing angles using parallel lines (Transversal, Alternate, Co-Interior)o Solving angles that are opposite (Opposite Angles)o Reviewing the symbols for parallel lines, equal lengths and congruent angleso Reviewing key terms: Congruent, corresponding, supplementary, acute, obtuse and right angleso Using the formula for the Pythagorean Theorem and using it to find a missing side lengtho Reviewing the property of triangles (all angles within a triangle add up to 180o

o Classifying triangles in four special types: Scalene, Isosceles, Equilateral and Right-Angled

2. Lesson: 7.1: Congruent & Similar Triangles (40 minutes) – see attached separate SMARTBoard document (not in the Appendix)

This SMARTBoard lesson will cover the definition of congruent and similar triangles as well as the three conditions of congruency and similarity. Furthermore, students will learn how to create a proportionality statement and understand that the proportionality statement creates a ‘scale factor,’ which students will learn is key to solving missing side lengths in similar triangles as well as proving that two triangles are similar to one another. In addition to this, several examples will be done in class, where students can practice determining and proving whether a triangle is congruent or similar. These questions will be similar to the questions assigned for homework.

Role of the Teacher:Diagnostic Assessment:

o The teacher will review the answers of the diagnostic assessment with the class. Once she has received the ‘marked’ diagnostic assessments, he/she will look through the results of the diagnostic assessment and make any necessary notes. The notes will include a description as to which students understood the content and which students need more help. The teacher will take this as an opportunity to improve the student’s overall learning.

Lesson:o The teacher will give each student a handout that corresponds to the SMARTBoard lesson. It has

exactly the same information as the information on the SMARTBoard; however, none of the questions are answered. Teacher will ask the students to pay attention to his/her explanations and fill in any of the questions that have been answered throughout the lesson. The teacher will also encourage students to make any additional notes that are not provided on the handout.

o Throughout the lesson, the teacher will encourage students to participate in asking questions and will ask for volunteers to come up to the front of the class and answer the question directly on the SMARTBoard.

Congruent Triangles:The teacher will:

o The teacher will explain what congruent triangles are (two triangles that have the same corresponding side length and same corresponding angles)

Similar Triangles:The teacher will:

o Explain what similar triangles are (2 triangles that have the same angles but are different in size)o Explain that the corresponding angles are equal and the corresponding sides are proportional.o Show the students how to make a proportionality statement and explain that the ratio of the

proportionality statement represents the ‘scale factor’o Explain what the different values of the ratio mean:

- If the scale factor is greater than 1, the triangles is an enlargement of the original triangle- If the scale factor is between 0 and 1, the triangles is a reduction of the original triangle- If the scale factor is 1, the triangles are congruent

o Explain that all congruent triangles are similar triangles but not all similar triangles are congruento Provide ‘tips’ for his/her students:

- When referencing a side, use the corner points (Example: Side AB)- When labeling a triangle, use all three corners (Example: ΔABC)

Conditions for Congruency:The teacher will explain the three conditions for congruency which are:

o Show the students what the congruency symbol iso SSS (Side, Side, Side)

– 3 sides of one triangles are equal to 3 corresponding sides of the other triangleo SAS (Side, Angle, Side)

– 2 sides and the contained angle of 1 triangle are equal to 2 sides and the contained angle of the

other triangleo ASA (Angle, Side, Angle)

– 2 angles and the contained side of one triangle are equal to 2 angles and the contained side of the other triangle

Conditions for Similarity:The teacher will explain the three conditions for similarity which are:

o SSS ~ (Side, Side, Side) – 3 pairs of corresponding sides of 2 triangles are proportional

o SAS ~ (Side, Angle, Side) – 2 pairs of corresponding sides are proportional and their contained angles are equal

o AA ~ (Angle, Angle) – 2 corresponding angles are equal

o Tell students that the symbol (~) means similarity

Example #1:Prove that ΔABC is ~ to ΔDEF using the condiitons of similarity1. DB = CA (S), 2. <B = < C (A), 3. BC = CB (S)Therefore, in using condition ‘SAS’, these two triangles are congruent

Example #2:Prove that ΔABC is ~ to ΔDEF using the condiitons of similarity

1. AB / DE = 5 / 2.5 = 2 (S)2. < B = < E (A)3. BC / EF = 12/6 = 2 (S)

Therefore, in using the condition ‘SAS ~’, these two triangles are similar

Example #3:State the triangles and then prove whether they are congruent or similar. Then, determine the unknown measures.

a) ΔXYZ is ~ to ΔWVZ (AA~)o < X = < W (A)o < XZY = < WZV (A)o 2 / x = 3 / 6, x = 4m

b) ΔADE is ~ to ΔABC (AA~)o < D = < B (A), < E = < C (A)o AD / AB = AE / AC, 9 / 9 + 4 = y / y + 3, y = 6.75

a) ΔBAC is congruent to ΔDCA (ASA)o < DAC = < ACB (A)o AC = CA (S)o <BAC = <DCA (A)

o X = 12 cm

Role of the Student:

While the teacher is taking up the diagnostic assessment, the students are expected to switch papers with the student sitting beside them, as they will engage in a peer-assessment. Students will be taking up their peer’s diagnostic assessment paper and will be giving them a mark at the top of the paper, indicating their overall understanding of the material.

As the teacher is explaining the lesson, students are expected to copy down the answers to the questions on the handout. They will listen to the teacher, ask questions when they need further clarification and follow the lesson by making additional notes as well as filling in the correct answer. Students know that the handout doesn’t include all the required information, thus, they are responsible for taking good notes in class and listening carefully to what the teacher is saying. Throughout the lesson, the teacher will be asking questions and students are expected to participate in answering the questions. Moreover, the teacher may ask for a volunteer in answering the question for the class directly on the SMARTBoard. At this point students will participate by volunteering to answer questions.

(The teacher will encourage students who are deaf and/or hard of hearing to ask questions wherever necessary and participate frequently during the lesson)

Supplies Needed:

o SMARTBoardo SMARTBoard Lesson on 7.1: Congruent and Similar Triangleso Handout on 7.1: Congruent & Similar Triangles for students to follow along and write ono Computer

PART 3: CONSOLIDATION AND CONNECTION(The teacher helps students demonstrate what they have learned and provide opportunities for consolidation and reflection. Formative feedback is actively provided to students to help prepare them for their evaluation)

Description:

Disagree/Agree Activity Sheet: - 15 minutes – See Appendix BAfter the lesson is taught, students will have a clearer understanding of what congruent and similar triangles are and how to prove that two triangles are congruent or similar. Therefore, after the lesson, students will be given the handout, ‘Disagree/Agree’ and are asked to complete the activity sheet individually. The activity consists of reading the statement and writing down whether you agree or disagree to the statement. Once the student has selected ‘agree’ or ‘disagree’ they must justify their answer in words (some may require the use of an example). After completing the activity sheet, students will switch papers with the person sitting beside them. Answers will be taken up on the SMARTBoard. Students will be marking their neighbour’s handout and will be assessing them by putting a mark out of the

total on the top right corner of the paper. Students will also assess their neighbor by determining how well they think their neighbor understands the content. During this take-up period, students will have an opportunity to ask any unanswered questions that they may have.

(After the ‘Disagree/Agree’ activity is completed, students will participate in a formative assessment called ‘Traffic Lights.’ (See Formative assessment for more detail).

Exit Slips: - 3 minutes – see Appendix BAt the last five minutes of class, students are asked to fill out an exit slip. This will take no more than 3 minutes to complete. With each exit slip, the teacher can determine which students understand the material well, need a little more practice or do not understand the material at all. In doing this, teachers can access the student’s answers and better adjust the instruction in order to accommodate students’ needs for the next class. It also helps the teacher identify which concept is the most difficult to understand for the students.

The Exit Slip will look like this:Write down:3 things you learned2 questions you still have1 connection you would like to share

Homework: Complete questions #3-6 For those who need extra help try Questions #1, 2For those who want more practice try Questions # 7-9For those who want more of a challenge, try questions # 10-12

(Assigning questions like this will cater to individual learning needs and assist in students’ learning process. This is considered a form of differentiated instruction)

Role of the Teacher:The main goal of this consolidation activity is for the teacher to answer any unanswered questions and to clarify any misunderstandings the students may have. The teacher will go over all the answers with the students and try to clear up any confusion they may have. The teacher will also take this time to record what he/she has observed in the class for this lesson. He/she will record the students’ progress in learning the material and any questions that they asked.

Role of the Student:Students are expected to answer the questions independently and then assess their peer’s work. If the student has any questions regarding the material taught in the day’s lesson, he/she should ask the teacher to gain a clearer understanding of the material.

Supplies Needed:o ‘Disagree or Agree’ Activity Sheeto Pencil/Pen

Formative Assessments

Throughout this lesson, formative assessments are taking place in many ways. It involves qualitative feedback, which focuses on improving overall student learning.

Assessment for Learning:1. Diagnostic Testing: (See Appendix A)This is a formative assessment tool that helps the teacher detect where the students stand academically in order to bring those students to where they need to be. It enables the teacher to assess the students’ strengths and weaknesses in a particular topic/unit. It shows the teacher how much the students know about a specific concept and also how much more they still need to know. The teacher reviews the results of the diagnostic test and forms an idea as to what he/she needs to re-teach or quickly review. Since this is the beginning of a new unit, students will need to know specific vocabulary. Thus, an activity worksheet will be given to the students, the day before, which involves reviewing key vocabulary words that are essential for being successfully in this new unit. Some of the vocabulary and concepts that they will need to know are: Isosceles Triangle, Equilateral Triangle, Scalene Triangle, Right-Angled Triangle, Pythagorean Theorem, Properties of a Triangle, Transversal Angles, Co-Interior Angles, Supplementary Angles, Complementary Angles and Corresponding Angles. They will also need to refresh their minds on mathematical symbols such as: parallel lines, equal lengths and equal angles. The Diagnostic Assessment can be seen in Appendix A.

2. Exit Slips (See Appendix C): Exit slips are written responses to questions that the teacher poses at the end of class to assess the students’ understanding of key concepts. Exit slips are short in length and take no more than three minutes to complete. With the exit slip, the teacher can determine which students understand the material well, need a little more practice or do not understand the material at all. By using exit slips, the teacher assesses the students’ answers and can better adjust his/her instruction in order to accommodate students’ needs for the next class.

The Exit Slip used will follow this format: Write Down: - 3 things you learned- 2 questions you still have- 1 connection you would like to share

3. Observation/Anecdotal Notes: The teacher knows how important it is to keep records of the students’ learning; therefore, the teacher records all observations in a notebook. As students are working on the minds on activity and the consolidation activity, the teacher is observing the students and taking notes on what he/she sees. This may include how engaged the student is in the activity, how long the student took to complete the activity, how difficult/easy the material in the activity was, if the student was engaged in the activity or not and the behaviour of the student. The teacher will use this information to assess learners’ day-to-day skills and progress. Furthermore, the data collected will be used to adjust instruction to meet student’s need.

Example of Sample Observation Note:Student Name: Joe (Hard of hearing student) Date: February 13th 2014

Activity Observations Time (minutes)

How many triangles?

&Diagnostic Assessment

- Very interested in the brainteaser- Concentrated - Came close to solving the answer correctly - Enjoyed working in pairs - Curious to see what the final answer was - Diagnostic assessment was done very well, he remembered the key terms and the concepts

5

SMARTBoard Lesson

- Asked a lot of questions- Needed extra clarification quite a few times - Asked to rephrase several statements- Participated in answering several questions- Once he got more comfortable with the material, he became more engaged in learning the material

10

Disagree or Agree Activity

- He answered the questions on the activity sheet correctly- Talking with his friends a lot - Completed the task rather quickly - Very easy for him to complete - Identified himself under the ‘Green Category’- Asked for more challenging work

6

Assessment as Learning:

1. Peer-Assessment:During this lesson, the students are also participating in peer assessment. Students are ‘marking’ their neighbour’s diagnostic assessment and consolidation activity sheet. It is important to note that the mark written on these assessments are not actually being recorded; the purpose of the mark is to indicate where the student stands academically. Students are asked to give their peers a mark that reflects their overall understanding of the material. By doing this, students will be motivated to work harder. They are able to better identify their comfort level with the material taught and seek help if needed.

2. Traffic Lights – (Self- Assessment)(It is important to note that this activity came from the textbook called, “Redefining Fair: How to plan, Assess, and Grade for Excellence in Mixed-Ability Classroom” written by Damian Cooper.

After the consolidation activity has been assessed, each student will look at the mark they received and have the opportunity to assess themselves using the ‘Traffic Lights’ Strategy. This technique will help the teacher assess the students’ understanding of the material. This technique uses chart paper that has been

divided into three categories: red, green and yellow. After the activity, the students will actively participate in writing down their name under the category that they identify the most with (the categories represented a student’s level of understanding). The meanings of each category are as follows: Green (I am very confident with this material), Yellow (I understand the material, but it would help if I received extra clarification) and Red (I feel like I don’t know what to do). Students who identify their level as green, will work on more challenging questions assigned for homework. Students who identify their level as yellow, will undertake moderately challenging work and may seek help from a peer. Students who identify their level as red, will work with the teacher in a small group or one-on-one. This will help students to constantly monitor their current skill level and understanding, to set new goals that reflect an appropriate challenge and to constantly adjust what they think and do in order to achieve these goals. In doing this, students become more aware of their personal strengths and weaknesses

Summative Assessment

Assessment of Learning:

1. Tests: Students will be tested on a per unit basis. Once a unit has been covered and fully taught, they will be tested on that unit and all the sections within that unit. Test questions will focus on the achievement chart, asking questions related to Knowledge and Understanding, Thinking, Application and Communication.

2. Quiz: Within a unit, the teacher uses quizzes to measure student’s knowledge of the sections taught; not on the full chapter/unit. For instance, if students are on Unit 7 and have already learned Section 7.1, 7.2 and 7.3, the teacher would give a quiz to assess students on their understanding of these sections. Quizzes usually take place mid-unit, for half of the period.

3. CPT (Culminating Performance Task): This is seen as an ‘end-of-the-year’ in-class assignment. This will be an evaluative assessment that will cover everything that was taught throughout the semester. It will have at least one question from every chapter. This will take the entire period to complete.

4. Final Exam: This is the final mark received for the class. It will be approximately 30% of the final grade. The exam includes everything that the students have learned throughout the semester and will include several questions from each chapter. This will take approximately 2-2.5 hours to complete.

Assessment PlanBased on the content in this lesson, teachers can start creating an assessment plan that fits within the Ontario Mathematics Curriculum Achievement chart for grades 9-12. The assessment plan is divided into four parts: Knowledge and Understanding, Communication, Application and Thinking.

1. Knowledge and Understanding:(In referencing the Ontario Ministry of Education curriculum documents, the ‘Knowledge and Understanding’ component will include the knowledge of content and the understanding of mathematical concepts. Thus, with this lesson, the content and concepts that will be assessed are the terms: congruent triangles, similar triangles, scale factor and proportionality statement).

o State the definition of Congruent and Similar Triangleso State the definition of Scale Factorso Explain what Congruent and Similar triangles areo Describe the conditions for Congruency and Similarityo Given triangles ΔABC and ΔDEF, discuss the reasons why ΔABC is similar to ΔDEFo Given triangles ΔABC and ΔDEF, discuss the reasons why ΔABC is congruent to ΔDEFo Given similar triangles ΔABC and ΔDEF, state the proportionality statemento Given similar triangles ΔABC and ΔDEF, identify the scale factor and determine whether ΔABC is

an enlargement of reduction of ΔDEF

2. Thinking:(In referencing the Ontario Ministry of Education curriculum documents, the ‘Thinking’ Component will use planning, processing and critical/creating thinking skills. Thus, with what students have learned in this lesson, they will be assessed on their ability to find missing side lengths and proving that two triangles are similar based on a real-life situation. Students are expected to create a visual for the scenario and show of their steps in answering the question).

o Given a real-life scenario, create two similar triangles with the information that is given and find the missing length. For example, the height of a tree is 10 m and at the top of the tree, a pigeon is looking down at the ground at a 50o angle. A boy, who is 1.5 m tall, is walking away from the tree. The boy notices a $100.00 bill on the floor, forming a 50o angle. The distance between the tree and the boy is 4 m. What is the distance between the boy and the $100.00 bill?

3. Communication:(In referencing the Ontario Ministry of Education curriculum documents, the ‘Communication’ component requires that students express and organize mathematical ideas using oral, visual and written forms).

o Given two triangles, ΔABC and ΔDEF, communicate what the scale factor must be if ΔABC is an enlargement of ΔDEF. Explain how you know.

o Given two triangles, ΔABC and ΔDEF, communicate what the scale factor must be if ΔABC is a reduction of ΔDEF. Explain how you know.

o Given two triangles, ΔABC and ΔDEF, communicate what the scale factor must be if ΔABC is the same shape and size as ΔDEF

o Communicate verbally that if <A = <X, <B = <Y and <C = <Z, and AB = XY, AC = XZ and BC = YZ, then ΔABC is congruent to ΔXYZ and AB/XY = BC/YZ = AC/XZ

o Communicate verbally that if <A = <X, <B = <Y and <C = <Z, then ΔABC is similar to ΔXYZ and AB/XY = BC/YZ = AC/XZ

4. Application:(In referencing the Ontario Ministry of Education curriculum documents, the ‘Application’ component expects students to transfer their knowledge of content and skills to new contexts).

o Demonstrate that ΔABC is congruent to ΔDEF in a word problem type questiono Demonstrate that ΔABC is similar to ΔDEF in a word problem type question