Topic/Theme: Foundations 20 Date/Time: March 15th

,

2016

Class Management

Considerations

Hands-up when

students want

to answer or

ask a question.

Students will

go with the

person sitting

next to them

On-task

discussion, use

the timer

Content Identification: Parallel Lines

Outcomes: FM20.4: Demonstrate

understanding of properties of angles and

triangles including:

- deriving proofs based on theorems

and postulates about congruent

triangles

- Solving problems

Indicators

(Evaluation/Assessment): “a” Identify and

describe situations

relevant to self, family, or

community that involve

parallel lines cut by

transversals.

Students will be able to

identify and describe three

characteristics of parallel

lines, noticing that there is

a transversal. From that,

they will identify, describe

and prove the existence of

one set of parallel lines

that exists around them.

Prerequisite Student Learnings: - Parallel lines

Set: (Using concept attainment) On the board we will draw a T-chart with

“Yes” and “No” columns. We will have six different pictures representing

lines that are & are not parallel. We will hold the picture up, and ask the

students “yes or no, does this have parallel lines?” Development:

1. In pairs, the students will look at the “Yes/No” chart on the board,

and determine three characteristics of the parallel lines in the

picture. We will share as a class the findings.

**NOTE: Students will notice that each situation in the picture has

a transversal. However, they will not know the actual term.

TASK 1 Using the alphabet; identify the letters that have parallel lines.

Prove why these lines are parallel using the characteristics discussed as a

class.

2. Pairs will share their findings with one other pair, and

compare/contrast their answers. Now as a group of four students,

they will add those letters to the Yes/No chart worksheet.

(Worksheet 1)

Lesson Plan #1 Foundations 20

TASK 2 Look around you: Throughout the classroom and school, identify

and describe a situation where parallel lines exist. Prove that they are

parallel.

Extension: Do you think the angles created by the transversal will have the

same measure? Prove your theory.

Quiet when

searching

through the

school

Closure: As a class, students will share their example they found in the

school. They will explain their thinking to the class and answer questions.

Their knowledge will be assessed based on the yes/no chart they created

along with Rubric 1

Materials and Aids: (1) Worksheet 1

This lesson uses inquiry to help meet the problem solving objective. We begin the lesson

using concept attainment to give the students a guide to use when solving the two tasks. The

“Yes/No” chart will help eliminate the confusion of the students, and allow them to use their

group as a resource instead of the teacher. The overall objective was for the students to be able to

identify and describe three characteristics of parallel lines, noticing that there is a transversal.

From that, they will identify, describe and prove the existence of one set of parallel lines that

exists around them. By using group work, the students came to the conclusion of three different

characteristics. They shared with the class to discuss and evaluate each other’s reasoning. This

helped the students gain a deeper understanding of parallel lines because they could discuss with

their peers and challenge each other’s thinking. The first task was more guided because the

students were to determine parallel lines in the alphabet based on the characteristics found as a

class. This eases the students into the last task of finding their own example of parallel lines. The

students again have the opportunity to discuss with the class the example that they found. This

time, they each must answer questions from the class and be able to explain their reasoning. This

allows for assessment because the students will have to meet the rubric requirements when

presenting their example to the class. The rubric gives the teacher the opportunity to make sure

they met the requirements of the objective without using a formal type of assessment like a test.

We chose this type of rubric because it allows the students to know the teachers expectations

before they begin. Overall, the two tasks in this lesson meet the objective and it allows for

discussion. As an extension of the lesson, the students will be asked to go back and look at their

example they found. They will be asked to think about the question: Do you think the angles

created by the transversal will have the same measure? Prove your theory. By using this as an

extension, it leads into the next indicator of finding the angles in parallel lines cut by a

transversal.

Alphabet Activity

Name: ______________________

A B C D E

F G H I J K

L M N O P

Q R S T U

V W X Y Z

Picture 1: http://plus.maths.org/content/sites/plus.maths.org/files/features/projective/tracks1_small.jpg

Picture 2:

http://media1.shmoop.com/images/module_images/ImageUpload_11302012/Parallel640x480.jpg

Picture 3: http://cx.aos.ask.com/question/aq/examples-vertical-angles-real-life_e45718bd19f1931b.jpg

Picture 4:

http://math8reviewpd5.wikispaces.com/file/view/4261451730_beeecbe471.jpg/225467862/249x187/42

61451730_beeecbe471.jpg

Picture 5: http://media.al.com/breaking/photo/i-565-f9b38dea87d757b3.jpg

Picture 6: http://www.geometryinreallife.com/uploads/4/8/2/5/482523/5397793.jpg

Rubric 1

Mathematical

Reasoning

Conceptual

Understanding

Problem Solving

Strategies

Communication

4 - can apply

knowledge of the

properties parallel

lines

- can fully explain

reasoning behind

solution path

- no errors in solution

path

- has reached a solution

and labeled the parallel

lines

-Can find parallel lines in

their surroundings as

well as transversals

- can find errors in other

group work and

can professionally

correct them

- uses a high

level strategy

- can fully

explain reasoning

for choosing that

strategy

- can identify

strategy used by

the other group

and explain their

reasoning

- can fully explain

their solution and

their reasoning

behind it

- can answer

questions

effectively

- uses a diagram

and labels each part

of the diagram

3 - can apply

knowledge of parallel

lines only to the

alphabet

- can adequately

explain reasoning

behind solution path

- complete solution with

the parallel lines labelled

but have trouble when

transversals are added

- can find errors in other

group work and can

adequately correct them

- uses a good

strategy

- can adequately

explain reasoning

for choosing that

strategy

- can identify the

strategy used by

the other group,

but can’t explain

their reasoning

- can explain their

solution but doesn’t

add to it

- no extensions

- can adequately

answer questions

- uses a diagram

and labels some

parts of the diagram

2 - can apply

knowledge of parallel

lines only using

examples from the

Yes/No Concept

attainment chart

- explains very

quickly their

reasoning behind the

solution path

- incomplete solution

- understands parallel

lines exist in the real

world but can only list

ones found on the board

- can find errors in other

group work but can’t

correct them

- has a strategy in

mind

- doesn’t know

how to act upon

that strategy

- can identify

how the other

group solved the

problem, but

can’t identify a

strategy

- hesitant to share

their solution

- very simple and

quick explanation

- answers questions

quickly without

thinking

1 - can’t apply

knowledge of parallel

lines

- can’t explain their

reasoning

- no solution

- can’t identify errors

- can’t correct errors

- cannot find parallel

lines in the real world

- can’t think of a

strategy to use

- can’t identify a

strategy in the

other group’s

work, and can’t

identify how they

solved it

- doesn't want to

share or explain

solution

- doesn’t answer

questions

- doesn’t use a

diagram

Lesson Plan #2

Topic/Theme: Determining angle

measures

Date/Time: March 16th

, 2016 Time &

Management

Considerations

Content Identification: (1) determining the angle measure created by a parallel line and a transversal

Outcomes: Demonstrate

understanding of

properties of angles and

triangles including:

- deriving proofs based

on theorems and

postulates about

congruent triangles

- solving problems.

Indicators (Evaluation/Assessment): “b” Develop, generalize, explain, apply, and

prove relationships between pairs of angles formed

by transversals and parallel lines, with and without

the use of technology.

Objective: Students will be able to demonstrate

their understanding of how to solve for an angle

measure formed by a transversal and parallel lines

by verbally sharing results, and through written

work.

Prerequisite Student Learnings: (1) know what parallel lines are (2) know

what an angle is (3) basic knowledge of how to solve an angle measure

Set: Using the examples of parallel lines found last day throughout the school;

discuss as a class whether angles are created, if they are important, and how

they could be used.

◄ 10 mins

- Noise Level

Down

- Raise Hands

Development: Teacher Task: Hand out rubric 2 and give students time to read it over

and develop an understanding of the expectations. Answer their

questions, and explain the importance of showing work when solving

problems.

1) Split the class into two groups. Each group will be given a large piece of

paper with parallel lines and a transversal.

Task 1 As a group, determine the measure of the indicated angles within the

parallel lines cut with a transversal on the large piece of paper given. Use

your group as a resource, but everyone needs to write their own work on the

worksheet. Teacher Task: Attached worksheet shows the problems the students will be

given. However, they will be on large poster board paper. The students will

each be given worksheet 4 so they can work individually while having their

group as a resource. The teacher should be acting as an observer, going

◄10-15 mins

- On-Task

- Noise Level

Down

◄10 mins

- On-Task

◄10 mins

- Noise Level

Down

◄3-5 mins

- On-Task

around to each different group asking questions about their thinking. The

teacher must step back for this activity and allow the students to work with the

knowledge of their peers.

2) After 10-15 minutes the groups will then switch papers. So, the groups will

each have a new large piece of paper with parallel lines cut by a

transversal.

Task 2 Part A) As a group, determine the measure of the indicated angles within the

parallel lines cut with a transversal on the large piece of paper given. Use

your group as a resource, but everyone needs to write their own work on the

worksheet. Teacher Task: Attached worksheet shows the problems the students will be

given. However, they will be on large poster board paper. The students will

each be given worksheet 4 so they can work individually while having their

group as a resource. The teacher should be acting as an observer, going

around to each different group asking questions about their thinking. The

teacher must step back for this activity and allow the students to work with the

knowledge of their peers. (Task 2 is similar to task 2 except they have a

different angle to work with)

Part B) Compare your group’s findings for both questions with those of the

other group and write them down on the back of the individual worksheet.

Reflect about the way your group found the angles. Be sure to talk about how

your group solved for the angles compared to the other group, whether you

got the same answers, and why you think your method works **To be handed

in at the end of class.

Closure: Individually, each student will fill out an exit slip where they

compare their group’s findings with those of the other group (Task 4). They

will also have to determine, individually, the measure of the indicated angle

given on the exit slip.

◄10 mins

- On-Task

- Noise Level

Down

Extension: Determine the angle measure of the example you found last class

throughout the school. You may use measurement tools if you think it is

necessary to help you find the angle.

Materials and Aids: 1. Two large task sheets

2. Exit slip

3. Measurement Tools available upon request

We created specific tasks that we believe will guide our students to reach the objective of

“Students will be able to demonstrate their understanding of how to solve for an angle measure

formed by a transversal and parallel lines by verbally sharing results, and through written work”.

First, the set expands on what we did in the last class and helps the students regain focus on what

was being done and how it will relate to today’s topic. Having the students talk about angles

before actually working with them will bring them to a better understanding of how they work

and where they could be found ( ie. parallel lines and transversal). To solve task 1, students will

use their previous knowledge from last class about parallel lines and transversals, and will use

their peers as productive resources to find a solution. Task 1 relates to the objective because they

are using their knowledge to solve the problem and are demonstrating their understanding of

parallel lines and transversals by consulting with their peers and writing their work down. Task 2

relates to task 1 because they are doing the same thing, just with a different problem. As you can

see, the time and management consideration for task 2 are shorter than that of task 1 because the

students would be more knowledgeable in solving for the angle measures since they already did

one. Task 3 is where you would be able to observe the students’ knowledge, because that is

where they will be presenting their solution path to the class. Through this, you will be able to

identify the strengths and weaknesses they had when solving for this problem, and you will also

be able to see which students understand how to solve angle measures formed by a transversal

and a parallel line, and which students do not understand. The final task, task 4, is for the

students to compare their findings, of both questions, with that of the other group. This is also

part of the exit slip which will be handed in at the end of class. Through this, you will be able to

see if the students found differences and similarities in their solution path and that of the other

group. Some students might notice that the other group did it differently, but in a way that they

understand better, so they might change their way of finding measurements. This is also where

you will see which strategies they used and how they incorporated those strategies to solve for

angle measure formed by a parallel line and a transversal. The closure has two parts: the

comparing part done in task 4, and solving for an angle measure. Through this, we will see how

the students solve for an angle measure that is formed by a parallel lines and a transversal. The

set, tasks, and closure stated in this lesson plan directly relate to our objective because our

students will be solving for angle measures formed by parallel lines and transversals through

written work and verbally sharing their solutions.

Find the angle measure associated with the variables x, y, z, and w. Show your work.

58°

w

y

x z

Find the angle measure associated with the variables x, y, z, and w. Show your work.

140°

Exit Slip Name___________________

Find the angle measure associated with the variable x, y, and z. Show your work.

*Attach to individual worksheet with your work, and where you compared your group’s finding

with those of the other group.

67°

Name: _____________________

Date:_______________________

Find the Angle Worksheet

First Diagram:

Second Diagram:

Find the Angle Worksheet (Answers)

First Diagram:

Second Diagram:

**NOTE: Students may solve using a different method. However, they must show their work to get the

marks. Diagrams are acceptable only if the student can explain the diagram appropriately.

Rubric #2

Communication Mathematical

Reasoning

Problem Solving

Strategies

Individual Work

(Exit Slip)

4 - effectively takes part

in group work

- encourages/

asks questions

- uses mathematical

language

- presentation is clear,

and informative

- can fully explain

their mathematical

reasoning

- uses a high-level

strategy

- can explain

reasoning behind

choosing that

strategy

- can identify all

three angles

- can explain their

reasoning through

their written work

3 - does what is needed

in group work

- can answer/ask some

questions

- occasionally uses

mathematical

language

- presents clearly

- can adequately

explain their

mathematical

reasoning

- uses a good

strategy

- can explain

reasoning behind

choosing that

strategy

- can identify all

three angles

- has little to no

written work

2 - poorly does what is

needed in group work

- rarely uses

mathematical

language

- answers questions

quickly

- doesn’t ask

questions

- rarely speaks in

presentation

- has trouble

explaining their

mathematical

reasoning

- has chosen a

strategy

- doesn’t know how

to act upon that

strategy

-can’t explain their

reasoning for

choosing it

- can only identify 2

angles

- has some written

work

1 - doesn’t take part in

group work

- doesn’t use

mathematical

language

- doesn’t answer /ask

questions

- lets the others

present for them

- cannot explain their

mathematical

reasoning

- has no strategy

- can’t identify any

angle

- has no written

work

EMTH Lesson #3

Topic/Theme: Sum of angles and

correcting errors

Date/Time: March 17, 2016 Time &

Management

Considerations

Content Identification: (1) determining the sum of the angles in a triangle

(2) identifying and correcting errors in others solutions

Outcomes: Demonstrate

understanding of

properties of angles and

triangles including:

- deriving proofs based

on theorems and

postulates about

congruent triangles

- solving problems.

Indicators (Evaluation/Assessment): C. Prove and apply the relationship relating the

sum of the angles in a triangle

E. Apply knowledge of angles formed by parallel

lines and transversals to identify and correct

errors in a given proof.

Objective: Students will be able to show their

understanding of angle measures and the sum of

all angles in a triangle by writing down their

solutions and correcting the solutions of others.

Prerequisite Student Learnings: (1) basic knowledge of an isosceles

triangle

Set: There will four different triangles drawn on the board. Triangle 1, 2, 3,

and 4. Separate the students into four different groups and give each group

one of the triangles. Group 1 gets triangle 1, group 2 gets triangle 2, and so

on. The students will have to make a list of characteristics about their

triangle. They will then have to choose the three most important

characteristics and will write them on the board under their specific triangle.

They will then share their findings with the rest of the class.

◄ 10 mins

- Noise Level

Down

Development

1) Show the students Rubric 3, and give them time to read it over to

understand the expectations of the task. Allow them to ask questions and

answer them accordingly! Divide the class into an even number of

groups, preferably six if , and give each group the task.

Task 1 The measure of an exterior angle at the base of an isosceles

triangle is 110°. Find the measure of the vertex angle, and the sum of all

angles in the triangle.

2) After solving the task 1, the groups will pass their work to another

group. (Group 1 and group 6 switch, group 2 and group 5 switch, group

3 and group 4 switch).

◄10 mins

- On-Task

- Noise Level

Down

◄10-15 mins

- On-Task

- Noise Level

Down

- Ask for

bathroom/ drink

Task 2: Go through the work that you just received and determine the

strategy they used to solve the question. Compare their work with the

knowledge you have of angles formed by parallel lines and transversals.

Determine if the question was solved correctly and if not, circle and correct

the errors. Teacher Task: Make sure you act as a facilitator by allowing the students

to work with their group members. Only answer questions to redirect and

probe for information if the students are struggling.

breaks

Closure: The groups will explain their solutions and the group who made

corrections to their work will explain if it was done incorrectly, and if so,

will explain the corrections. (ie. group 1 and group 6) They will then

compare and contrast their methods.

◄15 mins

- Noise Level

Down

- Raise Hands

- Listening

Extension: Use the knowledge you have gained from the isosceles triangle

in task 1 to determine the angle measure of a four-sided polygon.

Materials and Aids: 1. Task sheet ** Note that there will be 6 copies of the worksheet

Along with our set and closure, we created two specific tasks that relate directly to our objective

of “Students will be able to show their understanding of angle measures and the sum of all angles

in a triangle by writing down their solutions and correcting the solutions of others”. First, our set

lets our students explore what a triangle really is and they are to think of some characteristics

related to their specific triangle. Through this, they might realize that if their triangle is

equilateral, then all three sides are equal, and all three interior angles are equal as well. Our set

relates to our objective, because they are starting to explore triangles and their characteristics,

which will prepare them for the following tasks. Task 1 gives the students the opportunity to

expand on their knowledge about triangles and apply their knowledge to physically solve for an

angle. The students will need to solve for the vertex angle, and then the sum of all angles in the

triangle, which relates directly to our objective of determining angle measures and the sum of all

angles in a triangle. Some students might know that the sum of all angles in a triangle is 180°,

which is why we want them to solve for the vertex angle, which will help us know if they

understand the concept. Task 2 is where the students get to make corrections to another group’s

work. This will help the students develop a deeper understanding of the concept because they

will be thinking of how their peers were thinking, and they will be trying to determine the

solution path and errors their peers have made. They will be searching for errors, but they will

also be noticing the differences in their group’s work and that of the other group, which could be

beneficial for the students to see because they might notice a strategy that is easier for them to

use or they might find a different way to solve the problem. This relates to our objective because

the students will be demonstrating their understanding of angle measures and the sum of all

angles in a triangle by correcting and evaluating the work of their peers. Finally, the closure is

where the groups present their solution path and the correcting group explains the errors they

found and how to fix them. Once both groups (ie group 1 and group 6) have finished presenting

their solution and corrections, they will then compare their solution paths and point out the

similarities and differences. This directly relates to our objective because the students will be

sharing their corrections with the class, and will also be sharing their own solution paths they

used to solve the problem. The closure is where you will be able to identify how well the

students understand angle measures and the sum of all angles because this is where they will be

presenting all of their work. As you can see, the closure relates directly to our objective because

the students are explaining their solution paths they used to solve the problem, and they are also

explaining the correcting they made to the other group’s work. We believe that through these two

tasks, the set, and the closure, that our objective has been met and that our students will gain a

deeper understanding of the mathematical concept of angle measures and the sum of all angles in

a triangle.

Name_________________________

Triangle Worksheet

The measure of an exterior angle at the base of an isosceles triangle is 110°. Find

the measure of the vertex angle, and the sum of all angles in the triangle. Show

your work.

Name_________________________

Triangle Worksheet (Answers)

The measure of an exterior angle at the base of an isosceles triangle is 110°. Find

the measure of the vertex angle, and the sum of all angles in the triangle. Show

your work.

Rubric 3

Mathematical

Reasoning

Conceptual Understanding Problem Solving

Strategies

Communication

4 - can apply

knowledge of the

properties of

isosceles triangles

- can fully explain

reasoning behind

solution path

- no errors in

solution path

- has reached a solution and

labeled the vertex point, as

well as all other angles, and

found the sum of all angles

- can find errors in other

group work and

can professionally correct

them

- uses a high level

strategy

- can fully explain

reasoning for

choosing that

strategy

- can identify

strategy used by

the other group

and explain their

reasoning

- can fully explain

their solution and

their reasoning

behind it

- can answer

questions

effectively

- uses a diagram and

labels each part of

the diagram

3 - can apply

knowledge of

isosceles base

angles

- can adequately

explain reasoning

behind solution

path

- has 1-3 errors in

solution path

- complete solution with

the vertex point labeled, but

hasn’t labeled the other

points

- can find errors in other

group work and can

adequately correct them

- uses a good

strategy

- can adequately

explain reasoning

for choosing that

strategy

- can identify the

strategy used by

the other group,

but can’t explain

their reasoning

- can explain their

solution but doesn’t

add to it

- no extensions

- can adequately

answer questions

- uses a diagram and

labels some parts of

the diagram

2 - can apply

knowledge of the

sum of a triangle

- explains very

quickly their

reasoning behind

the solution path

- has 4-8 errors in

solution path

- incomplete solution

- knows what the sum of all

angles in a triangle is, but

can’t identify the

measurement for the vertex

angle

- can find errors in other

group work but can’t

correct them

- has a strategy in

mind

- doesn’t know

how to act upon

that strategy

- can identify how

the other group

solved the

problem, but can’t

identify a strategy

- hesitant to share

their solution

- very simple and

quick explanation

- answers questions

quickly without

thinking

- draws a triangle

but doesn’t label

anything

1 - can’t apply

knowledge of

triangles

- can’t explain

their reasoning

- has 9+ errors in

solution path

- no solution

- can’t identify errors

- can’t correct errors

- can’t think of a

strategy to use

- can’t identify a

strategy in the

other group’s

work, and can’t

identify how they

solved it

- doesn't want to

share or explain

solution

- doesn’t answer

questions

- doesn’t use a

diagram

Topic/Theme: Foundations 20 Date/Time: March 15th

,

2016

Class Management

Considerations

Hands-up when

students want

to answer or

ask a question.

On-task

discussion, use

the timer

Content Identification: Parallel Lines

Outcomes: FM20.4: Demonstrate

understanding of properties of angles and

triangles including:

- deriving proofs based on theorems

and postulates about congruent

triangles

- Solving problems

Indicators

(Evaluation/Assessment): “d” Generalize, using

inductive reasoning, a rule

for the relationship

between the sum of the

interior angles and the

number of sides (n) in a

polygon, with or without

technology.

Students will be able to

describe the relationship

between the sum of the

interior angles and the

number of sides in a

polygon by creating their

own formulas and

formulating their own

ideas within groups.

Prerequisite Student Learnings: - Parallel lines, interior angles, supplementary/complementary angles

Set: Ask the students to draw a square and determine the measure of the

interior angles. They will notice that a square has 4 right angles therefore

the measure is 360°. Development:

1. In groups of 3-5 students, give each group a polygon based on task 1.

TASK 1 Find a way to solve for any n-sided polygon

Group 1- 5-sided polygon

Group 2- 6-sided polygon

Group 3- 7-sided polygon

Group 4- 8-sided polygon

Determine the interior angle measure, and the sum of the angle. Show all

work on the worksheet.

*To be handed in (Work is graded by Rubric 4)

2. Group 1&3 / Group 2&4 will combine to share their findings and look

for similarities in their solutions. They will compare their polygons

see if their solution method works for a different sided polygon. If

Lesson Plan #4 Foundations 20

neither group’s original method works for both polygons, they need to

figure out why it doesn’t work and come up with a new solution

together.

Extension: Using your theory, find the sum of the angles in a 12-sided

polygon. Make sure to state in your answer what the measure of the

interior angles is.

Closure: Students will share their method with the class, stating if this was

the first method they used with their group or if they had to think of a new

method. (This closure is oral based and goes along with their mark on

Rubric 4, under communication.)

Materials and Aids: (1) Worksheet 1,2,3,4

This lesson involves groups of students each having a slightly different task. This is a more

complex method of group work that allows students to develop their own understanding about

their specific polygon. From their understanding of their own polygon, they combine with

another group to determine if their reasoning works for all polygons. We think this leads to a

deeper understanding because the students can question each other’s solutions and create their

own methods to solve a concept. This lesson uses a lot of inquiry so the students can do their

own learning. Group work is also used because it allows the teacher to spend more time with all

students instead of focusing their efforts on explaining the question students individually who do

not understand. The objective of this lesson was students will be able to describe the relationship

between the sum of the interior angles and the number of sides in a polygon by creating their

own formulas and formulating their own ideas within groups. This lesson meets this objective

through not only the tasks, but the closure as well. The students are given the opportunity to

work as a group to expand their knowledge, and to challenge the different solutions. They create

their own methods within their groups, thus creating their formula. We think this is an essential

part of this indicator, that students must develop a relationship between number of sides and the

measure of the interior angles. We only have one task in this lesson because there it involves a

lot of team work and communication among the groups. We think the task is fairy difficult

especially because each group has a different task. It is essential that the teacher is productive

with helping the groups. By this, we mean that they allow for the students to use their group

members as a resource instead of relying on the teacher for the answer. By using inquiry and

group work, the students will formulate their own reasoning. This is assessed using Rubric 4, so

the teacher can gage what thinking and discussion was occurring within the groups.

Group Names:_________________________________________________________

5-Sided Polygon Worksheet

Group Names:___________________________________________________________

Six-Sided Polygon Worksheet

Group Names:____________________________________________________________

Seven-Sided Polygon Worksheet

Group Names:____________________________________________________________

Eight-Sided Polygon Worksheet

Group Names:_________________________________________________________

5-Sided Polygon Worksheet (Answers)

Group Names:___________________________________________________________

Six-Sided Polygon Worksheet (Answers)

Group Names:____________________________________________________________

Seven-Sided Polygon Worksheet (Answers)

Group Names:____________________________________________________________

Eight-Sided Polygon Worksheet (Answers)

Rubric 4

Mathematical

Reasoning

Conceptual Understanding Problem Solving

Strategies

Communication

4 - can apply

knowledge of the

properties of a

polygon

- can fully explain

reasoning behind

solution path

- no errors in

solution path

- has reached a solution and

labelled the polygon, as

well as all other angles, and

found the sum of all angles

- can find errors in other

group work and

can professionally correct

them

- uses a high level

strategy

- can fully explain

reasoning for

choosing that

strategy

- can identify

strategy used by

the other group

and explain their

reasoning

- can fully explain

their solution and

their reasoning

behind it

- can answer

questions

effectively

- uses a diagram

and labels each part

of the diagram

3 - can apply

knowledge of

interior angles

- can adequately

explain reasoning

behind solution

path

- has 1-3 errors in

solution path

- complete solution with the

polygon labelled, but hasn’t

made all connections

- can find errors in other

group work and can

adequately correct them

- uses a good

strategy

- can adequately

explain reasoning

for choosing that

strategy

- can identify the

strategy used by

the other group,

but can’t explain

their reasoning

- can explain their

solution but doesn’t

add to it

- no extensions

- can adequately

answer questions

- uses a diagram

and labels some

parts of the diagram

2 - can apply

knowledge of the

interior angles

- explains very

quickly their

reasoning behind

the solution path

- has 4-8 errors in

solution path

- incomplete solution

- knows what the sum of all

angles in a triangle and in a

4-sided polygon but can’t

connect to their “n”-sided

polygon

- can find errors in other

group work but can’t

correct them

- has a strategy in

mind

- doesn’t know

how to act upon

that strategy

- can identify how

the other group

solved the

problem, but can’t

identify a strategy

- hesitant to share

their solution

- very simple and

quick explanation

- answers questions

quickly without

thinking

- draws a polygon

but doesn’t label

anything

1 - can’t apply

knowledge of

polygona

- can’t explain

their reasoning

- has 9+ errors in

solution path

- no solution

- can’t identify errors

- can’t correct errors

- can’t think of a

strategy to use

- can’t identify a

strategy in the

other group’s

work, and can’t

identify how they

solved it

- doesn't want to

share or explain

solution

- doesn’t answer

questions

- doesn’t use a

diagram

Topic/Theme: Foundations 20 Date/Time: March 15th

, 2016

Content Identification: Parallel Lines

Outcomes: FM20.4: Demonstrate understanding of properties

of angles and triangles including:

- deriving proofs based on theorems and postulates about

congruent triangles

- Solving problems

Indicators

(Evaluation/Assessment):

“g” Solve situational problems that

involve:

- angles, parallel lines, and

transversals

- angles in triangles

- angles in polygons.

Students will be able to solve

situational problems that involve

angles/parallel lines/transversals,

angles in triangles, and angles in

polygons by competing in an

“Amazing Race” styled classroom

competition and finishing with a

score of at least 60/100 obtained from

the Rubric 5.

Prerequisite Student Learnings: - Parallel lines, interior angles, supplementary/complementary angles, triangles, polygons,

transversals

Set: Students are placed into groups of 4, and given 5 minutes to create their team name and flag using

parallel lines, triangles and polygons. They must then give a quick explanation about their team name

and their flag. The purpose of this set is not to assess their knowledge, but to just get them thinking

about all the different concepts we have covered throughout this unit. Development:

1. In their groups of 4, the students will all begin in one corner of the classroom. This will be

labelled as “Canada” (The place where the school is). This is the starting corner, there are no

questions to be answered here, and they just have to wait until the signal when they can begin.

Two groups will work clockwise, two groups will work counter-clockwise.

2. The second corner will be labelled as “United States”. The students will be shown the American

flag, and the students will be asked to identify all the polygons in the flag, and determine the

interior measure of each type of polygon found. (Refer to Task 1)

3. The third corner will be labelled as “Europe”. The students will have to draw a map of a town in

France using parallel lines, and transversals. Then they will have to find the angles of the roads

they drew (Refer to Task 2)

4. The fourth corner will be labelled as Africa. The students will be told about Egypt and have to

find the measure of interior angles in a Pyramid (Refer to Task 3)

5. One the students return to the final corner, they will be given a time that it took to complete the

“Amazing Race”. This time will help determine the winter of the race. However, the winning

team will be the fastest time with the highest mark on Rubric 5. Each student will hand their

worksheets in to the teacher with the name of their team and return to their desk. If they have a

lot of extra time before other groups finish, they will be given the extension task.

Lesson Plan #5 Foundations 20

TASK 1 You are the President of the United States and you are looking at the flag of your country. Can

you state the different types of polygons found on the flag? Then, determine the measure of the interior

angles of each type of polygon found and the sum of those angles. If you find 12 squares, you do not

need to solve all 12. Just state you found 12 squares and solve the interior angle measure of one of them.

TASK 2 You are travelling around in the country of France, and you drive into a small town in the

countryside. The town has 2 roads that are parallel running North to South (Roads A and B), and 2

roads running parallel from North-East to South-West (Roads C and D). You are driving on a road that

is perpendicular to the two roads running North to South (Road E). The measure of one angle is 113°,

determine the measure of all other angles created by the roads.

TASK 3 A Pharaoh wants to build a pyramid to represent their life. This pyramid must be perfect, thus

you have been hired to create this pyramid. The Pharaoh tells you:

a. The pyramid must be a four sided polygon

b. The pyramid must have 6 congruent triangles

Determine the measure of the interior angles, and the sum of those angles. Create an explanation to the

Pharaoh how your pyramid meets his criteria.

Teacher Task: In this lesson, the teacher times the students as they make their way around the Amazing

Race. They cannot help the students out unless the question is appropriate and can be addressed to the

whole class. The teacher’s role is to strictly observe the students and how they participate in each of the

challenges. This will help when giving a final grade for the unit.

Extension: Going back to the flag you created with your group, determine if there is any parallel lines/

transversals, polygons, triangles. Then, solve for all findings. So if there is a triangle and a square, you

state there are two polygons and solve for their interior angles and the sum of those angles. In the

square there is parallel lines, solve the angles.

Closure: Students will reflect about the unit, stating three things they have learned and 3 things they

would change about the way they learned a concept. This will be done individually so the students have

a chance to wrap- up the unit in terms of their own understanding.

Materials and Aids: (1) Worksheet 1,2,3

This lesson plan takes the place of a formal test and gives the teacher the opportunity to assess

the students’ knowledge without using a test. We think this is helpful because our unit involves a

lot of inquiry based learning and cooperative learning. The objective for this lesson tied in all the

concepts we have included in this lesson, it states Students will be able to solve situational

problems that involve angles/parallel lines/transversals, angles in triangles, and angles in

polygons by competing in an “Amazing Race” styled classroom competition and finishing with a

score of at least 60/100 obtained from the rubric 5. This lesson gives the students the opportunity

to compete with each other, while giving the teacher the chance to assess their learning. Each

task relates to a different aspect of the indicator which is to solve situational problems that

involve angles, parallel lines, and transversals, angles in triangles and angles in polygons. We

think this lesson meets all criteria because it gives the students the opportunity to work

individually and contribute to the success of their group. We think the competition element of the

task gives the groups more pressure to show all their work and explain their reasoning

thoroughly. Without the competition aspect, they may not show all their work because they will

not be gaining anything from it. This lesson touches on everything the students have learned

throughout the unit, while maintaining the idea that they are to create their own methods of

solution. Personally, I think this lesson would go over really well in the classroom because it

involves real-life situations and competition. Students will work harder when they know there is

something to be gained.

Rubric 5

Communication Group Work Problem Solving

Strategies

Individual Work

85-100 - effectively takes

part in group work

- encourages/

asks questions

- uses mathematical

language

- Contributes to

discussion within the

group at each station

- All questions were

answered correctly with

the mathematical

reasoning used

- All group members had

excellent explanations

- Group solutions varied

slightly based on the

learner

- uses a high-level

strategy

- can explain

reasoning behind

choosing that

strategy

- Can relate the

strategy to the

mathematical

reasoning used

- All work is clear

and all steps are

explained when

obtaining the

solution

- can explain their

reasoning through

their written work

- Evident that they

played a vital role in

their group

70-84 - does what is needed

in group work

- can answer/ask

some questions

- occasionally uses

mathematical

language

- The students had one

wrong answer but still had

sufficient mathematical

reasoning used to explain

their solution

-Group solutions were

copied but every member

contributed to the learning

- uses a good

strategy

- can explain

reasoning behind

choosing that

strategy

- Most work is clear

and steps are

explained

adequately

60-69 - poorly does what is

needed in group work

- rarely uses

mathematical

language

- answers questions

quickly

- doesn’t ask

questions

- Has the wrong answers

but their work shows they

have an understanding of

their mathematical

reasoning used

- Copied from their group,

and did not contribute to

the learning in all corners

- has chosen a

strategy

- doesn’t know

how to act upon

that strategy

-can’t explain their

reasoning for

choosing it

- Has very little

written work, but

there is evidence

that the student was

thinking correctly

Below

59

(FAIL)

- doesn’t take part in

group work

- doesn’t use

mathematical

language in their

solution

- doesn’t answer /ask

questions

- lets the others do all

the work

- cannot explain and

mathematical reasoning

- did not participate in the

group learning

-let others do the work

-No solutions are correct

in the group

- has no strategy

- can’t identify any

solutions

- has no written

work

United States of America (Task 1)

You are the President of the United States and you are looking at the flag of your country. Can

you state the different types of polygons found on the flag? Then, determine the measure of the

interior angles of each type of polygon found and the sum of those angles. If you find 12 squares,

you do not need to solve all 12. Just state you found 12 squares and solve the interior angle

measure of one of them

Name: ___________________________

Group Name:______________________

“Amazing Race” Worksheet

Show ALL your work on these worksheets. Fill in the Destination blank with the name of the country you

are in. Good Luck!

Destination #1: _________________________________

Village in France (Task 2)

You are travelling around in the country of France, and you drive into a small town in the

countryside. The town has 2 roads that are parallel running North to South (Roads A and B),

and 2 roads running parallel from North-East to South-West (Roads C and D). You are driving

on a road that is perpendicular to the two roads running North to South (Road E). The measure

of one angle is 113°, determine the measure of all other angles created by the roads.

Destination #2: _____________________________________________________

Destination #3:________________________________________________

Egyptian Pharaoh Dilemma (Task 3)

A Pharaoh wants to build a pyramid to represent their life. This pyramid must be perfect, thus

you have been hired to create this pyramid. The Pharaoh tells you:

c. The pyramid must be a four sided polygon

d. The pyramid must have 6 congruent triangles

Determine the measure of the interior angles, and the sum of those angles. Create an

explanation to the Pharaoh how your pyramid meets his criteria.