Unit PlanPamela D’Andrea, Sabrina De Cicco, Laura Griffin, Jennifer Looi,

Jessica Patel and Lisa Vineberg

EDPE 340-Measurments and Evaluation

January 22, 2014

Unit Overview:

This unit, which is covered in a cycle one, year two mathematics course, examines shapes such as rectangles, triangles, polygons and circles and the relationships between their areas and perimeters. The goal of this unit will be to make sure students are able to identify different shapes and calculate their areas and perimeters as well as calculate the surface area of three dimension figures. This unit will be covered over one week of classes in 6 lessons.

Lessons Class OverviewLesson 1: Intro-Perimeter and Area of Shapes

This class will be an introduction to the unit. Student’s prior knowledge will be assessed. Students will learn the formulas for calculating the perimeter and area of different shapes excluding polygons and circles. They will practice using the formulas and obtain the perimeter and area of figures individually and in pairs.

Lesson 2: Perimeter and Area of Polygons

During this class students will be explained the formulas for finding the perimeter and area of polygons. Students will apply what they have learned in this class and the previous class by completing an in class assignment. The assignment will be tiered based on students readiness.

Lesson 3: Circumference and Area of Circles

During this class students will only focus of learning how to find the perimeter and area of a circle since the circle is the only shape with no sides. Students will complete a tiered activity based on their readiness.

Lesson 4: Surface Area of Prisms and Pyramids

Now that students know how to calculate the area and perimeter of two dimensional shapes they will apply their knowledge and learn how to calculate the surface area of three dimensional figures. Students will complete a tired activity based on their interests.

Lesson 5: Review Now that students have learnt all the formulas necessary to find the surface area of prisms and pyramids they will practice the new skills that they learn. Individually students will complete worksheets where they will be asked to solve problems about surface area.

Lesson 6: Assessment Students will complete an exam to test their knowledge on the unit.

Mathematic Competencies:

In math we evaluate students on the following two competencies:

Competency 1: Solves a situational problem. This competency ensures that students are able to interpret a situation problem and represent it mathematically. It also ensures that students are able to work out a mathematical solution and are capable of validating that solution.

Competency 2: Uses mathematical reasoning. This competency ensures that students are able to analyze a problem presented to them and solve it using concepts and processes they have learnt in class. Students should also show knowledge on how to create a proof using different types of reasoning.

Teaching Strategies:

Since this is a geometry unit the needs of visual learners are targeted. The class will be looking at many different shapes and their properties. This unit is also great for tactile learners since students will be manipulated two and three dimensional shapes. Like all the units covered throughout the year students are given the opportunity to work in pairs, individually and in groups. Brain based teaching is a theory used in this unit. The brain based teaching model implies that 80% of the lesson should be about engaging the students, making sure students are acquiring the proper knowledge and elaborating the students understanding of this knowledge. Making sure students are acquiring the proper knowledge and elaborating this knowledge is accomplished in this unit by tiered activities. Students are first lectured about the formulas or information they need and then take part in tired activities so that they may apply that knowledge and deepen their learning. Also during the tired activities students are grouped by readiness and interest.

Using teaching strategies are just as important as using educational theories to teach a class. Here are examples of teaching strategies that I will be using throughout the unit.

During the unit students will have individual, paired and group work to do. This is a strategy that works well in every unit because students have a chance to understand the information themselves and also work with others so that they can deepen their learning experience.

Another strategy is tiered assignments. This strategy works well because students are able to work on activities based on their readiness and on their interests which gets students motivated.

Problem solving is often modeled for students. Whenever students learn a new formula one to two examples are demonstrated to show the correct method to use the formula. This gives students a chance to see how a problem should be written up and organized.

Highlighting or underlining is an important strategy used throughout the year. Whenever notes are given to students, important information is always underlined. Students are encouraged to do the same when they are completing word problems.

Backward Design:

The Big Idea: students should be able to calculate the surface area of 3D solids

Unit Plan:

SECONDARY 2 MATHGEOMETRY UNIT-PERIMETER AND AREA OF TWO AND THREE DIMENSIONAL SHAPES

As a result of this unit, Students will understand that…

Perimeter and area are important concepts and are widely used in people’s everyday lives.

Different shapes have different areas and different perimeters

Some shapes can have the same perimeter but different areas.

Some shapes can have the same area but different perimeters

Different shapes may have different formulas to calculate area

The perimeter of a circle is known as circumference A prism is a three dimensional figure with a top and

bottom A pyramid is a three dimensional figure with one bottom.

Its triangular sides converge to one point at the top.Students will know…

Perimeter is the distance around a shape Perimeter is measured with units of length Area is the space inside a shape Area is measured with square units The formula to calculate the area of rectangles, triangles,

circles, and polygons respectively Surface area is the total space covered by the exterior of a

three dimensional figure The formula to calculate the surface area of prisms and

pyramids respectivelyStudents will be able to…

Calculate the perimeter and area of two dimension shapes Calculate the circumference and area of a circle Calculate the surface area of prisms and pyramids Select appropriate tools to measure perimeter and area of

real objects Use the appropriate units for perimeter and area

COMPETENCIES Competency 2 - Uses Mathematical Reasoning

Lesson 2:

LESSON PLAN

Date: November 5, 2012Time: NADuration: 75minsSchool: NA

Subject: MathematicsUnit: GeometryLevel: Secondary 2Group Size: 27

OBJECTIVE(S) By the end of this lesson,Students will understand that…

There is a difference between perimeter and area Different shapes have different areas and different

perimeters Some shapes can have the same perimeter but different

areas. Some shapes can have the same area but different

perimeters Different shapes may have different formulas to calculate

areaStudents will know…

Perimeter is the distance around a shape Perimeter is measured with units of length Area is the space inside a shape Area is measured with square units The formula to calculate the area of rectangles, triangles,

circles, and polygons respectively That apothem is the distance from the center of a polygon

to one of its sides.Students will be able to…

Calculate the area and perimeter of different shapes Use the appropriate units for perimeter and area

MATERIALS REQUIREDAND KEY

VOCABULARY

Material required: String, ruler, post-its, worksheet on perimeter and area, paper cut-outs of different shapes. At least 9 different shapes. Out of these 9 different shapes at least two must have the same perimeter and two must have the same area. Paper cut-outs of different sized rectangles and triangles. Paper cut-outs of identical triangles.

Key Vocabulary: Perimeter Area Length, width, height Units(cm, m, dm , cm2 , m2 , …) apothem

SUBJECT COMPETENCIES:

Competency 2 - Mathematical Reasoning

TIME STEP-BY-STEP PROCEDURE

5 minutes

25 minutes

40mins

HOOK: Greet the students as they walk in the door and give them a paper with the number 1, 2 or 3 on it. The classroom desks should be set up in three groups numbered 1-3. Students should sit at their designated numbers. Inform students that they will be taking part in an activity today involving area and perimeter. Give a brief review of what was covered last class by prompting students with questions such as:What is perimeter?What is area?What is the formula for the area of a rectangle and triangle?Do you think two figures can have the same area or the same perimeter?

INTRODUCTION/DEVELOPMENT:Introduce polygons to students. Explain that the name of polygon’s are based on the number of sides that the polygon has. Explain that a polygon is composed of triangles where the number of triangles is equal to the number of sides. Demonstrate this to the class visually.

To get the perimeter of a polygon, like any other shape, we add up the length of all the sides. Or in the case of a polygon multiply the length of one side by the number of sides of that polygon. Demonstrate this to the class with an example.

Show students the formula to calculate the area of a polygon. Depending on which formula you are using explain the different symbols. (ex: n=number of sides, a=apothem…) Demonstrate to the class how to use the formula by doing an example and then leaving them 2 minutes to do an example on their own.

Hand out instructions to the three groups. Students will take part in a tired activity based on readiness. I would have prepared the groups beforehand by my assessment of students work in the previous class and their work throughout the school year so far.

Low readiness group: This group will be completing practice problems where they must compute the perimeter and area of different figures. All the necessary measures are given. Students must find at least two shapes with the same area and two shapes with the same perimeter. They will record their calculations and submit the worksheet at the end of class. Middle readiness group: This group will be given string to calculate the perimeter of different shapes. They must find the

shapes with the same perimeters. They will then compute the area of the different shapes and find the shapes with the same area. They must then come up with two different shapes that have the same perimeter and the same area. They will record their calculations along an image of the shapes on a piece of paper to be submitted at the end of class.

High readiness group: This group will be given different sized rectangles, triangles and identical triangles and asked to make rectangles and polygons of different sizes using the cut-outs. Students will find the area of the shapes they have created by calculating the area of the shapes it is composed of. Students will have to make two shapes whose area and perimeter are the same. They will record their calculations as well as an image of the shapes on a piece of paper to be submitted at the end of class.

I will be circulating around the classroom to make sure students are on track and completing the activity properly. It is also important to make sure all students are working well in groups and participating.

ADAPTATIONS:Gifted students will be placed in the high readiness group since they are high achieving students. When I am circulating I will make sure that they are engaged and doing their work. If they finish early they can join other groups to help them out or do one of the other activities.

Struggling students will be placed in the low readiness group so they can practice doing basic calculations.

A student with Asperger’s can chose to work with a partner instead of in a large group.

Students with visual impairments will be placed in the high readiness group. They will benefit from working with cut-out shapes and will be able to feel the edges and be able to place them together as they are big enough for students to see. To record the measurements of the object these students will use a ruler I have made for them where the lines correspond to 5cm.

CLOSURE/ACTIVITY:Before students submit their papers ask them to discuss in their groups their findings and answer the question at the beginning of class.Can two figures have the same area or perimeter? Why ?

5 minutes ASSESSMENT: All students will submit their papers with their calculations.

LESSON PLAN REFLECTION

What went well?

What were the weak points?

How can this lesson be adapted to be better?

Lesson 4:

LESSON PLAN

Date: November 7, 2012Time: NADuration: 75 minutesSchool: NA

Subject: MathematicsUnit: GeometryLevel: Secondary 2Group Size: 27

OBJECTIVE(S) & LEARNING GOAL(S)

By the end of this lesson, Students will understand that…

A prism is a three dimensional figure with a top and bottom

A pyramid is a three dimensional figure with one bottom. Its triangular sides converge to one point at the top.

Prism and Pyramids are found in people’s everyday lives

The lateral area of a prism or pyramid is the area of its side excluding the base(s)

The slant height is the height from the top of the pyramid to the side of the pyramid.

Students will know… The formula to calculate the surface area of prism

and pyramids respectively The formula to calculate the lateral area of prism

and pyramids respectively Different prisms have different names depending

on their base. A prism with a circular base is called a cylinder

Students will be able to… Calculate the surface area of prisms and pyramids Calculate the lateral area of prisms and pyramids Calculate the area of the base of prisms or

pyramids Select appropriate tools to measure perimeter and

area of real objects

Use the appropriate units for perimeter and areaMATERIALS REQUIRED AND

KEY VOCABULARYMaterials required:Ruler, play dough, a glass, a note book, an unsharpened wooden pencil. Students will be using objects in the class but were also told they can bring objects from home whose area they wished to calculate. Worksheet on surface area of prisms and pyramids

Key Vocabulary: Prism, pyramid Surface area Lateral area Slant height Length, width, height Rectangular based prism, triangular based prism,

cylinder, rectangular based pyramid, triangular based pyramid.

SUBJECT COMPETENCIES: Competency 2 – Mathematical reasoning TIME STEP-BY-STEP PROCEDURE

15 minutes

50-55 minutes

HOOK: Greet students as they enter the class. Review information about circles from previous class. Review formula for circumference and area of a circle.

Inform students that the will be learning about prism and pyramids. Ask students if they can think of real life objects that take the form of a prism or pyramid. At this point I would show students some examples that I thought of. I would show them the glass, notebook and unsharpened pencil. As a class we would examine these objects noting if they had one base or two, what shapes were their bases, if they had a height, width and length. It is important at this time to allow students to note which sides of the objects we would consider, the exterior (surface) or interior.

INTRODUCTION/DEVELOPMENT:Students will be explained that the difference between calculating the area of a two dimensional figure and a three dimensional figure is that a three dimensional figure has a vertical height. Students will be explained the different types of prisms. They are to note the appropriate name of different prisms. For instance a prism with a circular base is called a cylinder. Students will be shown the formula to calculate the surface area of a prism. This includes the formula from lateral area and area of the

bases. Students will be shown how to use the formula through an example. Students will then be asked to calculate the surface area of one of the objects I brought in. (I will provide them with the measurements) Students will then be shown the formula for calculating the surface area of a pyramid. This includes the formula for lateral area and area of the base. At this point students should be explained the definition of slant height as it is used in the formula. Students will be shown how to use the formula through an example. Students will be given the dimensions of a real Egyptian pyramid and asked to calculate the surface area.

Students will take part in a tired activity based on interest. Give students instructions on activities so that they may choose. All the activities can be done either alone or in pairs.

Activity 1: Students will be given a worksheet to complete. The worksheet includes all types of prisms and pyramids.

Activity 2: Students will be given play dough and ask to form at least two solids (one prism and one pyramid) and calculate the surface area of both.

Activity 3: Students will calculate the surface area of at least two objects in the class or objects that they have brought from home.

ADAPTATIONS:Gifted students who have completed the activity early will be given a worksheet on computing the surface area of decomposable solids as extra work.

A student with Asperger’s can chose to work with a partner instead of in a large group.

Students with visual impairments will be encouraged to complete activity 2 as they will be able to make their objects as big as they need. To record the measurements of the object these students will use a ruler I have made for them where the lines correspond to 5cm.

CLOSURE/ACTIVITY:Ask some students to present the objects with which they

5-10 minutes

calculated surface area.Question students on their experience. Such questions can include:Did you enjoy the activity you choose? Out of the three activities which do you think has the most accurate measures?What methods did you use to get the most accurate measurements?Where their some objects in the classroom that did not have the shape of a regular prisms or pyramids?Where their some objects in the class that were composed of multiple prisms or pyramids?

ASSESSMENT:For students who have chosen activity 1 they will hand in the worksheet and calculations at the end of class. For students who have chosen activities 2 or 3 they must submit their calculations along with a sketch of the object with dimensions included.

LESSON PLAN REFLECTION What went well?

What were the weak points?

How can this lesson be adapted to be better?

Informal Assessment:

As mentioned above 80% of the lesson should be about engaging students and making sure they are acquiring the proper knowledge. The other 20% of the lesson is accounted for by reviewing at the beginning and end of class on information that students should already know or have learnt throughout the lesson. All students will receive an exam at the end of the unit to assess their knowledge of the unit. Also there are the tired activities throughout the lesson that allow the teacher to evaluate student’s progress.

These assessments is ongoing and formative; the teacher is constantly alert and checking that the students are following the lesson and that it is okay to proceed. Informal assessment will be of both oral and written tasks.

1. Oral Participation & Classroom AlertnessThe teacher develops a strategy of explaining the lesson that involves class participation. At the beginning of every class, there should be a short review of the topics learned in the previous lesson. For example, the teacher can remind the students about the shapes they have already learned, and ask for volunteers to draw them on the board. This checks that the students have the background knowledge to continue with the

next lesson. The teacher’s feedback to the students on these answers should not be discouraging, even if their answer is wrong, because we want them to feel confident to try answering again; and the purpose is not to evaluate individual students but make sure the class as a whole is ready to move on.

During the lesson, the teacher will explain the topic in such a way that does not just dictate but helps the students to come to the answers as a class. If the teacher notices some students starting to not pay attention then they can be gently asked if they know the answer. The teacher can ask probing questions such as: - If we know that the answer is an area, then what do the units have to be?- Where do those units come from? What two things do we have to have to multiply?

The teacher can keep in mind the ‘Know, Understand, Do’ (KUD) method of developing learning goals and so can base questions around these objectives:

- Do the students know the formula? Can they remember which formula goes to which shape?

- Do they understand where each number comes from, and why the formula makes sense?

- Can they apply them to different situations and shapes they haven’t seen before?

These questions don’t give the answer but help the teacher to see how much the students can deduce and how much they are actively thinking, not just repeating what they have already heard.

2. Paired and Group WorkHere the teacher can use their knowledge of their student’s personalities and abilities to group and pair them in the most beneficial ways, with the goal of having everyone participate. The teacher’s assessment involves systematic observation with the goal of monitoring each students involvement; and making sure that there is (as even as possible) participation within groups. The teacher can float between groups and make sure they are on the right track, check that they understand the concepts and vocabulary. The goal is for students to feel more confident to participate in small groups, even if they are not so confident at supplying answers and asking questions to the whole class; and that this more active participation will help them grasp the concepts better.

3. Classroom Written Activities and Exit CardsThese are still not formally graded, and so are used primary by the teacher to monitor progress and as formative assessment. The same ‘know-understand-do’ mental checklist can be used to ensure that the students are prepared to move onto the next lesson and that they have the background knowledge that will be built on in the next class.Exit cards should be questions that sum up the lesson and demonstrate the required understanding of the topic up to that point. For example at the end of Lesson 3, students should be able to find, given the dimensions, the area and perimeter of this ice cream cone. A correct solution would demonstrate knowledge of the formula, application to an unknown situation; mathematical reasoning (since you only need half the circle, and in 2D the middle line is not part of the perimeter). In the assessment, the teacher is looking at the steps the student took to solve these problems and checking for that understanding.

Formal Assessment:

Example of Summative Exam

Areas, Surface Areas, and Perimeters

Zombie Apocalypse Name: ____________________

Zombies are attacking Montreal and the Secondary 2 class must help to defend the school using their math skills. Be sure to show all your work!

1. As a preliminary defense, the principal decides to run a live wire around the school. She wants the wire to be woven through the gate surrounding the school. The gate surrounds the rectangular school yard, which has dimensions 350 x 250 m. How much wire does she need?

2. To stop the zombies in their tracks, the gym class decides to coat the school yard with super sticky tar. However, they need your help to figure out the area they would need to cover. Although the school yard measures 350 x 250 m, the school itself takes up 100 x 125 m. What is the remaining space that would have to be tarred?

3. The zombies are closing in. The wire and tar are working well but there are about 40 zombies that just aren’t slowing down. The school must work together to booby trap the windows and doors by rigging them with cylindrical garbage cans that will fall over the zombies, locking down their arms.

a) Ms. Looi estimates that the total length from shoulder to shoulder of any zombie should be no more than 55 cm. What must be the area of the base of the garbage can in order for the plan to work?

b) Assuming that the garbage can must also be at least 1 m in height for the zombie to be unable to get it off on his/her own, what must be the lateral area of the garbage can?

c) Just for fun, what would the total surface area of the garbage can be, not including the lid?

Zombie Attack!

For these questions, you’ll have to think fast and circle the correct answer to survive.

4. A zombie makes it past the garbage cans and comes after you. You must quickly pick a shield with the largest base area to defend yourself. Which do you choose?

a) a circular stool with radius 25 cm.

b) a rectangular textbook with dimensions 22 cm x 28 cm.

c) a square shelf with dimensions 25 cm x 25 cm.

d) a triangular sign with a height of 25 cm and a base of 25 cm.

5. You defend yourself and leave the zombie locked in a cupboard. You decide to mark it with a barred circle. If the front of the cupboard measures 1 m wide by 2 m high, what is the maximum radius of the circle you can make?

a) 0.5 m

b) 1 m

c) 1.5 m

d) 2 m

6. You hear helicopters overhead and run to the roof of the school, hoping to be lifted to safety. Unfortunately, so does everyone else. To choose who gets to go first, the pilot asks the following skill-testing question: Which has a greater perimeter? A square with sides 15 cm or an equilateral triangle with 19 cm sides?

a) The square.

b) The triangle.

c) Neither, the square and the triangle have the same perimeter.

Congratulations! You have been moved to the safe zone. For now...

Rubric:

Areas, Surface Areas, and PerimeterZombie Apocalypse

QUESTIONS POINTS TOTAL SCORE

Question # 1 +2 pt : Correctly chooses the perimeter formula to be used +2 pt : Correctly uses the given information in the formula to

5 points

obtain final answer.+1 pt: Correctly uses the correct units in the final solution

The following points will be deducted if :-3pt: The student did not show any work (solution steps) but gave the correct answer. -4pt: If the students explanation or solution steps does not correlate with work -- 1pt to 3pt: The student work is partially incorrect

Question # 2 +1 pt: Correctly chooses the correct formula to be used +3 pt: Correctly uses the given information in the formula to obtain final answer.+1 pt: Correctly uses the correct units in the final solution

The following points will be deducted from the total if: -3pt: The student did not show any work (solution steps) but gave the correct answer. -4pt: If the students explanation or solution steps does not correlate with work -- 1pt to 3pt: The student work is partially incorrect

5 points

Question #3 Part a)+2: The student correctly identifies the shape and correct formula to be used +1: Correctly uses the given information in the formula to obtain final answer.+1: Correctly uses the correct units in the final solution

Part b)+1: Correctly chooses the correct formula to be used+1: Correctly converts the meters given to centimeters +1: Correctly uses the given information in the formula to obtain final answer. +1: Correctly uses the correct units in the final solution

Part c) +1: Correctly chooses the correct formula to be used and realizes part a) and b) are to be used in this questions+2: Correctly uses the given information in the formula to obtain final answer. +1: Correctly uses the correct units in the final solution

12 points

The following points will be deducted from the total if: -3pt: The student did not show any work (solution steps) but gave the correct answer. -4pt: If the students explanation or solution steps does not correlate with work 0-1pt to 3pt: The student work is partially incorrect-1pt: if the area of the top cylinder is included when finding total surface area

Question #4 No partial marks are given for multiple choice questions 2 points

Question #5 No partial marks are given for multiple choice questions 2 points

Question #6 No partial marks are given for multiple choice questions 2 points

Total points 28 points

Example of correct solution:

Question 3

Part a) Find the radius of one of the bases: Since we are given the diameter, we divide it by 2 to obtain the radius.

Diameter = 55cmRadius = 55/2 = 27.5 cm

Find the area of the base. A = πr2A = π x 27.52A = π x 756.25 = 2375.83 cm2

Area of top and bottom = 2375.83 * 2 = 4751.66 cm2

Part b) Height = 1 m = 100 cm Lateral Surface Area = 2 πrh = 2 π * 27.5 *100 = 17278.76 cm2

Part c) Total surface area = Areas bottom (not including lid) + Lateral surface area = 2375.83 + 17278.76

= 19654.59 cm2