Unit Plan

EDCP 342A Unit planning: Rationale and overview for planning a 3 to 4 week unit of work in secondary school mathematics

Your name: Brianna Ball
School, grade & course: Lord Byng Secondary School, Math 9

Topic of unit: Polynomials

Preplanning questions:

(1) Why do we teach this unit to secondary school students?  Polynomials are important to learn because they are used frequently in everyday life. They are incredibly useful for modeling real life scenarios and studying patterns. Some people use polynomials in their heads every day without even realizing it, while others do it more consciously. For example, we often use polynomials in our heads when shopping to calculate total costs. Some careers obviously require using polynomials. Engineers, economists, and medical researchers use polynomials to model real life scenarios. However, non-STEM careers can involve the use of polynomials too. For example, a taxi driver may want to know how many miles they have to drive to earn a certain amount of money. Calculating this would require the use of a polynomial. Polynomials are included in the curriculum because they are among the simplest, most important, and most commonly used functions. They are helpful as a stepping-stone to introduce students to talking about simple functions before moving on to more complex functions.

(2) A mathematics project connected to this unit The project for this unit will be an interior design project. Students will be asked to design a bedroom and be given a list of furniture that must be included in the design. The students’ task will be to decide on the relative size of each item and then to create a scale model for each item using graph paper. They will also have to decide on a relative size and shape for the bedroom and draw it on graph paper. They will then cut out the furniture and arrange it in the room. The next task will be to calculate the area of each piece of furniture and the area of the room as well as the area not covered by furniture. The connection between this project and polynomials will be that the sizes of the items will all be relative and thus will be represented by polynomials. The students will be given a sheet with instructions about the sizing of the items. For example, “the bed must be twice as long as it is wide, with the width being 2x”. Thus, this project will require the students to perform various types of polynomial operations. The aim of this project will be to get students to work with polynomials but it will require deeper thinking about them since they will not just be given a series of equations to solve. They will actually have to produce the equations themselves and figure out what operations they need to perform to find the correct answers. The students will be assessed based on their ability to: ·      Create a bedroom and furniture that meets the criteria outlined in the instructions (i.e. a bed with a length twice as long as its width, etc.). Doing so will require finding polynomial expressions to represent the various dimensions of the room and furniture. ·      Use the appropriate polynomial operations to calculate the area of the room and of the furniture. The purpose of this assignment is to get students thinking about polynomials in a contextualized way and to demonstrate that they have a deeper understanding of polynomial operations than could be demonstrated by basic computational questions.

(3) Assessment and evaluation The formative assessment for this unit will be done informally/observationally and more formally. It will be done observationally through monitoring of students as they complete class work such as practice questions. It will be done formally through the use of exit slips. The exit slips will be given at the end of a lesson to check if students have understood the day’s lesson. If there are significant problems with comprehension, these issues can be addressed in the next class before attempting to build on that knowledge. There will also be a mid-unit quiz as a formative assessment to check that the first half of the material has been understood before moving on to the second half. It will be explicitly communicated to students that this quiz is low stakes and is not intended to cause stress but rather to see where they are at and where they need to go. The summative assessment for this unit will be from the project and the test. While the test will be useful to check that the learning goals have been achieved, the assessment of the project will be useful in checking for a deeper understanding of the material outside of a test environment which can be stressful for some students.

Elements of your unit plan:

Lesson	Topic
1	Defining Polynomials
2	Modeling Polynomials with Algebra Tiles*
3	Adding and Subtracting Polynomials*
4	Practice/Extension, Review, and Quiz
5	Multiplying Polynomials*
6	Dividing Polynomials
7	Start Project
8	Work Period (Project, Review, Ask questions, etc.)
9	Unit Review
10	Unit Test

LESSON PLAN #1

*This lesson includes elements of art and mathematics

Subject: Math 9	Duration: 80 minutes
Lesson Topic	Modeling Polynomials with Algebra Tiles

Big Ideas	The principles and process underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.
Curricular Competencies	Model mathematics in contextualized experiences Visualize to explore mathematical concepts Represent mathematical ideas in concrete, pictorial, and symbolic forms
Content/Learning Objectives	Students will learn how to represent polynomials visually through the use of algebra tiles. They will create their own set of algebra tiles that they will be able to use for future lessons.

Materials and Equipment Needed for this Lesson

Construction paper and pencil crayons for making algebra tiles

Lesson Stages	Learning Activities	Time Allotted
Introduction	Students will be asked to recall their learning from the previous lesson. They should be able to recall the meanings of certain key terms such as: variable, term, coefficient, polynomial, monomial, and degree	5 minutes
Presentation	Students will be introduced to algebra tiles as a form of representation for polynomials. As a group, we will determine what kinds of tiles we will be needing if we want to be able to represent the various types of polynomials they have encountered. We will also discuss what these tiles should look like.	15 minutes
Individual Practice	Students will be given the opportunity to construct their own set of algebra tiles. Based on the discussion, they should be able to figure out what kinds of tiles they will need to create and what those tiles should look like. They will be encouraged to exercise creativity in creating and decorating their tiles but there should be logic behind how they decide to represent the various terms. They will also be asked to create a legend that demonstrates what each tile represents.  After students finish constructing their algebra tiles, they will be assembled into groups of four and each group will be given a list of four polynomials. Each group member will have to represent one of the polynomials using their tiles. The group members should be encouraged to collaborate and discuss how each of the polynomials should be represented.	50 minutes
Closure	After each student has successfully represented their polynomial, the class will reassemble as a group. We will discuss how algebra tiles demonstrate why like terms can be added or subtracted but unlike terms cannot. This will help to prepare the students for the next lesson, which will be on adding and subtracting polynomials.	10 minutes

Assessment/Evaluation of Students’ Learning

The assessment of the lesson will be formative. As an informal form of assessment, the teacher will walk around the room and monitor the students as they construct their algebra tiles and as they work on the representation of their polynomials. The students will also be marked on their construction of the algebra tiles. They will be marked based on whether or not they create a set of tiles that can be used to accurately represent polynomial equations. They will also be marked based on the logic they used when deciding on the representation of the various terms.

LESSON PLAN #2

*This lesson includes "telling only what is arbitrary and having students work on what is necessary"

Subject: Math 9	Duration: 80 minutes
Lesson Topic	Adding and Subtracting Polynomials

Big Ideas	The principles and process underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.
Curricular Competencies	Develop, demonstrate, and apply mathematical thinking through play, inquiry, and problem solving Represent mathematical ideas in concrete, pictorial, and symbolic forms
Content/Learning Objectives	Students will learn how to add and subtract polynomial expressions. They will also learn how to model this addition and subtraction using algebra tiles.

Materials and Equipment Needed for this Lesson

Index cards, Exit slips

Lesson Stages	Learning Activities	Time Allotted
Introduction	Students will be asked to bring out their algebra tiles from the previous lesson. The teacher will review the end of the last lesson by asking the students to recall the rules about combining like/unlike terms.	10 minutes
Practice	The students will then be given a set of problems involving the addition and subtraction of polynomials. Working in small groups, the students will use their polynomials tiles to figure out the rules for adding and subtracting polynomials and answer the practice problems. Each group will be asked to come up with a list of rules for adding and subtracting polynomials.	30 minutes
Activity	To practice adding and subtracting polynomials, the students will play a game. Each student will come up with a polynomial expression and write it on an index card. The teacher will then play some music and ask the students to roam around the room. When the music stops, each student will have to find a partner with a different polynomial. Then, the teacher will either call out addition or subtraction. The students will have to work together to use that operation to put their polynomials together. The students will share their results and then the music will start again.	30 minutes
Closure	The lesson will end with the students completing an exit slip. The exit slip will contain a few basic problems that the students should be able to answer if they understood the day’s lesson.	10 minutes

Assessment/Evaluation of Students’ Learning

Formative assessment will take place while the students are creating their rules for adding and subtracting polynomials. During this time, the teacher will walk around the room and make sure the students are on the right track, providing hints when needed. Formative assessment will also take place during the game, as students will be required to share their answers. Finally, a more formal formative assessment will take place in the form of the exit slips to assess individual students’ level of comprehension.

LESSON PLAN #3

*This lesson includes “open-ended problem solving in groups at vertical erasable surfaces”

Subject: Math 9	Duration: 80 minutes
Lesson Topic	Multiplying Polynomials

Big Ideas	The principles and process underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.
Curricular Competencies	Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving Use mathematical vocabulary and language to contribute to mathematical discussions
Content/Learning Objectives	Students will learn how to multiply polynomial expressions.

Materials and Equipment Needed for this Lesson

Practice question sheets, vertical erasable surfaces/markers to write on surfaces

Lesson Stages	Learning Activities	Time Allotted
Introduction	Students will be asked to recall the distributive law. They will complete a few basic examples applying this property using integers.	10 minutes
Practice	Students will be told that the distributive law can be used to multiply polynomials as well. Students will be shown an example and then will have the opportunity to try a few examples themselves. Students who feel confident in their answers may wish to come up to the board and demonstrate their thinking.	15 minutes
Activity	The teacher will post polynomial multiplication problems around the classroom, each accompanied by a vertical erasable surface. Students will rotate around the classroom in small groups. They will have to solve the polynomial multiplication problem as a group on the vertical erasable surface. When the students believe they have the correct answer, they will record it on the back of the problem sheet and move onto the next problem.	40 minutes
Closure	The teacher will check the back of problem sheets and review the students’ solutions. If there are questions that many of the students got wrong, then the teacher will review the solutions to these problems with the class.	15 minutes

Assessment/Evaluation of Students’ Learning

Students will be assessed formatively as the teacher wanders around the room while they work on the activity. The teacher will assess the students’ understanding by looking at their work on the vertical erasable surfaces and by listening to the mathematical language they use as they discuss the problems with their fellow group members. The teacher will be able to gain a general understanding of the class’s level of comprehension by studying their answers recorded on the back of the problem sheets.