A30unitplan


 * //Section 1//**

//Introduction//

The formal introduction found in the Mathematics 30 curriculum states that, "The aim of the mathematics program is to graduate numerate individuals who value mathematics and appreciate its role in society" (A Curriculum Guide for the Secondary Level, 1996). Our goal as math teachers is to help students become engaged and interested in mathematics so that students can relate mathematical concepts to their own lives. Whether students learn to interpret quantitative information, estimate, perform calculations mentally, or develop an intuitive knowledge of measurement, math is being utilized daily in ways we may not recognize.

Throughout the //Polynomials and Rational Expressions// unit, students will learn to compute polynomials through various methods and will be able to demonstrate their ability to solve rational expressions. Students will be given the opportunity to become engaged in the classroom through various teaching instructions. They will also be evaluated and tested using various assessment methods as they learn to express their thinking processes while manipulating numbers and variables.

//Justification for the unit and real-life connections/examples//

Learning objective **C.9** states, "To solve and verify the solutions of quadratic equations involving rational algebraic expressions." This particular objective in the unit includes examples that relate to the real world. One example is: Joan drives 200 km at x km/hour. Franco then takes over, and drives 200 km at (x - 10) km/hour. The total time taken by the drivers is 9 hours. How fast did each drive? The idea is that rational algebraic expressions can be used to determine the speed and the amount of time it takes a driver to reach a certain destination. By performing the correct calculations, a student would be able to determine how fast each person was driving in this particular situation.

Students could be asked to search through reference books to find similar examples where these types of equations are used in other real-world situations. Reference books from other areas, such as commerce, administration, engineering, medical applications, and others could be utilized, as well as various mathematical texts.

Though most of the learning objectives don't seem to have real-life connections at this level, almost all carry significant components that need to be learnt if any further or more difficult math is to be done. For instance, learning objective C.5 relates to simplifying rational expressions involving opposites, C.6 relates to solving expressions with polynomial denominators, etc. These skills are the foundation to more difficult questions used extensively in future math classes; concepts such as calculating complex fractions, volumes, and calculus.

//Context (title, grade, student population)//

Mathematics A30 Concept C: Polynomials and Rational Expressions Grade 11 Student population of 800 (~25 in each class)

//Professional Development Goals/Targets (we want to make sure we cover...)//

Personal Goals:
 * To incorporate opportunities for experiental learning
 * To develop a lesson that incorporates technology
 * Develop unique assessment/evaluation strategies
 * Develop student projects whether it be a group project or individual report/reflection
 * Include interactive activities (i.e. the smartboard, concrete manipulatives such as algetiles etc.)
 * To instruct in different and creative ways so all students can understand and succeed

Goals for the unit:
 * We want to review with students how to factor polynomials by difference of squares, grouping, distribution etc. in order to build up prior knowledge and to check for understanding
 * Our goal is to teach students how to factor polynomials using various methods no matter the condition of the polynomial (i.e. factoring the sum/difference of cubes etc.)
 * To introduce to students useful theorems that will initiate student thought and understanding (the factor theorem and the remainder theorem)
 * Help students develop the abilities to simplify rational expressions using addition, subtraction, multiplication, and division
 * We want students to be able to solve and verify linear equations in one variable involving rational algebraic expressions
 * Finally, we want students to learn how to solve and verify the solutions of quadratic equations involving rational algebraic expressions


 * //Section 2//**

//Concept Devlopment (K-12)//

//Concept Web (apparently we do not have to include one)

Foundational and Learning Objectives//


 * Foundational Objectives**


 * To demonstrate ability in the addition, subtraction, multiplication, and division of rational expressions (10 03 01). Supported by learning objectives 1 to 7.
 * To demonstrate ability in solving equations involving rational expressions (10 03 02). Supported by learning objectives 8 and 9.

//Unit Plan Overview//


 * Specific topic/title:**
 * Review of Factoring (difference of squares, distribution, grouping etc.)
 * Factoring the difference of squares (of special polynomials)
 * Factoring the sum and difference of cubes
 * The Factor theorem
 * The Remainder theorem (to determine the remainder when a polynomial is divided by (x-r))
 * Simplifying rational expressions involving opposites and introduction to adding and subtracting rational expressions
 * Multiplying and Dividing rational expressions involving opposites
 * Solving linear equations in one variable involving rational algebraic expressions
 * Solving the solutions of quadratic equations involving rational algebraic expressions

Foundational Objectives: Learning Objectives:
 * Objectives (foundational and learning):**
 * To demonstrate ability in the addition, subtraction, multiplication, and division of rational expressions (10 03 01). Supported by learning objectives 1 to 7.
 * To demonstrate ability in solving equations involving rational expressions (10 03 02). Supported by learning objectivs 8 and 9.
 * **C.1** To factor the difference of squares of special polynomials.
 * **C.2** To factor the sum and difference of cubes.
 * **C.3** To factor polynomials using the factor theorem.
 * **C.4** To use the remainder theorem to determine the remainder when a polynomial is divided by (x-r).
 * **C.5** To simplify rational expressions involving opposites.
 * **C.6** To add and subtract rational expressions with polynomial denominators.
 * **C.7** To multiply and divide rational expressions involving opposites.
 * **C.8** To solve and verify linear equations in one variable involving rational algebraic expressions (including polynomial denominators).
 * **C.9** To solve and verify the solutions of quadratic equations involving rational algebraic expressions.


 * Major Activities/instructional strategies:** (we would fill this section in for each of our lessons but this is just a general overview)

Activities and instructional strategies will vary according to each lesson. Activities may include interactive games (i.e. smartboard, online websites), activities with manipulatives including "algetiles," or "magnetic" manipulatives.

Instructional strategies may include direct instruction (lecture), indirect instruction (high levels of student involvement), experiential learning (inductive, learner centered), independent study (individual student initiative, i.e. technology activities), and interactive instruction (discussion and sharing among peers).


 * Assessment strategies:**

Assessment strategies will vary according to each lesson. The types of assessments to be used are listed below.


 * Resources:**

Resources will vary and will be listed for each lesson being described.


 * //Section 3// (summaries of exactly how each of the following are incorporated into your plan)**

//Instructional Strategies//

Instructional strategies will vary according to each lesson. Instructional strategies will include methods of direct instruction (lecture), indirect instruction (high levels of student involvement), experiential learning (inductive, learner centered), independent study (individual student initiative, i.e. technology activities), and interactive instruction (discussion and sharing among peers).

//Assessment and Evaluation//

Types of assessment and evaluation will vary for each lesson (also depending on the chosen instructional strategy)

Students will be assessed and evaluated using a variety of strategies. Assessment tools include teacher checklists (for participation?), self/peer evaluations, tests (or quizzes), student reports, group work (possibly a group presentation), students working at the board, and homework checks.

For example, if students are working in pairs or groups, they may be asked to fill out an evaluation form showing how much they accomplished each class or how much time they spent on task. Tests and quizzes may address not only computational process, but also thinking processes used to solve those questions.

Assessing student knowledge can be a very difficult thing. Because every child is a unique learner, we want to incorporate a variety of assessment strategies in order to recognize the strengths of all students. Students are given the opportunity to share what they know in a number of different ways so that every individual can feel successful.

//Common Essential Learnings//

Use of: Communication (COM) - group presentations, peer evaluation, student/teacher talk Numeracy (NUM) - math assignments, in class discussion Critical and Creative Thinking (CCT) - student reports (problem solving) Technological Literacy (TL) - implemented technology activities (online), smartboard activities/reviews, recommend websites that they can explore at home. Personal & Social, Values & Skills (PSVS) - in class discussions, group work, addressing real-life problems relating to social issues. Independent Learning (IL) - reflective journals, in class/at home assignments

//Adaptive Dimension (what can we do for enrichment?)//

If students are engaging in an activity in groups, one way to simply adapt to every learner is to group together the stronger math students with the weaker math students. This way, the stronger math students can "teach" their peers, while the weaker math students can ask questions and gain a better understanding of the content. However, all students are learning from one another which makes this particular adaptation very beneficial.

For meeting the needs of weaker students, for some assignments/quizzes you may have them show you the process or how to solve a questions using manipulatives rather then having them write it out.

One other way to take care of your "top 1/3 students," is to include questions on a test or quiz that propose more of a challenge. Questions such as these would be included as bonus questions.

In the extention activities, teachers can always include readings or other worksheets that include more questions as well. This way students who finish an assignment early in class are still able to work and feel engaged.

//Curriculum Initiatives (Gender, Indian & Metis, etc//.)

In this particular math unit, there is no specific place to incorporate Indian and Metis content without it resembling tokenism. Rather, the classroom environment itself is where we want to recognize different student's identity and to reduce the stereotypes surrounding race and gender. In general, it is our policy that we recognize the uniqueness and importance of the Indian and Metis peoples in our society today. Saskatchewan Education recognizes that education programs must meet the needs of Indian and Metis peoples and that changes to existing programs are necessary if they are to benefit all students. As teachers, we want to provide quality education for all students and to continue our efforts so that equality of benefit or outcome may be achieved no matter if students are a different race or gender. Schools also want to decrease sex-role expectations and attitudes and to create an educational environment free of gender bias. We want to educate students through balanced material and strategies so that they can create positive views towards their peers. It is important that teachers create an environment free of bias so that all students can develop their abilities and talents to the fullest.