Principles of Mathematics, Grade 10 (Academic)

MPM2D

Principles of Mathematics, Grade 10 (Academic)

Course Description

This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Overall Course Expectations

A: Quadratic Relations of the Form y= ax2 + bx + c
  1. determine the basic properties of quadratic relations;
  2. relate transformations of the graph of y = x2 to the algebraic representation y = a (x – h)2 + k;
  3. solve quadratic equations and interpret the solutions with respect to the corresponding relations;
  4. solve problems involving quadratic relations.
B: Analytic Geometry
  1. model and solve problems involving the intersection of two straight lines;
  2. solve problems using analytic geometry involving properties of lines and line segments;
  3. verify geometric properties of triangles and quadrilaterals, using analytic geometry. Specific Expectations
C: Trigonometry
  1. use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
  2. solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
  3. solve problems involving acute triangles, using the sine law and the cosine law.

Course Outline

Unit 1-A Chapters 3&4
26 hours

Graphs of Quadratic and Factoring Algebraic Expressions

  • Determine the basic properties of quadratic relations
    • Collect data (investigation or secondary sources) that can be represented as a quadratic relation, graph it and draw a curve of best fit
    • Recognize y = ax2 + bx + c is a parabola and table of values yields a constant second difference
      • Key features of a parabola
      • Axis of symmetry
      • Coordinates of the vertex
      • y-intercept
      • Zeros
      • Max/min value
  • Compare the graphs of y = x2 and y = 2x and
    • determine the meaning of a negative and zero exponent
    • Solve quadratic equations and interpret the solutions with respect to the corresponding relations
    • Expand and simplify second-degree polynomial expressions
    • Factor polynomial expressions (common factoring, trinomials, and difference of squares)
    • Investigate connections between factors of a quadratic expression and the x-intercepts of the
      graph expressed in the form y = a(x-r) (x-s)
    • Express y = ax2 + bx + c in the form y = a(x-h)2 + k by completing the square
    • Graph y = ax2 + bx + c using a variety of methods
    • Solve quadratic equations using a variety of methods (factoring, quadratic formula)

Unit 2-A Chapters 5&6
28 hours

Applying Quadratic Models and Quadratic Equations

  • Solve problems involving quadratic relations
    • Determine zeros and max/min of a quadratic relation from its graph or equation
    • Solve problems arising from realistic situations
  • Relate transformations of the graph of y = x2 to the algebraic representation y = a(x-h)2 + k
    • Identify by investigation the effect of transformations to the graph of y = x2
    • Explain the roles of a, h, and k and identify key features
    • Sketch the graph of y = a(x-h)2 + k by applying
      transformations to the graph of y = x2
    • Write the equation, in the form of y = a(x-h)2 + k of a given graph

Unit 3-B Chapters 1&2
25 hours

Analytic Geometry

  • Model and solve problems involving the intersection of 2 straight lines
    • 2 linear equations with 2 variables using substitution or elimination
    • Solving problems described in words or represented by equations algebraically or graphically
  • Solve problems involving properties of line segments
    • Develop the formula for midpoint of a line segment and use it to solve problems
    • Develop the formula for length of a line segment and use it to solve problems
    • Develop the equation of a circle with center (0, 0)
    • Determine the radius/equation of circles
  • Verify properties of triangles and quadrilaterals Determine (by investigation) and verify characteristics and properties of geometric figures

Unit 4-C Chapters 7&8
26 hours

Trigonometry

  • Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity
    • Properties of similar triangles
    • Concepts of similarity and congruence
    • Solve problems involving similar triangles
  • Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean Theorem
  • Solve problems involving acute triangles, using the sine law and cosine law
    • Explore development of the sine and cosine law within acute triangles

ISP, Review and Final exam
5 hours

Total Hours: 110

Teacher and Learning Strategies

Strategies marked with “x” are used in the course.
Direct Instruction (teacher-led)xClass Activity (teacher facilitation)x
Direct Instruction (discussion possible)xExperiential learning (learn by doing)
Class Discussion (teacher facilitated)xWorksheets/Surveys
Small Group DiscussionxIndividual or Group Research
Partner Discussion/ConferencingxTeacher modelingx
1:1 Conferencing Teacher & Student Text-based modeling
Teacher reading to class Use of Computers / Internetx
Silent individual reading Use of video tape or audio materials
Group based reading Role Playing
Independent Work (teacher facilitation)xPresentationsx
Group Work (teacher facilitation) Guest Speaker / Interviews / Questions
BrainstormingField Trip

Assessment & Evaluation

Purpose
The primary purpose of assessment is to improve student learning. Assessment relates directly to the expectations for the course.

A variety of assessments for and as learning are conducted on a regular basis to allow ample opportunities for students to improve and ultimately demonstrate their full range of learning and in order for the teacher to gather information to provide feedback. Assessment tasks relate to the success criteria set out in lesson plans. Success criteria allow students to see what quality looks like.

Evaluation is the process of judging the quality of student work in relation to the achievement chart categories and criteria, and assigning a percentage grade to represent that quality. Evaluation is based on gathering evidence of student achievement through:

  • Products
  • Observations
  • Conversations

Assessment for Learning – we provide feedback and coaching
Assessment FOR Learning is the process of seeking and interpreting evidence for the use of learners and their teachers to decide where the learners are in their learning, where they need to go, and how best to go there.

Assessment as Learning – we help students monitor progress, set goals, reflect on their learning
Assessment AS Learning is the process of the explicit fostering of students’ capacity over time to be their own best assessors, but teachers need to start by presenting and modelling external, structured opportunities for students to assess themselves.

Assessment of Learning – we use assessments as ways of providing evaluative statements about the level of achievement of students
Assessment OF Learning is the assessment that becomes public and results in statements of symbols (marks/grades/levels of achievement) about how well students are learning. It often contributes to pivotal decisions that will affect students’ future.

Grading

  • The final grade is based on performance in 3 areas: products, observations, conversations.
  • 70% of the grade is based on evaluations conducted throughout the course.
  • 30% is based on a final evaluation.

Weighting of categories

  • Knowledge & Understanding – 25%
  • Thinking – 25%
  • Communication – 25%
  • Application – 25%
Assessment for Learning Assessment as Learning Assessment of Learning
Quizzes Journal Tests
TestsExit and Entrance CardsPresentations
Presentations KWL Chart Journals
Journals Self/Peer assessment Essays
Essays Feedback Logs Independent Study Assignment
Models Conferencing with teacherProjects
Projects 60-second think/self-evaluation of learningConferencing
Demonstrations Concept sun – individual brainstorm web, then teacher conversation
ConferencingFeedback Sandwich (good/bad/good news) did well, need improvement, future goal
Questioning Venn Diagram (2 circles overlapping: know, confused, don’t know)
Independent Study AssignmentBrainstorming
Art ExhibitsIndependent work
Researching
Reading Aloud
Problem Solving (process focused)
Debates
Work Sheets
Role Playing
Direct Instruction
Class Discussion
Small Group Discussion
Pair/Share
Teacher reading to class
Silent individual reading
Group based reading

Program Planning Considerations

Instructional Approaches
Students come to secondary school with a natural curiosity developed throughout the elementary grades. They also bring with them individual interests and abilities as well as diverse personal and cultural experiences, all of which have an impact on their prior knowledge about science, technology, the environment, and the world they live in. Effective instructional approaches and learning activities draw on students’ prior knowledge, capture their interest, and encourage meaningful practice both inside and outside the classroom. Students at Leslie Academy will be engaged when they are able to see the connection between the scientific concepts they are learning and their application in the world
around them and in real-life situations.

Health and Safety in Science
This course will provide the reading and analytical skills for the student to be able to explore the variety of concepts relating to health and safety in the workplace. The teachers at Maple Ridge Academy will also take the necessary steps to ensure that students have the knowledge and skills for safe participation in Science activities.

Program Considerations for English Language Learner
English language learners (students who are learning English as a second or additional language in English-language schools) bring a rich diversity of background knowledge and experience to the classroom. These students’ linguistic and cultural backgrounds not only support their learning in their new environment but also become a cultural asset in the classroom community. Teachers at Maple Ridge Academy will find positive ways to incorporate this diversity into their instructional programs and into the classroom environment.

Environmental Education
Environmental education is an approach to critical thinking, citizenship, and personal responsibility. It is a context that can enrich and enliven education in all subject areas, and offer students the opportunity to develop a deeper connection with themselves, their role in society, and their interdependence on one another and the earth’s natural systems. The teacher at Leslie Academy will emphasize on relating science to technology, society, and the environment (STSE) within the Ontario curriculum to provide meaningful contexts for applying what has been learned about the environment.

Antidiscrimination Education
Diverse groups of people involved in scientific activities and careers will be explored in case studies. The examples used to illustrate knowledge and skills, and the practical applications and topics that students explore as part of the learning process will vary so that they appeal to both boys and girls and relate to students’ diverse backgrounds, interests, and experiences. It will include opportunities for students at Maple Ridge Academy to describe, study, or research how women and men from a variety of backgrounds, including Aboriginal peoples, have contributed to science, used science to solve problems in their daily life and work, or been affected by scientific processes or phenomena.

Critical Thinking and Critical Literacy in Science
At Leslie Academy critical thinking includes skills such as questioning, predicting, hypothesizing, analyzing, synthesizing, examining opinions, identifying values and issues, detecting bias, and distinguishing between alternatives. Students will use critical thinking skills in science when they assess, analyze, and/or evaluate the impact of something on society and the environment; when they form an opinion about something and support that opinion with logical reasons; or when they create personal plans of action with regard to making a difference. The teacher will educate the student about critical literacy as the capacity for a particular type of critical thinking that involves looking beyond the literal meaning of a text to determine what is present and what is missing, in order to analyze and evaluate the text’s complete meaning and the author’s intent.

Literacy, Mathematical Literacy, and Investigation (Inquiry/Research) Skills
When reading in science, students will use a different set of skills than they do when reading fiction or general non-fiction. They will need to develop / understand vocabulary and terminology that are unique to science, and must be able to interpret symbols, charts, diagrams, and graphs. In addition, they will work on their ability to make sense of the organization of science textbooks, scientific journals, and research papers. Teachers at Leslie Academy will model and teach the strategies that support learning to read while students are reading to learn in science. Writing in science employs special forms and therefore also requires specific and focused learning opportunities. Students will use writing skills to describe and explain their observations, to support the process of critically analyzing information in both informal and formal contexts, and to present their findings in written, graphic, and multimedia forms. Students are expected to use appropriate and correct terminology, and are encouraged to use language with care and precision in order to communicate effectively.

The Role of Information and Communications Technology in Science
Students at Leslie Academy will develop transferable skills through their experience with word processing, internet research, presentation software, and telecommunication tools, as would be expected in any environment. Technology will also be used for simulations, for instance, when field
studies on a particular topic are not feasible or dissections are not acceptable due to various possible reasons.

The Ontario Skills Passport and Essential Skills
The skills described in the OSP are the Essential Skills that the Government of Canada and other national and international agencies have identified and validated, through extensive research, as the skills needed for work, learning, and life. These Essential Skills provide the foundation for learning all other skills and enable people to evolve with their jobs and adapt to workplace change. For further information on the OSP and the Essential Skills, visit http://skills.edu.gov.on.ca.

Career Education
Ongoing scientific discoveries and innovations coupled with rapidly evolving technologies have resulted in an exciting environment in which creativity and innovation thrive, bringing about new career opportunities. Throughout the course, courses, students at Leslie Academy will develop a variety of important capabilities, including the ability to identify issues, conduct research, carry out experiments, solve problems, present results, and work on projects both independently and as a team. Students will also be given opportunities to explore various careers related to the areas of science under study and to research the education and training required for these careers.

Pathways and Programs
At Leslie Academy Islamic school, the teachers will partner with community members with scientific professions to help develop a pathway for student interested in acquiring academic knowledge and skills important to particular industry sectors and required for success in the workplace and postsecondary education, including apprenticeship. Science courses may also be combined with cooperative education credits to provide the workplace experience required for some programs. In addition, the Vice Principals and Guidance councillors assist in student services for post-secondary planning by holding formal sessions on College and University options for parents and guardians.

Planning Science Programs for Students with Special Education Needs *currently, there are no students enrolled at Maple Ridge Academy with Special Needs.

Cooperative Education and other forms of Experimental Learning *currently not offered at Maple Ridge Academy.

Resources

In addition to the lessons and activities found in this course, students are also referred to additional books, handouts, worksheets and websites. It is the students’ responsibility to keep track of any changes/updates on the course webpage, including calendar/homework/handouts etc. The course webpage can be accessed anytime by following the link that will be provided. In case of webpage accessibility issues the student must notify the teacher in order to get assistance. Textbook

  1. Physics 12. Nelson Education Ltd., 2010 Internet Sources:

  2. http://www.interactivephysics.com (A source of a variety of Physics simulations).

  3. https://phet.colorado.edu/ (A source of a variety of Physics simulations).

  4. http://www.disctronics.co.uk/dvd/dvdspecs/dvdphys.htm (Describes differences between CDs and DVDs)

  5. http://atschool.eduweb.co.uk/rmext04/92andwed/pf_quant.html (Resource explaining oddities of quantum, particle and special relativity physics)

  6. http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html (Simulation of the interference of electrons or larger particles)

  7. http://www-ed.fnal.gov/projects/labyrinth/games/index1.html (Games and simulations to demonstrate different concepts of quantum physics)

  8. http://www.howstuffworks.com/relativity.htm (A resource describing special relativity)

  9. http://www.elibrary.com (A site containing a wide variety of recent newspaper and magazine articles)