Principles of Mathematics, MPM1D , Grade 9, Academic
Policy Document: The Ontario Curriculum, Grades 9 and 10, Mathematics, 2005.
Prerequisite: Grade 8 Mathematics
This course enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Units: Titles and Times
|Unit 1||Number Sense and Algebra||25 hours|
|Unit 2||Linear Relations and Equations||25 hours|
|Unit 3||Analytic Geometry and Investigating Relationship||25 hours|
|Unit 4||Measurement and Geometry||25 hours|
|Unit 5||ISU Course Summative||10 hours|
Outline of Course Content: Throughout this course students will:
- develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
- develop and apply reasoning skills (e.g., recognition of relationships, generalization through inductive reasoning, use of counter-examples) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
- demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
- select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
- make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
- create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
- Communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
Teaching and Learning Strategies
Teachers will bring enthusiasm and varied teaching and assessment approaches to the classroom, addressing individual students’ needs and ensuring sound learning opportunities for every student. The activities offered should enable students to relate and apply these concepts to the social, environmental, and economical conditions and concerns of the world in which they live. Opportunities to relate knowledge and skills to these wider contexts will motivate students to learn in a meaningful way and to become life-long learners. The Mathematics curriculum is based on the premise that all students can be successful learners. One of the keys to student success in mastering language skills is high-quality instruction. Teachers who provide quality instruction respect students’ strengths and address their learning needs, using assessment information to plan instruction. They clarify the purpose for learning, help students activate prior knowledge, and differentiate instruction for individual students and small groups according to need. Teachers explicitly teach and model learning strategies and encourage students to talk through their thinking and learning processes. They also provide many opportunities for students to practise and apply their developing knowledge and skills. Effective teaching approaches involve students in the use of higher-level thinking skills and encourage them to look beyond the literal meaning of texts and to think about fairness, equity, social justice, and citizenship in a global society. Online & Offline Components The design of this course is intended to offer a rich balance between online and offline elements. The following is a summary of the course components and their delivery format. Please refer to the individual unit outlines for specific details. Course content & instruction: online; Communication between teacher and students: online & offline Collaboration between students: online; Assessment & evaluation: online & offline; Practise exercises, textbook work, readings etc: offline
Assessment & Evaluation for Student Achievement
The primary purpose of assessment and evaluation is to improve student learning. Information gathered through assessment helps teachers to determine students’ strengths and weaknesses in their achievement of the curriculum expectations in each course. This information also serves to guide teachers in adapting curriculum and instructional approaches to students’ needs and in assessing the overall effectiveness of programs and classroom practices. As part of assessment, teachers provide students with descriptive feedback that guides their efforts towards improvement. Evaluation refers to the process of judging the quality of student work on the basis of established criteria, and assigning a value to represent that quality. All curriculum expectations must be accounted for in instruction, but evaluation focuses on students’ achievement of the overall expectations. A students’ achievement of the overall expectations is evaluated on the basis of his or her achievement of related specific expectations. Teachers will use their professional judgement to determine which specific expectations should be used to evaluate achievement of overall expectations, and which ones will be covered in instruction and assessment but not necessarily evaluated. In order to ensure that assessment and evaluation are valid and reliable, and that they lead to the improvement of student learning, teachers must use assessment and evaluation strategies that:
- Address both what students learn and how well they learn;
- Are based both on the categories of knowledge and skills and on the achievement level descriptions given in the achievement chart
- Are varied in nature, administered over a period of time, and designed to provide opportunities for students to demonstrate the full range of their learning;
- Are appropriate for the learning activities used, the purposes of instruction, and the needs and experiences of the students;
- Are fair to all students;
- Accommodate students with special education needs, consistent with the strategies outlined in their Individual Education Plan;
- Accommodate the needs of students who are learning the language of instruction;
- Ensure that each student is given clear directions for improvement;
- Promote students’ ability to assess their own learning and to set specific goals
- Include the use of samples of students’ work that provide evidence of their achievement;
- Are communicated clearly to students and parents at the beginning of the school year and at other appropriate points throughout the school year.
The achievement chart for science outlines four categories of knowledge and skills. They include; knowledge and understanding, thinking and investigation, communication and application. Teachers will ensure that student work is assessed and/or evaluated in a balanced manner with respect to the four categories, and that achievement of particular expectations is considered within the appropriate categories. A final grade is recorded for this course, and a credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade for this course will be determined as follows:
- Seventy percent of the grade will be based on evaluations conducted throughout the course. This portion of the grade should reflect the student’s most consistent level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement. The 70% will be distributed in the following achievement chart categories: 20% knowledge and understanding, 20% application, 15% communication, 15% thinking. Student work will be assessed and evaluated in a balanced manner with respect to the four categories within each unit throughout the course.
- Thirty percent of the grade will be based on a final evaluation in the form of a written examination and a media and oral portfolio completed towards the end of the course.
Accommodations All students can succeed. Some students are able, with certain accommodations, to participate in the regular course curriculum and to demonstrate learning independently. Accommodations allow access to the course without any changes to the knowledge and skills the student is expected to demonstrate. The accommodations required to facilitate the student’s learning must be identified in his or her Individual Education Plan (IEP). Instruction based on principles of universal design and differentiated instruction focuses on the provision of accommodations to meet the diverse needs of learners. Examples of accommodations (but not limited to) include:
- Adjustment and or extension of time required to complete assignments or summative tasks
- Providing alternative assignments or summative tasks
- Use of scribes and/or other assistive technologies
- Simplifying the language of instruction
Teachers will bring additional resources and teaching materials that provide a rich and diverse learning environment.