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Course Profile
(for a locally developed course)
Essential Mathematics, Grade 9
Course Overview
Course Profiles are professional development materials designed to help teachers implement the new Grade 9 secondary school curriculum. These materials were created by writing partnerships of school boards and subject associations. The development of these resources was funded by the Ontario Ministry of Education. This document reflects the views of the developers and not necessarily those of the Ministry. Permission is given to reproduce these materials for any purpose except profit. Teachers are also encouraged to amend, revise, edit, cut, paste, and otherwise adapt this material for educational purposes.
Any references in this document to particular commercial resources, learning materials, equipment, or technology reflect only the opinions of the writers of this sample Course Profile, and do not reflect any official endorsement by the Ministry of Education or by the Partnership of School Boards that supported the production of the document.
ã Queen’s Printer for Ontario
Public and Catholic School Board Writing Team – Essential Mathematics
John Dallan, Lead Writer, Upper Grand District School Board
Bernie McGarry, Halton District School Board
Tina Noel, Renfrew County Catholic District School Board
Rob Samson, Simcoe Muskoka Catholic District School Board
Shirley Scott, District School Board of Niagara
Emilia Veltri, Lakehead Public District School Board
Jim Vincent, Peel District School Board
Lead Board
Halton District Secondary School Board
Kit Rankin
Susan Orchard
Larry Zavitz
Kelly Terry
With assistance from:
The writing team for the Applied and Academic Grade 9 Public Course Profile
|
The new Ontario
Secondary Schools, Grades 9 to 12: Program and Diploma Requirements (OSS),
1999 enables school boards to develop three local compulsory-credit courses, one
in each of the following subjects: English, Mathematics, and Science. To
provide a model of how these courses could be developed, the Ministry of
Education has funded the following sample Course Profiles: “Essential
English,” “Essential Mathematics,” and “Essential Science.” The Guide to Locally Developed Courses, Grades 9 and 10: Approval Requirements and Procedures provides information to assist school boards in preparing their requests to the Ministry of Education for approval of their own Grade 9 locally developed courses, to be offered in the 1999-2000 school year, under OSS. The document is available on the ministry’s web site at http://www.edu.gov.on.ca. |
Course Overview (for a locally developed course)
Essential Mathematics, Grade 9
School:
Department: Mathematics
District:
Course Title: Essential Mathematics
Grade: 9
Ministry Course Code:
Credit Value: 1.0
This course provides students who have experienced significant difficulties in previous Mathematics courses an opportunity to obtain sufficient background and skill development to prepare them for Grade 11 and 12 Workplace Preparation courses. Whenever possible, ideas will be presented in a real-life context, providing students with the opportunity to explore, organize, interpret, and use mathematical models to solve problems. Technology and manipulative materials will be used wherever appropriate. Assessment and evaluation will be done using a wide variety of strategies.
|
Unit 1 |
Making Sense
of Data |
28 hours |
|
Unit 2 |
Applying Ratio
and Rate |
18 hours |
|
Unit 3 |
Investigating
Two-Dimensional Figures |
14 hours |
|
Unit 4 |
Investigating
the Marketplace |
18 hours |
|
Unit 5 |
Exploring
Geometric Relationships |
8 hours |
|
Unit 6 |
Investigating
Three-Dimensional Figures |
14 hours |
|
Unit 7 |
Summative
Assessment Activities |
10 hours |
Time: 28 hours
Students develop an understanding of data analysis as a powerful tool for decision-making. Students are involved in activities to collect, organize and display data from primary and secondary sources. There are many contextual problems presented in which students construct, read, and interpret tables, charts, and graphs and select appropriate methods for displaying data from real-world situations. Points of emphasis include identifying patterns and relationships, summarizing trends, making predictions, and communicating observations. Through the use of tables, charts, mean line of best fit, and pattern descriptions, students conduct investigations, with and without technology, to verify or refute their own conjectures.
Specific
Expectations: all those from the
Relationship Strand as identified in the activities and some others from the
Number Sense Strand
Time: 18 hours
Students explore ratio and rate in real-life contexts. They apply proportional reasoning through investigations in real-life contexts to solve problems related to measurement, geometry, and data management. Students build on and extend their understanding of fractions to include ratios, decimals, proportions, and percent. Students use manipulative materials, diagrams, charts, and drawings to gain a greater understanding of concepts such as scale drawings, unit pricing, and sampling. Students develop the facility to translate between and among equivalent numerical forms choosing the representation to best fit the context of the problem. Opportunities to practise the skills of estimation and judging the reasonableness of an answer are provided throughout the unit.
Specific Expectations: all those from the Number Sense Strand as identified in the activities and some others from the Relationship Strand
Time: 14 hours
Students are engaged in a variety of activities dealing with two-dimensional geometry that allows them to solve measurement problems in real-life contexts. Through the use of concrete materials students develop and apply formulas. They select appropriate tools that allow them to measure to the degree of accuracy required. Concrete materials, drawings, and technology are used to investigate the effect that varying one dimension has on perimeter and area. Opportunities are also given to explore geometric properties and optimal values of various measurements of two-dimensional figures. Students communicate their findings and apply them to identify and solve familiar problems. The Pythagorean theorem is developed through the use of concrete materials and is used to solve simple problems. Students continue to develop skills for estimation and judging the reasonableness of an answer.
Specific Expectations: all those from the
Measurement and Geometry Strand as identified in the activities and some others
from the other Strands
Time: 18 hours
Students are involved in various investigations and
activities that allow them to use their knowledge of ratios and rates to
understand and apply percent. They illustrate the meaning of percent and solve
simple contextual problems. The marketplace is rich with applications as well
as opportunities to use rates, ratios, and percents to solve problems that increase
student awareness as consumers and decision-makers. Some activities provide
opportunities to use previously developed methodologies and strategies for
investigations. Technology is used to aid in the analysis of data. Students are
encouraged to use mental mathematics and estimation to ensure that their
calculations, use of technology, and problem-solving strategies produce
reasonable results.
Specific Expectations: all those from the Number Sense Strand as identified in the activities and some other from the Relationship Strand
Time: 8 hours
Students use concrete materials, diagrams, drawings and dynamic geometric software to develop their spatial sense. Students explore geometric patterns and use appropriate mathematical language in identifying and applying geometric concepts to gain a better understanding of geometric relationships. Investigations include those related to angle properties of parallel lines and two-dimensional figures. Through the use of the tools of dynamic geometry software, students construct geometric designs, explore and solve simple problems and then clearly explain the use of geometric properties in constructions.
Specific Expectations: all those from the Measurement and Geometry Strand as identified in the activities and some other from the other Strands
Time: 14 hours
Students engage in a variety of activities dealing with three-dimensional geometry that allows them to solve measurement problems in real-life contexts. With or without the aid of technology, students construct three-dimensional models. Through the use of concrete materials, drawings, and technology, students investigate the effect that varying one dimension has on surface area and volume. They also investigate optimal values of various measurements of three-dimensional figures. Students communicate their findings and apply them to identify and solve problems in familiar settings.
Specific Expectations: all those from the Measurement and Geometry Strand as identified in the activities and some others from the other Strands
Time: 10 hours
This unit models a final assessment in Grade 9 Mathematics. Individual and group performance skills are assessed using traditional and performance-based tasks, over a period of several days. Thirty per cent of the final evaluation is based on this summative unit, which includes performance tasks and pencil and paper tests.
To address the particular needs of students, assessment activities are paired so that students have more than one opportunity to demonstrate their level of understanding of course materials. That is, two similar evaluation tools may be administered consecutively so students can focus on key expectations. This allows students to gain a better understanding of the expectations of a summative assessment and gain confidence in their abilities.
It is suggested that the form and substance of this summative assessment unit be shared with students, their parents, resource teachers, and other support staff near the beginning of the course, so that each student’s energies can be directed towards acquisition of the required skills and knowledge.
In this summative assessment unit, students demonstrate their achievement of the expectations of the course. They do this by demonstrating their abilities to solve problems, which require them to:
· model appropriate strategies used in investigations;
· gather, organize, and display data for a purpose;
· decide, with awareness, what is important and what can be ignored within a problem;
· communicate reasoning and results;
· use technology as a tool for enhancing their learning;
· carry out paper and pencil routines.
· Skills in context
Students who have yet to master the ability to punctuate are not stopped from the experience of reading a book or writing a poem. Similarly, students who have yet mastered basic arithmetic skills should not be denied the opportunity to experience mathematics in real contexts, gain some understanding of its power, and be given opportunities to engage in the joy of discovery. Within these broader experiences, students also have opportunities to further develop key numeric skills.
· Student as learner
A primary goal of this course is to expand and develop students' knowledge and ability to apply mathematical concepts in real life applications. It should foster confidence in their ability to do mathematics. Students arrive in the classroom from varied backgrounds with a wide range of experiences and for many, with limited success in mathematics. Attention must be given to both cognitive and affective issues. Academic weaknesses may be centred in a specific area, but in many cases these are broad-based and to low self-esteem and other attitudinal concerns. Keeping this in mind, it is important to structure the program and classroom routines to strengthen common weaknesses so that learning may take place.
· Learning environments
Students require an appropriate or reasonable length of time and varied experiences to come to understand mathematical concepts. A climate that actively involves students in doing mathematics is beneficial. Along with opportunities for skills development, particular attention might be given to providing opportunities for students to be engaged in explorations, investigations and instances for them to communicate their understanding. By encouraging students to justify and clarify their thinking and to be open to opposing opinions, students foster genuine respect for another's point of view.