MAP4C – Foundations for College Mathematics Grade 12

Course Type: University & College Preparation

Credit: 1.0

Ontario Curriculum: MAP4C – Foundations for College Mathematics – Grade 12

MAP4C Prerequisite: MBF3C, Foundations for College Mathematics, Grade 11, College Preparation or MCF3M, Functions and Applications, Grade 11, University / College Preparation

MAP4C course enables students to broaden their understanding of real-world applications of mathematics. Students in MAP4C will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning accommodation; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This MAP4C course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades.

MAP4C Course Outline

UNIT 1: GEOMETRY AND TRIGONOMETRY
In this unit students will perform required conversions between the imperial system and the metric system. Solve application problems involving the areas of rectangles, triangles, and circles, and of related composite shapes and solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite figures. In addition, recognize and explain the significance of optimal perimeter, area, surface area, and volume in various applications. Then in trigonometry students will solve application problems by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios, and of acute triangles using the sine law and the cosine law. Followed by making connections between primary trigonometric ratios of obtuse angles and of acute angles. Determine the values of the sine, cosine, and tangent of obtuse angles. Solve problems involving oblique triangles, using the sine law and cosine law. Gather, interpret, and describe information about applications of trigonometry in occupations, and about college programs that explore these applications.

UNIT 2: DATA MANAGEMENT
This unit is designed to help students analyze data and trends. They are to distinguish situations requiring one-variable and two-variable data analysis, describe the associated numerical summaries and graphical summaries, and recognize questions that each type of analysis addresses. Also, describe characteristics of an effective survey and design questionnaires or experiments for gathering data. Then they will collect data from primary sources, through experimentation involving observation or measurement, or from secondary sources, and organize and store the data. They will create a graphical summary of the data using a scatter plot and determine algebraic equations of the variables that appear to be linearly related. In addition, students will describe possible interpretations of the line of best fit of a scatter plot and reasons for misinterpretations. They will recognize and interpret statistical terms and expressions used in the media and describe examples. Students will interpret statistics presented in the media, and explain how the media, the advertising industry, and others use and misuse statistics to promote a certain point of view. They will then assess the validity of conclusions presented in the media by examining sources of data, including Internet sources, methods of data collection, and possible sources of bias, and by questioning the analysis of the data. Finally, they will gather, interpret, and describe information about applications of data management in occupations, and about college programs that explore these applications.

UNIT 3:MATHEMATICAL EXPRESSIONS AND FUNCTIONS
This unit will have students interpret graphs to describe a relationship and use the trends to make predictions or justify decisions. Students will recognize that graphs and tables of values communicate information about rate of change, and use a given graph or table of values for a relation. They will identify when the rate of change is zero, constant, or changing, given a table of values or a graph of a relation, and compare two graphs by describing the rate of change. Additionally, Recognize properties of a linear and an exponential model and select a model to represent the relationship between numerical data graphically and algebraically. Students will make connections between formulas and linear, quadratic, and exponential functions. In the next part students will determine, through investigation, the exponent laws for multiplying and dividing algebraic expressions and the exponent law for simplifying algebraic expressions involving a power of a power. Followed by simplifying algebraic expressions containing integer exponents using the exponent laws. Solve exponential equations in one variable by determining a common base. Select models (i.e., linear, quadratic, exponential) to represent the relationship between numerical data graphically and algebraically and solve related problems. Using a formula drawn from an application make connections between formulas and linear, quadratic, and exponential functions. Lastly, gather, interpret, and describe information about applications of mathematical modelling in occupations, and about college programs that explore these applications.

UNIT 4: FINANCIAL MATHEMATICS
Students will gather and interpret information about annuities, describe the key features of an annuity, and identify real-world applications. Solve problems, using technology, that involve the amount, the present value, and the regular payment of an ordinary simple annuity. Investigate the advantages of starting deposits earlier when investing in annuities gather and interpret information, describe and compare mortgages. Read, interpret, and generate an amortization table for a mortgage, calculate the total interest paid over the life of a mortgage, and compare the total interest with the original principal. Determine the effects of varying/regular payment periods and interest rates on the length of time needed to pay off a mortgage. Students will then gather and interpret information about the procedures and costs involved in owning and in renting accommodation. Compare renting accommodation with owning accommodation. Gather, interpret, and describe information about living costs, and estimate the living costs of different households in the local community. Design, explain, and justify a monthly budget suitable for an individual or family described in a given case study that provides the specifics of the situation. Identify and describe the factors to be considered in determining the affordability of accommodation in the local community, and consider the affordability of accommodation under given circumstances and make adjustments to a budget to accommodate changes in circumstances.

Unit 1
By the end of this course, students will:
1. solve problems involving measurement and geometry and arising from real-world applications;
2. explain the significance of optimal dimensions in real-world applications, and determine
optimal dimensions of two-dimensional shapes and three-dimensional figures;
3. solve problems using primary trigonometric ratios of acute and obtuse angles, the sine law, and
the cosine law, including problems arising from real-world applications, and describe
applications of trigonometry in various occupations.

Unit 2
By the end of this course, students will:
1. collect, analyse, and summarize two-variable data using a variety of tools and strategies, and
interpret and draw conclusions from the data;
2. demonstrate an understanding of the applications of data management used by the media and
the advertising industry and in various occupations.

Unit 3
By the end of this course, students will:
1. evaluate powers with rational exponents, simplify algebraic expressions involving exponents,
and solve problems involving exponential equations graphically and using common bases;
2. describe trends based on the interpretation of graphs, compare graphs using initial conditions
and rates of change, and solve problems by modelling relationships graphically and
algebraically;
3. make connections between formulas and linear, quadratic, and exponential relations, solve
problems using formulas arising from real-world applications, and describe applications of
mathematical modelling in various occupations

Unit 4
By the end of this course, students will:
1. demonstrate an understanding of annuities, including mortgages, and solve related problems
using technology;
2. gather, interpret, and compare information about owning or renting accommodation, and solve
problems involving the associated costs;
3. design, justify, and adjust budgets for individuals and families described in case studies, and
describe applications of the mathematics of personal finance.

In this course, students will experience the following activities.

Presentations with embedded videos are utilized to outline concepts, explain theory with the use
of examples and practice questions, and incorporate multi-media opportunities for students to
learn more (e.g. online simulations, quizzes, etc.).

End of unit conversations and Poodlls are opportunities for students to express their ideas,
problem solving, and thought processes with a teacher who provides timely feedback.

Reflection is an opportunity for students to look back at concepts and theories with new eyes, to
relate theory to practice, and to align learning with their own values and beliefs.

Discussions with the instructor are facilitated through video conferencing, discussing the concepts
and skills being studied. This enables two-way communication between the student and the
instructor, to share ideas and ask questions in dialogue. This also helps to build a relationship
between the student and instructor.

Instructor demonstrations (research skills, etc.) are opportunities for the instructor to lead a
student through a concept or skill through video conferencing, videos, or emailing with the
student.

Discussion forums are an opportunity for students to summarize and share their ideas and
perspectives with their peers, which deepens understanding through expression. It also provides
an opportunity for peer-to-peer feedback.

Practical extension and application of knowledge are integrated throughout the course. The goal
is to help students make connections between what they learn in the classroom and how they
understand and relate to the world around them and their own lives. Learning becomes a dynamic
opportunity for students to be more aware that their learning is all around them and enable them
to create more meaning in their lives.

Individual activities/assignments assessments are completed individually at a student’s own pace
and are intended to expand and consolidate the learning in each lesson. Individual activities allow
the teacher to accommodate interests and needs and to assess the progress of individual students.

For this reason, students are encouraged to discuss IEPs (Individual Education Plans) with their
teacher and to ask to modify assessments if they have a unique interest that they feel could be
pursued in the assessment. The teacher plays an important role in supporting these activities by
providing ongoing feedback to students, both orally and in writing.

Research is an opportunity to apply inquiry skills to a practical problem or question. Students
perform research to gather information, evaluate quality sources, analyze findings, evaluate their
analysis, and synthesize their findings into conclusions. Throughout, students apply both creative
thinking and critical thinking. New questions are also developed to further learning.

Writing as a learning tool helps students to think critically about course material while grasping,
organizing, and integrating prior knowledge with new concepts. Good communication skills are
important both in and out of the classroom.

Virtual simulations are interactive websites that provide students with an opportunity to ask
questions, explore hypotheses, relate variables, examine relationships, and make connections
between theory and application in a safe environment that promotes intellectual risk taking and
curiosity.

Virtual labs are interactive websites that provide students with an opportunity to follow a
procedure to test hypotheses using scientific apparatus, gather and record observations, analyze
observations using formula and relevant theory/concepts, and then formulate conclusions that
relate hypotheses to analysis.

Diagrams are visual representations of scientific ideas and concepts. They provide another
perspective to organize ideas. Visuals are thought to promote cognitive plasticity – meaning, they
can help us change our minds or help us to remember an idea.

Graphics/images are visual representations of ideas/concepts. Visuals are thought to promote
cognitive plasticity – meaning, they can help us change our minds or help us to remember an idea.

Charts are visual representations of scientific ideas and concepts using math that support analysis.
For example, you can have a pie chart that shows Canada’s energy sources.

Tables involve organizing information in terms of categories (rows and columns). This helps us to
understand the relationships between ideas and data, as well as highlight trends.

Drawings and schematics are scientific and engineering ideas explained visually. For example, an
electric circuit can be explained using symbols, which makes it possible to communicate ideas
universally, clearly, and succinctly.

Articles are examples of concepts and theories being discussed in the public realm and with
respect to current events. They are snapshots not only of why scientific
theories/concepts/applications are relevant but also provide a window into the broader context of
scientific knowledge and understanding. Students learn through reading and analysis that science
is deeply related to, and intertwined with, society and the diverse perspectives of lived experience.

Practice problems provide students with a scenario/problem to solve by applying concepts and
skills learned in a context. This helps students to understand the relevance of their learning.

As summarized in Growing Success 2010, 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 final grade will be determined as follows:

❑ 70% of the grade will be based on evaluation 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 will be given to more recent
evidence of achievement.

❑ 30% of the grade will be based on a final evaluation administered at or towards the end of
the course. This evaluation will be based on evidence from one or a combination of the
following: an examination, a performance, and/or another method of evaluation suitable to
the course content. The final evaluation allows the student an opportunity to demonstrate
comprehensive achievement of the overall expectations for the course.

(Growing Success: Assessment, Evaluation and Reporting in Ontario Schools. Ontario
Ministry of Education Publication, 2010 p.41)

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 can be identified by the teacher, but recommendations from a School Board generated Individual Education Plan (IEP) if available can also be consulted. 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

To learn more go to our Individual Education Plan (IEP) page.

To learn more about this course including tests and exams please visit our FAQ page