Pure Math 10

Course name and abbreviation:

Pure Mathematics 10 (PM10)

Grade Level:

Grade 10

Summary of course content and activities:

This course includes the following strands:

Sequences and Data Tables
Exponents and Radicals
Line Segments and Graphs
Relations and Functions
Algebraic Expressions
Trigonometry

Who should be taking this course? For whom is this course designed and intended?

Pure Mathematics 10 is the first course in the Pure Mathematics 10-20-30 sequence. Pure Mathematics 10 is designed to follow Grade 9 Mathematics.

Philosophy statement for and/or behind teaching this course:

Pure mathematics emphasizes mathematical theory and the testing of mathematical hypotheses. The pure mathematics approach, which is often deductive and symbolic, endeavors to show that concepts are valid all the time, or valid within a well-defined set of restrictions. Real-life problems are then presented in order for students to apply previously learned mathematical concepts and procedures. Students will make use of algebra and graphing to solve problems.

Students are required to demonstrate effective communication skills. This includes understanding, using, and interpreting various mathematical concepts and processes. Students will be expected to explain, to illustrate, to reason and to make connections. Multiple solution strategies to problems and problem contexts will be expected as students work through both routine and non-routine problems. Tasks vary from short procedural items that help students develop skills in the language of mathematics, to longer tasks that require students to test either subtle conjectures or apply mathematical knowledge to real-life problems.

Technology is a part of pure mathematics. The graphing calculator is the primary technological tool used by students for mathematical exploration, modeling and problem solving. The use of spreadsheets, with functions defined by the student, can be profitable in many contexts.

Major course goals:

Sequences and Data Tables (3 Lessons)

1.1       Use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are not related recursively.
1.2       Use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are related recursively.
1.3       Choose, justify and apply sampling techniques that will result in an appropriate, unbiased sample from a given population.
1.4       Defend or oppose inferences and generalizations about populations, based on data from samples.
1.5       Create and modify tables from both recursive and non-recursive situations.
1.6       Use and modify a spreadsheet template to model recursive situations.
1.7       Generate number patterns exhibiting arithmetic growth.
1.8       Use expressions to represent general terms and sums for arithmetic growth, and apply these expressions to solve problems.
1.9       Generate number patterns exhibiting geometric growth.

Exponents and Radicals (3 Lessons)

2.1       Classify numbers as natural, whole, integer, rational or irrational, and show that these number sets are nested within the real number system.
2.2       Use approximate representations of irrational numbers.
2.3       Communicate a set of instructions used to solve an arithmetic problem.
2.4       Perform arithmetic operations on irrational numbers, using appropriate decimal approximations.
2.5       Explain and apply the exponent laws for powers of numbers and for variables with rational exponents.
2.6       Perform operations on irrational numbers of monomial and binomial form, using exact values.

Line Segments and Graphs (3 Lessons)

3.1       Plot linear and nonlinear data, using appropriate scales.
3.2       Solve problems involving distances between points in the coordinate plane.
3.3       Solve problems involving midpoints of line segments.
3.4       Solve problems involving rise, run and slope of line segments.
3.5       Determine the equation of a line, given information that uniquely determines the line.
3.6       Solve problems using slopes of parallel lines and perpendicular lines.

Relations and Functions (2 Lessons)

4.1       Represent data, using function models.
4.2       Use a graphing tool to draw the graph of a function from its equation.
4.3       Describe a function.
4.4       Use function notation to evaluate and represent functions.
4.5       Determine the domain and range of a relation from its graph.
4.6       Determine characteristics of the graph of a linear function, given its equation.
4.7       Use direct variation, partial variation, and arithmetic sequences as applications of linear functions.
4.7       Relate arithmetic sequences to linear functions defined over the natural numbers.

Algebraic Expressions (3 Lessons)

5.1       Factor polynomial expressions of the form ax² +bx+c, and a²x² –b²y² .
5.2       Find the product of polynomials.
5.3       Divide an integral polynomial by a binomial.
5.4       Determine equivalent forms of single- variable rational expressions with polynomial numerators and denominators.
5.5       Determine the non permissible values for the variable in single- variable rational expressions.
5.6       Perform the operations of addition, subtraction, multiplication and division on single-variable rational expressions.
5.7       Find and verify the solutions of rational equations that reduce to linear equations.

Trigonometry (2 Lessons)

6.1       Solve problems involving two right triangles.
6.2       Extend the concepts of sine and cosine for angles from 0º to 180º.
6.3       Apply the sine and cosine laws, excluding the ambiguous case, to solve problems.

Pre-requisite(s):

Students taking PM10 are presumed to have reached the acceptable standard or better in Math 9

Number of credits that this course is worth:

5 credits

Materials and resources provided by NSA, purchased by student, and/or recommended:

Provided by NSA:

Mathematics 10 textbook, Western Canadian Edition, published by Addison Wesley Longman (1998)
The Learning Equation Disk (TLE disk)
Addison Wesley Math 10 Independent Study Guide
Pure Math 10 Workbook

Purchased by student:

Microsoft Office (greater than 97) especially Word and Excel
A graphing calculator. The textbook and my lesson examples will use a TI-83 but a TI-83 Plus is very similar.

Recommended but not required:

A geometry set (compass, protractor, ruler and triangles)
Notebook for pencil and paper assignments.

Forecasted amount of time required to complete each week’s lesson:

Semester students can expect to complete the course in about 8-10 hours per week over eighteen weeks. Full year students will complete the course in about 4-5 hours per week over thirty-six weeks.

Description of student evaluations, quizzes, and tests:

Assignments: 70%
Exams: 30%

Exams and assignments throughout the course are worth 70% of the final mark. The final exam is worth 30% of the final mark.

NorthStar Academy Canada
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1-403-335-9587
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