Level IV Mathematics. Unit 1 Mathematics Portfolio

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1 Level IV Mathematics Unit 1 Mathematics Portfolio Unit 2 Mathematics Fundamentals The student uses the portfolio to demonstrate his or her understanding and knowledge of mathematical concepts. Determine what goes into the portfolio. Organize and display the contents in an effective format. Use an appropriate selection criteria to choose the samples of his or her best work. Provide an annotated list of the resources he or she has consulted, used, and read during the course. Present the portfolio to the class. The student objectively evaluates his or her own work and the process of completing the work. Select the work that best illustrates his or her skills and knowledge in mathematics. Use an appropriate selection criteria to select the samples. Establish and follow a time line. Use a rubric or standard to evaluate the portfolio and the portfolio process. The student gauges his or her own growth and accomplishments in mathematics. Explain in writing the challenges he or she faced during the course. Perform the four mathematical operations with real numbers and be able to manipulate certain algebraic expressions. Translate and evaluate algebraic expressions by substitution. Name integers that correspond to reallife situations. Graph rational numbers on a number line. Determine the difference between the symbols (>) greater and (<) smaller and to find the absolute value of a real number.

2 Add, subtract, multiply and divide real numbers without using the number line. Find the opposite or addictive inverse of a real number. Find the reciprocal of real numbers. Solve expressions by simplifying and using the rules of order of operations.

3 Unit 3 Measurement The student will solve equations using the addition principle, multiplication principle and/or a combination of both. Find whether a given number is a solution of a given equation. Solve equations using the addition principle. Solve equations using the multiplication principle. Solve equations using both principles together. The student will solve word problems, percent problems and formulas for a specific letter. Solve real life problems by translating to equations. Solve problems involving percents. Solve formulas for specific letters. The student will solve inequality expressions and word problems using inequalities. Graph an inequality on a number line. Determine whether a given number is a solution of an inequality. Solve an inequality using the addition principle. Solve an inequality using the multiplication principle. Solve an inequality using the addition and multiplication principle together. Translate number sentences to inequalities. Solve problems using inequalities. The student will solve problems using the English and Metric Units of Measurement. Manipulate given English and Metric length, area, volume, capacity measures as larger and smaller units Convert measurements from one system to another Use scientific notation in measurement The student will discriminate between accuracy precision and tolerance of measurement.

4 Determine the degree of precision and accuracy desirable in any measurement. Record measurements with the proper significant figures. Calculate the correct number of significant figures in an answer obtained from measured quantities.

5 Unit 4 Consumer Finances The student will use a number of measurement tools. Describe the rules of operation for at least three measurement tools. Read measurement results in both English and Metric graduations. Demonstrate the mastery of measurement techniques. Students will analyze and use the financial services that are available to enhance their lives. Use the following terms correctly: Depositor, Automatic teller machine, Deposit slip, Cheque register, Cheque stub, Cheque, Endorsement, Bank statement, Deposit in transit, Outstanding cheque, Service charge, Adjusted balance, Electronic bank transfer, Chequing account, Savings account, Joint account, Amortization, residential mortgage, mortgagor, mortgagee, mortgage contract, equity, first mortgage, second mortgage, demand (variable rate) mortgage, fixed rate mortgage. determine the adjusted bank balance reconcile a bank statement correctly Calculate the correct number of days between two calendar dates. Compute the exact interest using the formula I=Prt. Find principal, rate or time using the formula. Interpret the letter symbols used in the formula. Compute the exact interest using the formula S = P(1+i) N Solve the equation for P, i, or N. Compare the similarities and differences of the terms and conditions for usage of credit cards. Decide the appropriate choice for their particular needs. Calculate the annual interest charge of a

6 purchase. Calculate the actual consumer cost of a purchase using a revolving credit card using a variety of payback schedules. Calculate the cost of a purchase using a line of credit as the financing vehicle. Compute the periodic payment needed to service a residential mortgage. Compare and contrast the periodic payments when the terms and percentage rate are varied. Calculate present and future value of investment dollars.

7 Unit 5 Algebra Students will examine some of the tax collection systems currently used by municipal, provincial and federal governments. Determine residential tax rate. Express the tax rate in proper units. Calculate the residential tax due. Calculate the sales tax due on goods purchased. Calculate the sales tax rate. Complete a basic Canadian income tax form. Students will explore and analyze the types and terms of a variety of insurance options. Use the following terms correctly: Premiums, policy, coinsurance, beneficiaries, term life, straight life, limited pay life, endowment life, workers compensation, salary continuance, liability, collision, comprehensive, collision, deductibles. Calculate premiums for a variety of insurance products. The student will simplify expressions involving exponents, integers and scientific notation. Explain the meaning of exponential notation. Evaluate exponential expression with exponents of 0 and 1. Evaluate algebraic expression counting exponents. Use product rule to multiply exponential expressions with like bases. Use the quotient rule to divide exponential expressions with like bases. Express an exponential expression evaluating negative exponents with positive exponent. Raise powers to powers using power rule. Raise a product to a power and a quotient to a power. Convert between decimal notation and scientific notation.

8 Multiply, divide and solve problems using scientific notation. Solve problems using scientific notation.

9 The student will add and subtract polyomials. Evaluate a polynomial. Identify like term, coefficient of polynomials. Collect like terms of a polynomial. Arrange a polynomial in descending order and ascending order. Identify the degree of each term and the degree of the polynomial. Classify a polynomial or a monomial, binomial, trinomial or none of the above. Add, subtract and solve problems of polynomials. Solve and subtract a polynomial addition and subtraction of polynomials. The student will multiply, divide polyomials and perform operations with polyomials in several variables. Multiply a monomial with a polynomial. Multiply any monomial. Multiply two binomials. Multiply any two polynomials. Square a binomial. Multiply the sum and difference of two terms. Evaluate a polynomial in several variables. Divide a polynomial by a monomial. The student will demonstrate the ability to factor various types of polyomials. Factor monomials. Factor trinomials of the 2 type x + bx + c. Factor a trinomial square and a difference of squares. The student will multiply, divide, and simplify rational expressions. Find all numbers for which a rational expression is undefined. Multiply a rational expression by 1, that is, using an expression such as x/x.

10 Simplify rational expressions by factoring the numerator and the denominator and removing factor of 1. Multiply rational expressions and simplify. Finding the reciprocal. Divide and simplify.

11 The student will be able to add and subtract rational expressions with common denominators. Add and subtract rational expressions with the same denominators. Simplify combined addition and subtraction of rational expressions. The student will graph linear equations. Plot points associated with ordered pairs of numbers. Find the quadrant in which a point lies. Determine the coordinate of a point on a graph. Determine if an ordered pair is a solution of an equation with two variables. Graph linear equations of the type y = mx + b and Ay + By = c, along with identifying the y intercept. Solve applied problems involving graphs of linear equations. Find the intercepts of a linear equation, and graph using intercepts. Graph equations of the type x = s and y = t. The student will find the slope and the equation of a line. Find the slope of a line when given the coordinates of two points on the line. Find the slope of a line from an equation. Find the rate of change or slope in an applied problem involving slopes. Find the slope and the y intercept of an equation in the form of y = mx + b. Find an equation of a line when the slope and the y intercept are given. Finding an equation of a line when the slope and point on the line are given. Find an equation of a line when two points on the line are given. Solve two linear equations to determine if the lines are parallel or perpendicular. The student will graph inequalities in

12 two variables. Determine whether an ordered pair of numbers is a solution of an inequality in two variables. Graph linear inequalities.

13 Unit 6 Statistics and Probability The student will multiply, divide and simplify radical expressions. Find the square roots and their opposites of whole numbers. Find the square root of a number using a calculator. Solve applied problems involving square roots. Identify a radical expression and a radicand. Simplify a radical expression with a perfect square radicand. Simplify a radical expression. Simplify radical expressions where radicands are powers. Multiply and simplify radical expression if possible. Divide and simplify radical expressions. The student will solve Radical Equations. Solve radical equations using the principle of squaring one. Solving applied problems using radical equations. Solve applied problems involving the right triangle. The student collects, reads, and interupts data using charts, diagrams and graphs. analyze mean, mode, median and range plot data on charts and diagrams use the data to make predictions and solve problems conduct survey to collect, analyze and graph data use Chi square to test hypotheses The student uses probability to solve problems. use fundamental counting principles to determine different ways to perform multi step operations construct a sample space for two or three events classify events as independent or dependent

14 use the probabilities as mutually exclusive and complementary events determine permutations and combinations

15 Unit 7 Trigonometry Unit 8 Independent Project The student calculates and applies normal distribution to statistical data. distinguish between mathematical usage and common usage find the standard deviation use technology to find a standard deviation plot a Bell curve determine if a given distribution is normal use the Z score to solve problems Upon completion of this unit the student will be able to: Solve a right triangle for all its angles and sides. Solve oblique triangle using the Law of Sine and Law of Cosine. The student will solve a right triangle for all its angles and sides. Identify the four types of triangles. Identify the sides of a right triangle with reference to any angle. Find the missing angle of a triangle. Find the missing angles of many triangles within one triangle. Use Pythagorean Theory to solve a triangle. Solve a triangle using trig ratios The student will solve oblique triangle using the Law of Sine and Cosine. Solve oblique triangle using the Law of Sine. Solve an oblique triangle using the Law of Cosine. The student applies mathematical concepts to the design of a Independent Project. Choose a project topic sufficient for the scope of the project Identify and list the mathematical concepts involved in the completion of the project Identify the types and sources of information used to carry out the project

16 Determine and list the sequence of steps necessary for completion of the project Estimate time needed for completion of the project Produce a time line to reflect the time required for the project Decide on an appropriate format for presentation of the project Produce a project proposal outline for approval by their instructor The student manages his or her Independent Project. Follow the project schedule as determines, including meeting timelines and adjusting and communicating timelines as needed Meet with instructor as necessary to propose changes to project goals and Timelines Provide regular updates to course instructor Completes a weekly log to reflect on their activities and learning in a personal learning journal Records in their personal learning journal a list of the mathematical concepts learned. The student demonstrates the completion of an Independent Project. List the sources of information used during this project List the mathematical concepts learned Organize and display the results of the learning in a suitable format as agreed with instructor.

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