Page 40 - Math 9-10 (2009)

FOUNDATIONS OF MATHEMATICS, GRADE 9, APPLIED (MFM1P) 39
Number Sense and Algebra
Overall Expectations
By the end of this course, students will:
• solve problems involving proportional reasoning;
• simplifynumericalandpolynomialexpressionsinonevariable,andsolvesimplefirst-degree equations.
Specific Expectations
Solving Problems Involving Proportional Reasoning
By the end of this course, students will:
– illustrate equivalent ratios, using a variety of tools (e.g., concrete materials, diagrams, dynamic geometry software) (e.g., show that 4:6 represents the same ratio as 2:3 by showing that a ramp with a height of 4 m and a base of 6 m and a ramp with a height of 2 m and a base of 3 m are equally steep);
– represent, using equivalent ratios and pro- portions, directly proportional relationships arising from realistic situations (Sample problem:You are building a skateboard ramp whose ratio of height to base must be 2:3. Write a proportion that could be used to determine the base if the height is 4.5 m.);
– solve for the unknown value in a propor- tion, using a variety of methods (e.g., con- crete materials, algebraic reasoning, equiva- lent ratios, constant of proportionality)
(Sample problem: Solve = .);
– make comparisons using unit rates (e.g., if 500 mL of juice costs $2.29, the unit rate is 0.458¢/mL; this unit rate is less than for 750 mL of juice at $3.59, which has a unit rate of 0.479¢/mL);
– solve problems involving ratios, rates, and directly proportional relationships in vari- ous contexts (e.g., currency conversions, scale drawings, measurement), using a variety of methods (e.g., using algebraic
reasoning, equivalent ratios, a constant of proportionality; using dynamic geometry software to construct and measure scale drawings) (Sample problem: Simple inter- est is directly proportional to the amount invested. If Luis invests $84 for one year and earns $1.26 in interest, how much would he earn in interest if he invested $235 for one year?);
– solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms (e.g., calculating simple interest and sales tax; analysing data) (Sample problem: Of the 29 students in a Grade 9 math class, 13 are taking science this semester. If this class is representative of all the Grade 9 students in the school, estimate and calculate the percent of the 236 Grade 9 students who are taking sci- ence this semester. Estimate and calculate the number of Grade 9 students this per- cent represents.).
Simplifying Expressions and Solving Equations
By the end of this course, students will:
– simplify numerical expressions involving integers and rational numbers, with and without the use of technology;*
– relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations;
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4
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*The knowledge and skills described in this expectation are to be introduced as needed and applied and consoli- dated throughout the course.