Number+Sense+and+Algebra

=Number Sense and Algebra=

NA1.01 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);

NA1.02 represent, using equivalent ratios and proportions, 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.);

NA1.03 solve for the unknown value in a proportion, using a variety of methods
(e.g., concrete materials, algebraic reasoning, equivalent ratios, constant of proportionality) (Sample problem: Solve x/4 = 15/20.);

NA1.04 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);

NA1.05 solve problems involving ratios, rates, and directly proportional relationships in various 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 interest 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?);

NA1.06 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 science this semester. Estimate and calculate the number of Grade 9 students this percent represents.).

NAV.02 simplify numerical and polynomial expressions in one variable, and solve simple first-degree equations
.

NA2.01 simplify numerical expressions involving integers and rational numbers, with and without the use of technology

 * *The knowledge and skills described in this expectation are to be introduced as needed and applied and consolidated throughout the course;

NA2.03 describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three
[i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional, can be represented by (x)(x) or x2; volume, which is three dimensional, can be represented by (x)(x)(x), (x2)(x), or x3];

NA2.04 substitute into and evaluate algebraic expressions involving exponents
(i.e., evaluate expressions involving natural-number exponents with rational-number bases) [e.g., evaluate (3/2)3 by hand and 9.83 by using a calculator]) (Sample problem: A movie theatre wants to compare the volumes of popcorn in two containers, a cube with edge length 8.1 cm and a cylinder with radius 4.5 cm and height 8.0 cm. Which container holds more popcorn?);* *The knowledge and skills described in this expectation are to be introduced as needed and applied and consolidated throughout the course;

NA2.05 add and subtract polynomials involving the same variable up to degree three
[e.g., (2x + 1) + (x2 - 3x + 4)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);

NA2.06 multiply a polynomial by a monomial involving the same variable to give results up to degree three
[e.g., (2x)(3x), 2x(x + 3)], using a variety of tools (e.g., algebra tiles, drawings, computer algebra systems, paper and pencil);

NA2.07 solve first-degree equations with nonfractional coefficients, using a variety of tools
(e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies) (Sample problem: Solve 2x + 7 = 6x - 1 using the balance analogy.);

NA2.08 substitute into algebraic equations and solve for one variable in the first degree
(e.g., in relationships, in measurement) (Sample problem: The perimeter of a rectangle can be represented as P = 2l + 2w. If the perimeter of a rectangle is 59 cm and the width is 12 cm, determine the length.).