General Outcome: Develop algebraic reasoning and number sense.
Specific Outcomes: It is expected that students will:
Demonstrate an understanding of
the absolute value of real
numbers.
[R, V]
1.1 Determine the distance of two real numbers of the form ±a, a ∈ R , from 0 on a number line, and relate this to the absolute value of a ( |a| ).
1.2 Determine the absolute value of a positive or negative real number.
1.3 Explain, using examples, how distance between two points on a number line can be expressed in terms of absolute value.
1.4 Determine the absolute value of a numerical expression.
1.5 Compare and order the absolute values of real numbers in a given set.
Solve problems that involve operations
on radicals and radical expressions with numerical and variable radicands.
[CN, ME, PS, R]
Radical Intro: Pythagorean Spiral
2.1 Compare and order radical expressions with numerical radicands in a given set.
2.2 Express an entire radical with a numerical radicand as a mixed radical.
2.3 Express a mixed radical with a numerical radicand as an entire radical.
2.4 Perform one or more operations to simplify radical expressions with numerical or variable radicands.
2.5 Rationalize the denominator of a rational expression with monomial or binomial denominators.
2.6 Describe the relationship between rationalizing a binomial denominator of a rational expression and the product of the factors of a difference of squares expression.
2.7 Explain,using examples,that (−x)2 = x2, and ; e.g., .
2.8 Identify the values of the variable for which a given radical expression is defined.
2.9 Solve a problem that involves radical expressions.
Solve
problems that involve radical equations (limited to square roots).
[C, PS, R]
(It is intended that the equations will have no more than two radicals.)
3.1 (It is intended that the equations will have no more than two radicals.)
3.2 Determine any restrictions on values for the variable in a radical equation.
3.3Determine the roots of a radical equation algebraically, and explain the process used to solve the equation.
3.3Verify, by substitution, that the values determined in solving a radical equation algebraically are roots of the equation.
3.4 Explain why some roots determined in solving a radical equation algebraically are extraneous.
3.5 Solve problems by modelling a situation using a radical equation.
Determine equivalent
forms of rational expressions (limited to numerators and denominators
that are monomials, binomials or trinomials).
[C, ME, R]
4.1 Compare the strategies for writing equivalent forms of rational expressions to the strategies for writing equivalent forms of rational numbers.
4.2 Explain why a given value is non-permissible for a given rational expression.
4.3 Determine the non-permissible values for a rational expression.
4.4 Determine a rational expression that is equivalent to a given rational expression by multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the non-permissible values of the equivalent rational expression.
4.5 Simplify a rational expression.
4.6 Explain why the non-permissible values of a given rational expression and its simplified form are the same.
4.7 Identify and correct errors in a simplification of a rational expression, and explain the reasoning.
Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials). [CN, ME, R]
5.1 Compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational numbers.
5.2 Determine the non-permissible values when performing operations on rational expressions.
5.3 Determine, in simplified form, the sum or difference of rational expressions with the same denominator.
5.4 Determine, in simplified form, the sum or difference of rational expressions in which the denominators are not the same and which may or may not contain common factors.
5.5 Determine, in simplified form, the product or quotient of rational expressions.
5.6 Simplify an expression that involves two or more operations on rational expressions.
Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials). [C, PS, R]
(It is intended that the rational equations be those that can be simplified
to linear and quadratic equations.)
6.1 Determine the non-permissible values for the variable in a rational equation.
6.2 Determine the solution to a rational equation algebraically, and explain the process used to solve the equation.
6.3 Explain why a value obtained in solving a rational equation may not be a solution of the equation.
6.4 Solve problems by modelling a situation using a rational equation.
and 
; e.g., 
.