Number Sense and Algebra
Operating with Exponents
Review the exponential notations and practice evaluating natural-number exponents with rational-number bases. Use the multiplication rule to derive the exponent rules: $$x^m \times x^n = x^{m+n}$$ $$\frac{x^m}{x^n} = x^{m-n}$$ $$(x^m)^n = x^{m\times n}$$ $$x^{-n} = {1\over{x^n}}$$ $$x^0 = 1$$
Introduce scientific notation. Describe the relationship between algebraic and geometric representation of a variable with degree up to three (eg, length, area, volume) Powers of 10 - Java applet to visually demonstrate the power of powers.
Manipulating Expressions and Solving Equations
Simplify numerical expressions involving integer and rational number. Solve problems requiring the manipulation of expressions arising from percent, ratio, rate and proportion. Relate the inverse operation with square roots and use it to solve equations. Add and subtract polynomials with up to two variables. Multiply a polynomial with a monomial. Expand and simplify polynomial expressions in one variable. Solve first degree equations Rearrange formula involving first degree equations Solve problems that can be modeled with first degree equations.
Linear Relations
Stress that it is a relationship, if you know one variable, you can find the other. When working with slope-intercept form, make sure you work it both ways.