Mathematics: Intermediate Level—Algebraic
Estimation is a skill that should be emphasized. Students should also be strongly encouraged to check answers and that solutions are reasonable in the context.
Learning Outcomes
1. Operations with Rational Numbers
It is expected that learners will be able to:
- write fractions as decimals and decimals as fractions
- add, subtract, multiply, divide, and simplify rational numbers
- use order of operations
- graph rational numbers on the number line
- define absolute value
2. Measurement
It is expected that learners will be able to:
- use the common metric units for temperature, length, area, volume/capacity, and mass
- use the common Imperial or US Customary units for temperature, length, area, volume/ capacity, and force
- convert between and within metric and Imperial or US Customary units using tables and/or calculators
- use proportional reasoning for conversions
3. Perimeter, Area, and Volume
It is expected that learners will be able to:
- find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures using formulas
- find areas of the above shapes using formulas
- find the surface areas of cubes, rectangular solids, right cylinders, spheres, and composite solids using formulas
- find the volumes of cubes, rectangular solids, right cylinders and cones, spheres, and composite solids using formulas
- distinguish between concepts of perimeter and area and their respective units
4. Ratio, Proportion and Percent
It is expected that learners will be able to:
- read, write, interpret, and compare ratios
- read, write and identify proportions and use them to solve problems
- use ratio and proportion to interpret and make scale drawings
- use ratio and proportion to solve problems involving similar triangles
- use ratio and proportion to solve problems including:
- finding percent when part and whole are known
- finding part when percent and whole are known
- finding whole when part and percent are known
5. Algebra
It is expected that learners will be able to:
- explain the use of variables
- evaluate algebraic expressions using substitution
- combine like terms and remove parentheses
- solve first degree equations in one variable
- translate a problem into an equation
- use equations to solve problems
- solve simple formulas for a given variable
- use formulas to solve problems
6. Linear Equations and Graphing
It is expected that learners will be able to:
- draw a Cartesian co-ordinate system
- plot and name points in a Cartesian co-ordinate system
- given an equation in two variables:
- determine if an ordered pair is a solution
- find ordered pairs which are solutions
- graph equations of the form x = a and y = b,
- define slope and relate to grade and pitch
- graph linear equations using
- slope and y-intercept
- two intercepts
- a table of values
- find x- and y-intercepts
- determine the equation of a line, y = mx + b, given
- its graph
- its slope and a point on the line
- two points on the line
- solve problems using graphs of linear equations
7. Powers, Roots, and Scientific Notation
It is expected that learners will be able to:
- read and write numbers expressed as powers
- evaluate powers with integral exponents
- apply laws of exponents to simplify expressions
- express numbers using scientific notation
- convert between scientific and standard notation
- determine the square root of a perfect square
- express a square root as a mixed radical in simplest form (numerical radicands only)
- approximate square roots of real numbers using a calculator
8. Polynomials
It is expected that learners will be able to:
- distinguish between monomials, binomials, trinomials and other polynomials in one variable only
- apply the laws of exponents to variable expressions with integral exponents
- evaluate polynomials by substitution
- add, subtract, and multiply polynomials in one variable
- factor polynomials by removing the largest common factor
- factor binomials of the form a2x2 – b2y2
- factor trinomials of the form ax2 + bx + c with a = 1 ONLY
- divide a polynomial by a monomial
9. Trigonometry
It is expected that learners will be able to:
- name parts of a triangle
- find missing side of a right triangle using the Pythagorean Theorem
- find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios
- solve problems using right angle trigonometry