Mathematics
Mathematics: Intermediate Level—Developmental
Goal Statement
The goal of Intermediate Mathematics is to enable adult learners to acquire mathematical knowledge, skills, and strategies needed to enter appropriate higher level courses or to satisfy personal or career goals.
I. Core Learning Outcomes
1. Estimating Skills/Calculator Use
It is expected that learners will be able to:
- estimate answers to problems
- use a scientific calculator to calculate and solve problems involving adding, subtracting, multiplying and dividing whole numbers, fractions and decimals
- check that answers and solutions to problems are reasonable in the context of the given question
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
- take and read measurements with common measuring tools (e.g. thermometer, ruler, measuring tape, triple beam balance, bathroom scale, stop watch, Vernier caliper, micrometer) (optional)
- describe and apply precision, accuracy and tolerance (optional)
- estimate in metric and Imperial or US customary units of measurement (optional)
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 by measuring and using formulas
- find areas of the above shapes by measuring and using formulas
- find the surface areas of cubes, rectangular solids, cylinders, cones, spheres, and composite solids by using formulas
- find the volumes of cubes, rectangular solids, cylinders, cones, spheres, and composite solids by using formulas
- distinguish between concepts of perimeter and area and their respective units
4. Ratio and Proportion
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 proportions to solve problems involving similar triangles
5. Percent
It is expected that learners will be able to:
- use ratios and proportions to solve problems involving:
- finding the percent when the part and whole are known
- finding the part when the percent and whole are known
- finding the whole when the part and percent are known
6. Geometry
It is expected that learners will be able to:
- name and draw points, lines, rays, segments, and angles
- name and draw triangles, quadrilaterals, other common polygons, and circles
- construct with a compass and straight edge:
- the perpendicular bisector of a line segment
- the bisector of an angle
- a copy of an angle (optional)
- parallel lines (optional)
- 30°, 45°, and 60° angles (optional)
- classify and distinguish among acute, right, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles
- describe the angle relationships created when parallel lines are cut by a transversal
- measure angles with a protractor
- classify triangles according to sides and angles
- identify similar and congruent figures
7. Statistics
It is expected that learners will be able to:
- conduct a survey to collect data
- tabulate the data
- calculate median, mean, mode, and range
- graph the data
- interpolate and extrapolate from the information provided
8. Signed (Rational) Numbers
It is expected that learners will be able to:
- add, subtract, multiply, and divide signed (rational) numbers
- demonstrate order of operations with signed (rational) numbers
- graph signed (rational) numbers on the number line
- define absolute value
9. 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 one variable
- use formulas to solve problems
II. Additional Learning Outcomes
To complete the course, students should choose option A or B:
A. This option helps prepare students for math at the advanced level.
1. Powers, Roots, and Scientific Notation
- read and write numbers expressed as powers
- calculate powers with integral exponent
- use the rules of exponents to calculate products and quotients of powers with the same base
- use the rules of exponents to calculate the powers of powers
- express numbers using scientific notation
- convert between scientific and standard notation
- read and write numbers expressed as roots
- calculate using roots
2. Polynomials
- add and subtract polynomials
- multiply and divide polynomials by a monomial
- factor out the greatest common factor from polynomials
3. Trigonometry
- name the parts of a right triangle
- find the 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
4. Graphing
- 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
- create a table of values
- graph linear equations
- determine the slope of a line given two points on the line
- relate slope to grade and pitch
- find x- and y-intercepts
- solve problems using graphs of linear equations
B. This option is intended for students exiting the ABE structure at the Intermediate Level and contains additional material pertaining to specific vocations