MATH 030 - Intermediate Mathematics

Intermediate Math reviews the fundamental arithmetic skill to introduce beginning algebra and problem-solving in preparation for more advanced work in mathematics and the sciences. Units of work include: percent with applications, measurement of area and perimeter, practical geometric construction, right-angled trigonometry, signed numbers and algebraic expressions, linear equations, polynomials, simple factoring, graphing linear equations, and scientific notation.

It is expected that learners will be able to:

a) estimate answers to problems

b) use a scientific calculator to calculate and solve problems involving adding, subtracting, multiplying and dividing whole numbers, fractions and decimals

c) 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:

a) use the common metric units for temperature, length, area, volume/capacity, and mass

b) use the common Imperial units for temperature, length, area, volume/capacity, and force

c) convert between and within metric and Imperial units using tables and/or calculators

d) 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)

e) describe and apply precision, accuracy and tolerance (optional)

f) estimate in metric and Imperial units of measurement (optional)

3. Perimeter, Area, and Volume

It is expected that learners will be able to:

a) find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures by measuring and using formulas

b) find areas of the above shapes by measuring and using formulas

c) find the surface areas of cubes, rectangular solids, cylinders, cones, spheres, and composite solids by using formulas

d) find the volumes of cubes, rectangular solids, cylinders, cones, spheres, and composite solidsby using formulas

e) distinguish between concepts of perimeter and area and their respective units

4. Ratio and Proportion

It is expected that learners will be able to:

a) read, write, interpret, and compare ratios

b) read, write and identify proportions and use them to solve problems

c) use ratio and proportion to interpret and make scale drawings

d) use proportions to solve problems involving similar triangles

5. Percent

It is expected that learners will be able to:

a) use ratios and proportions to solve problems involving:

i. finding percent when part and whole are known

ii. finding part when percent and whole are known

iii. finding whole when part and percent are known

6. Geometry

It is expected that learners will be able to:

a) name and draw points, lines, rays, segments, and angles

b) name and draw triangles, quadrilaterals, other common polygons and circles

c) construct with a compass and straight edge:

i. the perpendicular bisector of a line segment

ii. the bisector of an angle

iii. a copy of an angle (optional)

iv. parallel lines (optional)

v. 30°, 45°, and 60° angles (optional)

d) classify and distinguish among acute, right, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles

e) describe the angle relationships created when parallel lines are cut by a transversal

f) measure angles with a protractor

g) classify triangles according to sides and angles

h) identify similar and congruent figures

7. Statistics

It is expected that learners will be able to:

a) conduct a survey to collect data

b) tabulate the data

c) calculate median, mean, mode, and range

d) graph the data

e) interpolate and extrapolate from the information provided

8. Signed (Rational) Numbers

It is expected that learners will be able to:

a) add, subtract, multiply, and divide signed (rational) numbers

b) demonstrate order of operations with signed (rational) numbers

c) graph signed (rational) numbers on the number line

d) define absolute value

9. Algebra

It is expected that learners will be able to:

a) explain the use of variables

b) evaluate algebraic expressions using substitution

c) combine like terms and remove parentheses

d) solve first degree equations in one variable

e) translate a problem into an equation

f) use equations to solve problems

g) solve simple formulas for one variable

h) use formulas to solve problems

ADDITIONAL COURSE CONTENT Students can opt to complete outcomes 10-13, or complete 14

10. Powers, Roots, and Scientific Notation

a) read and write numbers expressed as powers

b) calculate powers with integral exponent

c.) use the rules of exponents to calculate products and quotients of powers with the same base

d) use the rules of exponents to calculate the powers of powers

e) express numbers using scientific notation

f) convert between scientific and standard notation

g) read and write numbers expressed as roots

h) calculate using roots

11. Polynomials

a) add and subtract polynomials

b) multiply and divide polynomials by a monomial

c) remove common factors from polynomials

12. Trigonometry

a) name the parts of a right triangle

b) find the missing side of a right triangle using the Pythagorean Theorem

c.) find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios

d) solve problems using right angle trigonometry

13.Graphing

a) draw a Cartesian co-ordinate system

b) plot and name points in a Cartesian co-ordinate system

c) given an equation in two variables:

i. determine if an ordered pair is a solution

ii. find ordered pairs which are solutions

iii. create a table of values

d) graph linear equations

e) determine the slope of a line given two points on the line

f) relate slope to grade and pitch

g) find x- and y-intercepts

h) solve problems using graphs of linear equations

OR

14. Solve Vocational word problems

CORE LEARNING OUTCOMES

1. Estimating Skills/Calculator Use

It is expected that learners will be able to:

a) estimate answers to problems

b) use a scientific calculator to calculate and solve problems involving adding, subtracting, multiplying and dividing whole numbers, fractions and decimals

c) 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:

a) use the common metric units for temperature, length, area, volume/capacity, and mass

b) use the common Imperial units for temperature, length, area, volume/capacity, and force

c) convert between and within metric and Imperial units using tables and/or calculators

d) 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)

e) describe and apply precision, accuracy and tolerance (optional)

f) estimate in metric and Imperial units of measurement (optional)

3. Perimeter, Area, and Volume

It is expected that learners will be able to:

a) find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures by measuring and using formulas

b) find areas of the above shapes by measuring and using formulas

c) find the surface areas of cubes, rectangular solids, cylinders, cones, spheres, and composite solids by using formulas

d) find the volumes of cubes, rectangular solids, cylinders, cones, spheres, and composite solidsby using formulas

e) distinguish between concepts of perimeter and area and their respective units

4. Ratio and Proportion

It is expected that learners will be able to:

a) read, write, interpret, and compare ratios

b) read, write and identify proportions and use them to solve problems

c) use ratio and proportion to interpret and make scale drawings

d) use proportions to solve problems involving similar triangles

5. Percent

It is expected that learners will be able to:

a) use ratios and proportions to solve problems involving:

i. finding percent when part and whole are known

ii. finding part when percent and whole are known

iii. finding whole when part and percent are known

6. Geometry

It is expected that learners will be able to:

a) name and draw points, lines, rays, segments, and angles

b) name and draw triangles, quadrilaterals, other common polygons and circles

c) construct with a compass and straight edge:

i. the perpendicular bisector of a line segment

ii. the bisector of an angle

iii. a copy of an angle (optional)

iv. parallel lines (optional)

v. 30°, 45°, and 60° angles (optional)

d) classify and distinguish among acute, right, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles

e) describe the angle relationships created when parallel lines are cut by a transversal

f) measure angles with a protractor

g) classify triangles according to sides and angles

h) identify similar and congruent figures

7. Statistics

It is expected that learners will be able to:

a) conduct a survey to collect data

b) tabulate the data

c) calculate median, mean, mode, and range

d) graph the data

e) interpolate and extrapolate from the information provided

8. Signed (Rational) Numbers

It is expected that learners will be able to:

a) add, subtract, multiply, and divide signed (rational) numbers

b) demonstrate order of operations with signed (rational) numbers

c) graph signed (rational) numbers on the number line

d) define absolute value

9. Algebra

It is expected that learners will be able to:

a) explain the use of variables

b) evaluate algebraic expressions using substitution

c) combine like terms and remove parentheses

d) solve first degree equations in one variable

e) translate a problem into an equation

f) use equations to solve problems

g) solve simple formulas for one variable

h) use formulas to solve problems

ADDITIONAL LEARNING OUTCOMES Students can opt to complete outcomes 10-13, or complete 14

10. Powers, Roots, and Scientific Notation

a) read and write numbers expressed as powers

b) calculate powers with integral exponent

c.) use the rules of exponents to calculate products and quotients of powers with the same base

d) use the rules of exponents to calculate the powers of powers

e) express numbers using scientific notation

f) convert between scientific and standard notation

g) read and write numbers expressed as roots

h) calculate using roots

11. Polynomials

a) add and subtract polynomials

b) multiply and divide polynomials by a monomial

c) remove common factors from polynomials

12. Trigonometry

a) name the parts of a right triangle

b) find the missing side of a right triangle using the Pythagorean Theorem

c.) find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios

d) solve problems using right angle trigonometry

13.Graphing

a) draw a Cartesian co-ordinate system

b) plot and name points in a Cartesian co-ordinate system

c) given an equation in two variables:

i. determine if an ordered pair is a solution

ii. find ordered pairs which are solutions

iii. create a table of values

d) graph linear equations

e) determine the slope of a line given two points on the line

f) relate slope to grade and pitch

g) find x- and y-intercepts

h) solve problems using graphs of linear equations

OR

14. Solve Vocational word problems

**Hours:**120 (Lecture Hours: 6)

**Total Weeks:**20

**Prerequisites:**

**
**MATH 026 (Fundamental Mathematics) or demonstrated skill at Grade 8 level; OR permission of instructor.

**Non-Course Prerequisites:**None

**Co-requisites:**None

**Course Content:**

1. Estimating Skills/Calculator UseIt is expected that learners will be able to:

a) estimate answers to problems

b) use a scientific calculator to calculate and solve problems involving adding, subtracting, multiplying and dividing whole numbers, fractions and decimals

c) 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:

a) use the common metric units for temperature, length, area, volume/capacity, and mass

b) use the common Imperial units for temperature, length, area, volume/capacity, and force

c) convert between and within metric and Imperial units using tables and/or calculators

d) 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)

e) describe and apply precision, accuracy and tolerance (optional)

f) estimate in metric and Imperial units of measurement (optional)

3. Perimeter, Area, and Volume

It is expected that learners will be able to:

a) find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures by measuring and using formulas

b) find areas of the above shapes by measuring and using formulas

c) find the surface areas of cubes, rectangular solids, cylinders, cones, spheres, and composite solids by using formulas

d) find the volumes of cubes, rectangular solids, cylinders, cones, spheres, and composite solidsby using formulas

e) distinguish between concepts of perimeter and area and their respective units

4. Ratio and Proportion

It is expected that learners will be able to:

a) read, write, interpret, and compare ratios

b) read, write and identify proportions and use them to solve problems

c) use ratio and proportion to interpret and make scale drawings

d) use proportions to solve problems involving similar triangles

5. Percent

It is expected that learners will be able to:

a) use ratios and proportions to solve problems involving:

i. finding percent when part and whole are known

ii. finding part when percent and whole are known

iii. finding whole when part and percent are known

6. Geometry

It is expected that learners will be able to:

a) name and draw points, lines, rays, segments, and angles

b) name and draw triangles, quadrilaterals, other common polygons and circles

c) construct with a compass and straight edge:

i. the perpendicular bisector of a line segment

ii. the bisector of an angle

iii. a copy of an angle (optional)

iv. parallel lines (optional)

v. 30°, 45°, and 60° angles (optional)

d) classify and distinguish among acute, right, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles

e) describe the angle relationships created when parallel lines are cut by a transversal

f) measure angles with a protractor

g) classify triangles according to sides and angles

h) identify similar and congruent figures

7. Statistics

It is expected that learners will be able to:

a) conduct a survey to collect data

b) tabulate the data

c) calculate median, mean, mode, and range

d) graph the data

e) interpolate and extrapolate from the information provided

8. Signed (Rational) Numbers

It is expected that learners will be able to:

a) add, subtract, multiply, and divide signed (rational) numbers

b) demonstrate order of operations with signed (rational) numbers

c) graph signed (rational) numbers on the number line

d) define absolute value

9. Algebra

It is expected that learners will be able to:

a) explain the use of variables

b) evaluate algebraic expressions using substitution

c) combine like terms and remove parentheses

d) solve first degree equations in one variable

e) translate a problem into an equation

f) use equations to solve problems

g) solve simple formulas for one variable

h) use formulas to solve problems

ADDITIONAL COURSE CONTENT Students can opt to complete outcomes 10-13, or complete 14

10. Powers, Roots, and Scientific Notation

a) read and write numbers expressed as powers

b) calculate powers with integral exponent

c.) use the rules of exponents to calculate products and quotients of powers with the same base

d) use the rules of exponents to calculate the powers of powers

e) express numbers using scientific notation

f) convert between scientific and standard notation

g) read and write numbers expressed as roots

h) calculate using roots

11. Polynomials

a) add and subtract polynomials

b) multiply and divide polynomials by a monomial

c) remove common factors from polynomials

12. Trigonometry

a) name the parts of a right triangle

b) find the missing side of a right triangle using the Pythagorean Theorem

c.) find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios

d) solve problems using right angle trigonometry

13.Graphing

a) draw a Cartesian co-ordinate system

b) plot and name points in a Cartesian co-ordinate system

c) given an equation in two variables:

i. determine if an ordered pair is a solution

ii. find ordered pairs which are solutions

iii. create a table of values

d) graph linear equations

e) determine the slope of a line given two points on the line

f) relate slope to grade and pitch

g) find x- and y-intercepts

h) solve problems using graphs of linear equations

OR

14. Solve Vocational word problems

**Learning Outcomes:**

Students will meet the competencies for ABE Intermediate Level Developmental Mathematics as stated in the 2014-2015 Articulation Handbook:CORE LEARNING OUTCOMES

1. Estimating Skills/Calculator Use

It is expected that learners will be able to:

a) estimate answers to problems

b) use a scientific calculator to calculate and solve problems involving adding, subtracting, multiplying and dividing whole numbers, fractions and decimals

c) 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:

a) use the common metric units for temperature, length, area, volume/capacity, and mass

b) use the common Imperial units for temperature, length, area, volume/capacity, and force

c) convert between and within metric and Imperial units using tables and/or calculators

d) 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)

e) describe and apply precision, accuracy and tolerance (optional)

f) estimate in metric and Imperial units of measurement (optional)

3. Perimeter, Area, and Volume

It is expected that learners will be able to:

a) find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures by measuring and using formulas

b) find areas of the above shapes by measuring and using formulas

c) find the surface areas of cubes, rectangular solids, cylinders, cones, spheres, and composite solids by using formulas

d) find the volumes of cubes, rectangular solids, cylinders, cones, spheres, and composite solidsby using formulas

e) distinguish between concepts of perimeter and area and their respective units

4. Ratio and Proportion

It is expected that learners will be able to:

a) read, write, interpret, and compare ratios

b) read, write and identify proportions and use them to solve problems

c) use ratio and proportion to interpret and make scale drawings

d) use proportions to solve problems involving similar triangles

5. Percent

It is expected that learners will be able to:

a) use ratios and proportions to solve problems involving:

i. finding percent when part and whole are known

ii. finding part when percent and whole are known

iii. finding whole when part and percent are known

6. Geometry

It is expected that learners will be able to:

a) name and draw points, lines, rays, segments, and angles

b) name and draw triangles, quadrilaterals, other common polygons and circles

c) construct with a compass and straight edge:

i. the perpendicular bisector of a line segment

ii. the bisector of an angle

iii. a copy of an angle (optional)

iv. parallel lines (optional)

v. 30°, 45°, and 60° angles (optional)

d) classify and distinguish among acute, right, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles

e) describe the angle relationships created when parallel lines are cut by a transversal

f) measure angles with a protractor

g) classify triangles according to sides and angles

h) identify similar and congruent figures

7. Statistics

It is expected that learners will be able to:

a) conduct a survey to collect data

b) tabulate the data

c) calculate median, mean, mode, and range

d) graph the data

e) interpolate and extrapolate from the information provided

8. Signed (Rational) Numbers

It is expected that learners will be able to:

a) add, subtract, multiply, and divide signed (rational) numbers

b) demonstrate order of operations with signed (rational) numbers

c) graph signed (rational) numbers on the number line

d) define absolute value

9. Algebra

It is expected that learners will be able to:

a) explain the use of variables

b) evaluate algebraic expressions using substitution

c) combine like terms and remove parentheses

d) solve first degree equations in one variable

e) translate a problem into an equation

f) use equations to solve problems

g) solve simple formulas for one variable

h) use formulas to solve problems

ADDITIONAL LEARNING OUTCOMES Students can opt to complete outcomes 10-13, or complete 14

10. Powers, Roots, and Scientific Notation

a) read and write numbers expressed as powers

b) calculate powers with integral exponent

c.) use the rules of exponents to calculate products and quotients of powers with the same base

d) use the rules of exponents to calculate the powers of powers

e) express numbers using scientific notation

f) convert between scientific and standard notation

g) read and write numbers expressed as roots

h) calculate using roots

11. Polynomials

a) add and subtract polynomials

b) multiply and divide polynomials by a monomial

c) remove common factors from polynomials

12. Trigonometry

a) name the parts of a right triangle

b) find the missing side of a right triangle using the Pythagorean Theorem

c.) find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios

d) solve problems using right angle trigonometry

13.Graphing

a) draw a Cartesian co-ordinate system

b) plot and name points in a Cartesian co-ordinate system

c) given an equation in two variables:

i. determine if an ordered pair is a solution

ii. find ordered pairs which are solutions

iii. create a table of values

d) graph linear equations

e) determine the slope of a line given two points on the line

f) relate slope to grade and pitch

g) find x- and y-intercepts

h) solve problems using graphs of linear equations

OR

14. Solve Vocational word problems

**Grading System:**Letters

**Passing Grade:**D (50%)- a grade of B (75%) is required to study Math 040

**Percentage of Individual Work:**100%

**Text Books:**

Textbooks are subject to change. Please contact the bookstore at your local campus for current book lists.