Solve Applications of Systems, Solve 3x3 Systems Algebraically

 Comic of the Day

"The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill" - Albert Einstein

Announcements

Week 1-2 Quiz (3 attempts) due on Mon Feb 12

Week 3-5 Quiz (3 attempts) due on Mon Feb 12

Next unit exam (Algebraic Functions and Systems) on Mon Feb 12

Seminars

Seminar 5 (Jan 31 or Feb 1) - Train Function Junction (systems of equations)

Pre-lab consists of two questions in Mobius on solving a system of equations for a line between two points, and using function notation to interpret the location of a train as a function of time.

Today - Solve Applications of Systems, Solve 3x3 Systems Algebraically
Instead of finding the intersection of 2 lines, a 3x3 system looks for the intersection of 3 planes:
https://www.geogebra.org/m/uVwfjJjE
Notes from Moodle
Read Algebra and Trig 11.2

For More Information
Systems of Equations Word Problems (great practice exercises and videos)

https://www.khanacademy.org/math/algebra/systems-of-equations-word-problems/e/understanding-systems-of-equations-word-problems

Solving 3x3 systems of equations elimination
http://patrickjmt.com/solving-a-system-of-equations-involving-3-variables-using-elimination-by-addition-example-1/
http://patrickjmt.com/solving-a-system-of-equations-involving-3-variables-using-elimination-by-addition-example-2/
http://patrickjmt.com/solving-a-system-of-equations-involving-3-variables-using-elimination-by-addition-example-3/
http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/systems-of-three-variables
http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/systems-of-three-variables-2
Practice solving 3x3 systems
https://www.geogebra.org/m/j7zRFgks

Next Lecture - Solve 2x2 and 3x3 Systems with Determinants
Pre-read Algebra and Trig 11.8
Watch this 2:38 primer video on determinant of a 3x3 matrix

https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-determinants-and-inverses-of-large-matrices/v/finding-the-determinant-of-a-3x3-matrix-method-1 

Simplify and Operations with Rational Expressions

  Comic of the Day

Tip: Most of math is just a buildup to a good punchline

Announcements

Next unit exam (Algebraic Functions and Systems) on Mon Feb 12

Seminars

Seminar 3 (Jan 24-25) - Rational Equations Card Sort (Desmos)

Pre-lab consists of one long question in Mobius on solving a rational equation, which requires identifying a lowest common denominator, multiplying rational expressions, and factoring to solve.

Today - Simplify and Operations with Rational Expressions
Notes from Moodle
Read Algebra and Trig 1.6

For More Information
Simplifying Rational Expressions
http://patrickjmt.com/rational-expressions-writing-in-lowest-terms-ex-1/
http://patrickjmt.com/rational-expressions-multiplying-and-dividing-ex-1/
https://www.khanacademy.org/math/algebra/rational-expressions/simplifying-rational-alg/e/dividing_polynomials_by_binomials_1
https://www.khanacademy.org/math/algebra/rational-expressions/simplifying-rational-alg/e/simplifying_rational_expressions_2
https://www.khanacademy.org/math/algebra/rational-expressions/simplifying-rational-alg/e/simplifying_rational_expressions_3
Multiply and Divide Rational Expressions
https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/multiplying_and_dividing_rational_expressions_1
https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/multiplying_and_dividing_rational_expressions_2
https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/multiplying_and_dividing_rational_expressions_3
https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/multiplying_and_dividing_rational_expressions_4
https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/multiplying_and_dividing_rational_expressions_5
http://patrickjmt.com/rational-expressions-multiplying-and-dividing-ex-1/
http://patrickjmt.com/rational-expressions-multiplying-and-dividing-ex-2/
http://patrickjmt.com/rational-expressions-multiplying-and-dividing-ex-3/
Adding and Subtracting Rational Expressions
http://patrickjmt.com/rational-expressions-adding-and-subtracting/
http://patrickjmt.com/rational-expressions-adding-and-subtracting-ex-1/
http://patrickjmt.com/rational-expressions-adding-and-subtracting-ex-2/
https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/adding_and_subtracting_rational_expressions_0.5

https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/adding_and_subtracting_rational_expressions

https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/adding_and_subtracting_rational_expressions_1.5

https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/adding_and_subtracting_rational_expressions_2

https://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/e/adding_and_subtracting_rational_expressions_3

Next Lecture - Rational Equations
Pre-read Algebra and Trig 2.2, 2.6
Watch this 5:11 primer video on solving rational expressions
https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/equations-with-two-rational-expressions

Quadratic Formula and Graphs of Quadratic Functions

Comic of the Day

Tip: Use tests and quizzes as an opportunity to demonstrate what you learned in class.  Failing that, use your sense of humour.

Announcements

Next unit exam (Algebraic Functions and Systems) on Mon Feb 12

Seminars

Seminar 2 (Jan 17-18) - Fire Control (Excel) PRE-LAB REQUIRED

Today - Quadratic Formula and Graphs of Quadratic Functions
Notes from Moodle
Read Algebra and Trig 2.5, 5.1
Standard form y=ax²+bx+c
Factored form y=a(x-x1)(x-x2)
Vertex form y=a(x-h)²+k

For More Information
Solving quadratic equations by factoring
http://patrickjmt.com/solving-quadratic-equations-by-factoring-basic-examples/
http://patrickjmt.com/solving-quadratic-equations-by-factoring-another-example/
Using the quadratic formula to solve quadratic equations
http://patrickjmt.com/using-the-quadratic-formula/
http://patrickjmt.com/deriving-the-quadratic-formula/
http://patrickjmt.com/solving-quadratic-equations-using-the-quadratic-formula-ex-1/
http://patrickjmt.com/solving-quadratic-equations-using-the-quadratic-formula-ex-2/
http://patrickjmt.com/solving-quadratic-equations-using-the-quadratic-formula-ex-3/

Graphing quadratics

http://www.khanacademy.org/math/algebra/quadtratics/v/graphing-a-quadratic-function/

http://patrickjmt.com/graphing-quadratic-functions-ex-1/
http://www.khanacademy.org/math/algebra/quadratics/e/graphing_parabolas_0.5
http://www.khanacademy.org/math/algebra/quadtratics/e/graphing_parabolas_1
http://www.khanacademy.org/math/algebra/quadratics/v/graphs-of-quadratic-functions
http://www.khanacademy.org/math/algebra/quadratics/v/quadratic-functions-3

Next Lecture - Simplify and Operations with Rational Expressions
Pre-read Algebra and Trig 1.6
Watch this 4:36 primer video on subtracting rational expressions

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/adding-and-subtracting-rational-expressions/v/adding-and-subtracting-rational-expressions-3 

Operations with Radical Expressions

 Comic of the Day

Tip: Don't be ashamed of your mathletic prowess

Announcements
Getting to Know You questionnaire due Mon Jan 15 at 4pm
Incoming Student Assessment (optional, to collect data to compare incoming students from different programs and over time)

Next unit exam (Algebraic Functions and Systems) on Mon Feb 12

Seminars

Seminar 2 (Jan 17-18) - Fire Control (Excel) PRE-LAB REQUIRED

Today - Operations with Radical Expressions
Notes from Moodle
Read Algebra and Trig 1.3

For More Information
Simplifying radicals
http://patrickjmt.com/simplifying-numbers-under-square-roots/
http://patrickjmt.com/radical-notation-and-simplifying-radicals/
http://patrickjmt.com/radicals-simplifying-radical-expressions-involving-variables-ex-1/
https://www.khanacademy.org/math/arithmetic/exponents-radicals/radical-radicals/e/simplifying_radicals
https://www.khanacademy.org/math/arithmetic/exponents-radicals/radical-radicals/e/multiplying_radicals
Rationalizing Denominators
http://patrickjmt.com/rationalize-the-denominator/
http://patrickjmt.com/rationalizing-the-denominator-ex-1/
https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/how-to-rationalize-a-denominator
Adding and Subtracting Radicals
https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/adding-and-simplifying-radicals
https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/subtracting-and-simplifying-radicals
More rationalizing denominators
http://patrickjmt.com/rationalizing-the-denominator-ex-3/
https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/how-to-rationalize-a-denominator

Next Lecture - Quadratic Formula and Graphs of Quadratic Functions

Pre-read Algebra and Trig 2.5, 5.1
Watch this 5:34 primer on using the quadratic formula
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/v/quadratic-formula-1

Fraction Operations, Exponents, Simplify Radicals

  Comic of the Day

Tip: Know your roots

Announcements
Getting to Know You questionnaire due Mon Jan 15 at 4pm
Incoming Student Assessment (optional, to collect data to compare incoming students from different programs and over time)

Next unit exam (Algebraic Functions and Systems) on Mon Feb 12

Seminars

Seminar 2 (Jan 17-18) - Fire Control (Excel) PRE-LAB REQUIRED

Today - Fraction Operations, Exponents and Simplify Radicals
Notes from Moodle
Read Algebra and Trig 1.3

For More Information
Exponent Property Review (Exercises)
https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-exp-prop-review/e/exponent_rules
https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-exp-prop-review/e/powers-of-powers-int-exp
https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-exp-prop-review/e/properties-of-integer-exponents
Fractional Exponents
https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/rational-exponents-intro/v/basic-fractional-exponents
https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/rational-exponents-intro/v/rewriting-roots-as-rational-exponents
Simplifying radicals
http://patrickjmt.com/simplifying-numbers-under-square-roots/
http://patrickjmt.com/radical-notation-and-simplifying-radicals/
http://patrickjmt.com/radicals-simplifying-radical-expressions-involving-variables-ex-1/
https://www.khanacademy.org/math/arithmetic/exponents-radicals/radical-radicals/e/simplifying_radicals
https://www.khanacademy.org/math/arithmetic/exponents-radicals/radical-

Next Lecture - Operations with Radical Expressions
Pre-read Algebra and Trig 1.3
Watch this 4:57 primer video on rationalizing denominators of radical expressions

https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/miscellaneous-radicals/v/rationalizing-denominators-of-expressions

Factoring quadratics

 Comic of the Day

Tip: It's a trap!  There's a better flowchart for factoring on Moodle anyway

Announcements

Introduction to Desmos activity and Seminar 1 Pre-lab due before your first seminar

"Getting to  Know You" questionnaire now available on Brightspace

Next unit exam (Algebraic Functions and Systems) on Mon Feb 12 (BYOFS)

Seminars
Introduction to Desmos (on your own time)

Seminar 1 (Jan 10-11) - Sporting Goods Factory (Desmos) PRE-LAB REQUIRED

Today - Factoring quadratics
Business index cards (write your preferred name and registered name)

Demonstrate expanding (x+3)(x+4) including area model

What do we have to multiply to get (....)(....)=x² + 10x + 16  ?

Random groups

Each group will work on one problem strip at a time, when you are done go to the pile and swap it for a different one.

Consolidation into meaningful notes for your future forgetful self

• Fill in the blank steps to factor 4x²+5x-6
• Practice factoring 4x²-12x+9 in any way
• Choose your own adventure (come up with your own example)
• Things to remember (hints, patterns, steps, etc.)

Notes from Moodle
Read Algebra and Trig 1.5

Next Lecture - Fraction Operations, Exponents, Simplify Radicals
Pre-read Algebra and Trig 1.3
Watch this 4:59 primer on rational (fractional) exponents
https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/introduction-to-rational-exponents-and-radicals/v/basic-fractional-exponents

For More Information
Factoring Videos
http://patrickjmt.com/factoring-a-number/
http://patrickjmt.com/finding-the-greatest-common-factor-gcf/
http://patrickjmt.com/factoring-using-the-great-common-factor-gcf-ex-1/
http://patrickjmt.com/factoring-by-grouping/
http://patrickjmt.com/factoring-by-grouping-ex-1/
http://patrickjmt.com/factoring-by-grouping-ex-2/
http://patrickjmt.com/factoring-trinomials-a-quadratic-trinomial-by-trial-and-error/
http://patrickjmt.com/factoring-trinomials-by-trial-and-error-ex-2/
http://patrickjmt.com/factoring-trinomials-factor-by-grouping-ex-1/
http://patrickjmt.com/factoring-trinomials-factor-by-grouping-ex-2/
https://www.khanacademy.org/math/algebra2/polynomial-functions/factoring-polynomials-quadratic-forms-alg2/v/factoring-trinomials-by-grouping-4
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/v/factoring-quadratic-expressions
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/v/factoring-polynomials-1
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/v/factoring-trinomials-with-a-leading-1-coefficient
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/e/factoring_polynomials_1
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/e/factoring_polynomials_2
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-by-grouping/v/factor-by-grouping-and-factoring-completely

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-by-grouping/v/factoring-trinomials-with-a-non-1-leading-coefficient-by-grouping  

Notation, Units, Solving Formulas

  Comic of the Day

Tip: Notation is everything

Announcements
Introduction to Desmos activity and Seminar 1 Pre-lab due before your first seminar

Next unit exam (Algebraic Functions and Systems) on Mon Feb 12 (BYOFS)

Seminars
Introduction to Desmos (on your own time)

Seminar 1 (Jan 10-11) - Sporting Goods Factory (Desmos) PRE-LAB REQUIRED

Today - Notation, Units, Solving Formulas
Week 1 notes (blank and annotated key on Moodle)

For More Information
Scientific Notation
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-scientific-notation/e/scientific_notation
Significant Figures (Digits)
https://www.khanacademy.org/math/arithmetic/decimals/significant_figures_tutorial/e/significant_figures_1
Converting Units
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-unit-conversion/e/converting-units
Rearranging Formulas
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/e/manipulating-formulas

Next Lecture - Factoring quadratics
Pre-read A&T 1.5
Watch this 3:54 primer video on factoring quadratics
https://www.khanacademy.org/math/algebra2/polynomial-functions/factoring-polynomials-quadratic-forms-alg2/v/factoring-trinomials-by-grouping-4