Quadratic Functions - March 31st

Topics for Today:

Quadratic functions are still the topic of the day.  Today we worked with the axis of symmetry and used it to find our vertex.  Because parabolas are symmetric, we are able to find points on one side of the axis of symmetry and reflect them to the other side of the axis of symmetry.  Once we have the vertex, and a few points on either side of the axis of symmetry, we can easily draw our parabola.

Sections Covered in Textbook:

10-2: Quadratic Functions (pages 517-523)

Resources & Tutorials:

1) How do you find the axis of symmetry?
2) Find the axis of symmetry and your vertex
3) Quadratic Functions Class notes
4) Video recording of today's class

Assignments:

Quadratic Functions Worksheet

Exploring Quadratic Graphs - March 30th

Topics for Today:

Today we began our work on quadratic functions.  Quadratic functions, simply stated, are functions that have a variable with the highest degree exactly equal to two.  We looked at the standard form of a quadratic function and looked at graphs of different parabolas.

Vocabulary: quadratic function, standard form of a quadratic function, parabola, axis of symmetry, vertex, minimum, maximum

Sections Covered in Textbook:

10-1: Exploring Quadratic Graphs (pages 510-516)

Resources & Tutorials:

1) What is a quadratic function?
2) What is a parabola?
3) Video Recap of Exploring Graphs Lesson (sound is not great!)
3) Class Notes - Exploring Quadratic Graphs

Assignments:

1) Exploring Quadratic Graphs Worksheet
2) Chapter 9 Test Corrections due Tuesday

Chapter 9 Test - March 26th

Topics for Today:

Today we took a test on Chapter 9.  Remember that the purpose of a test is to find out where you have gaps in understanding.  Tests are a learning tool and should be viewed as such.  Because of this approach, test corrections are encouraged.  The best way to learn is through failure.  Making mistakes is a part of life; how you deal with failure and mistakes will define you as a person.

Tests are to be submitted through Google Classroom.  If you are unsure of how to do this, please ask.   Tests are due by midnight tonight. 

Sections Covered in Textbook:

None

Resources & Tutorials:

Find the test on Google Classroom - turn the test in there. 

Assignments:

Tests due by Midnight tonight.
Go outside and play!

Chapter 9 Review - March 25th

Topics for Today:

Today we wrapped up our discussion of polynomials and factoring, and we discussed degrees of polynomials, names for them based upon the number of terms.  We also covered multiplying binomials and polynomials as well as factoring.  Students were given a review sheet to help organize and prepare for the chapter test tomorrow.  I will be available tonight by appointment if anyone needs extra help.

Sections Covered in Textbook:

Chapter 9:  Polynomials and Factoring (pages 455-506)

Resources & Tutorials:

1) Chapter 9 Review Sheet Answers
2) Answers to Summary of Factoring HW

Assignments:

1) Chapter 9 Review Sheet
2) Chapter 9 Test tomorrow

Summary of Factoring Part 2 - March 24th

Topics for Today:

Today we used our strategies to review factoring of all types.  Students are clearly rusty with these topics so we'll spend a full day tomorrow reviewing all concepts for Chapter 9 before we move on with our test.

Sections Covered in Textbook:

No new sections were covered today.

Resources & Tutorials:

1)  Factoring Decision Tree
2)  Answers to Summary of Factoring Part 1

Assignments:

1)  Complete the 2nd column of the Summary of Factoring Worksheet.
2)  Chapter 9 Test on Thursday.
3)  OPTIONAL:  Delta Math Multiplying Binomials

Summary of Factoring - March 23rd

Topics for Today:

We have completed work in Chapter 9, and are reviewing all the concepts for factoring.  Students practiced decision-making, and which different processes we can use to factor polynomials.  We will tackle this topic over two days, and students will first determine the factoring method and why they chose that method, and on the second day, we'll actually do the factoring work. 

Sections Covered in Textbook:

No new sections covered.

Resources & Tutorials:

1)  Class Notes - Summary of Factoring
2)  Factoring Decision Tree

Assignments:

1. Summary of Factoring Worksheet (Grey column only). 
2. Delta Math:  Factoring - Determining First Step RACE!

Getting Started on Zoom - March 19th

Topics for Today:

Our main goal for today was to get everyone connected via Zoom and to check in with each other.  Mission accomplished!  It was so nice to see everyone and I'm looking forward to completing our Algebra year together. 

Sections Covered in Textbook:

No new sections were covered today.

Resources & Tutorials:

1)  Delta Math Website 

Assignments:

Complete the three lessons on Delta Math.  Everything is due by Monday at 12pm.  Please ignore the note about late credit - I am still learning how this thing works!

Your student page should look like this:

Factoring Special Cases - March 12th

Topics for Today:

We are back to pattern recognition for factoring.  When we multiplied binomials by squaring them or by multiplying a difference, we noted a pattern for the resulting products.  Today, we worked backward from the trinomial (in the case of perfect square trinomials) or the binomial (in the case of difference of squares) to determine the two binomial factors. 

Students are reminded that now would be a good time to memorize the common perfect squares.  We also talked about square roots in the context of being the opposite of squaring numbers.  We'll deal with radicals a little later on, in May. 

For perfect square trinomials, students should be asking the questions:

• Is the first variable term a perfect square?
• If yes, is the constant term a perfect square?
• If yes, is the middle term equal to two times the square roots of the first and third terms?

What about factoring difference of squares?  We have another pattern to follow for this type of polynomial.  For the difference of squares, students should be asking the questions:

• Is the variable piece a perfect square?
• Is the constant piece a perfect square?
• Is the operation being performed subtraction?

Sections Covered in Textbook:

9-7: Factoring Special Cases

Resources & Tutorials:

1) How to use a shortcut to factor a perfect square trinomial
2) How do you factor using the difference of squares

Assignments:

1) Factoring Special Cases Worksheet

Factoring Trinomials Part 2 - March 11th

Topics for Today:

We expanded our discussion today to include factoring polynomials where the leading coefficient is not 1.  We used the product-sum game to work with factors so we could "split the middle" of the equation, and then factor by grouping.

Sections Covered in Textbook:

9-6: Factoring Trinomials of the type ax² + bx + c (where a ≠ 1)

       (pages 486-489)

Resources & Tutorials:

1) Factor a trinomial using A-C method
    (This is a different method from what was introduced in class.)
2) Factor a trinomial with a > 1
    (This method is more like what was introduced in class.)

Assignments:

Factoring Trinomials Part 2 Worksheet

Factoring Trinomials Part 1 - March 10th

Topics for Today:

Our discussion about factoring moved to factoring trinomials today.  We played a game called the "Product-Sum" game where we analyzed a set of two numbers to see what factors create both a product and a sum.  We then related this game to how we factor trinomials.  We will always be looking to create a product (answer to a multiplication problem) and a sum (answer to an addition problem) at the same time.  Notice the coefficient that precedes the first term is one.  We'll address scenarios where the leading coefficient is NOT one in tomorrow's lesson.

Sections Covered in Textbook:

9-5: Factoring Trinomials of the type ax² + bx + c (where a=1)
       (pages 481-485)

Resources & Tutorials:

1) How do you factor a trinomial?
2) How to factor quadratic equations.

Assignments:

Factoring Trinomials Part 1 Worksheet

Factoring by Grouping - March 9th

Topics for Today:

We continued our discussion of factoring polynomials today with a brief review of the Greatest Common Factor (GCF) and how we can divide the GCF out of a polynomial by using the distributive property in reverse.

Over the next several days we will tackle factoring of many different scenarios.  Factoring by grouping is a method than is used to deal with polynomials that have more than three terms.  Most people are familiar with factoring trinomials (3-terms), so when we are faced with more factors, our options are limited for how we can proceed.

In factoring by grouping, we will take two sets of two terms and pull out/factor out a GCF.  The goal is to have a leftover quantity for both groups that match one another.  If we do get our desired outcome, then we can further factor out the quantity, leaving us with a product of two binomials.

Sections Covered in Textbook:

9-8:  Factoring by Grouping (pages 496-501)

Resources & Tutorials:

1) How do you factor a 4-term polynomial by grouping?
2) The easiest way to factor a polynomial with four terms by grouping.

Assignments:

1) Factoring by Grouping Worksheet

Multiplying Special Cases - March 5th

Topics for Today:

We expanded our discussion on multiplying binomials today to include some common patterns:  squaring sums, squaring differences, and the product of a sum and a difference.  For each of these cases, we can always use the distributive property or FOIL methods to expand the product; however, as with many aspects in mathematics, recognizing patterns can save a lot of time.

Sections Covered in Textbook:

Multiplying Special Cases (pages 474-479)

Resources & Tutorials:

1) What is the formula for the square of a sum?
2) What is the formula for the square of a difference?
3) What's formula for the product of a sum and a difference?

Assignments:

1) Multiplying Binomials Special Cases worksheet

Multiplying Binomials - March 4th

Topics for Today:

Our topic for today was multiplying polynomials.  We focused our time mostly on multiplying two binomials together (recall that a binomial is the sum or difference of two monomials).  We focused on the number of individual products to ensure we did not leave any steps out.  Most people are familiar with the FOIL method for multiplying two binomials:

Sections Covered in Textbook:

9-3: Multiplying Binomials (pages 467-472)

Resources & Tutorials:

1) Multiply Binomials using the Distributive Property
2) Multiply Binomials using the FOIL method
3) How to Multiply Trinomials 

Assignments:

1) Multiplying Binomials worksheet
2) Chapter 8 Test Corrections due tomorrow

Multiplying and Factoring - March 3rd

Topics for Today:

We explored multiplying a monomial by a polynomial today, and doing the reverse by factoring out the greatest common factor.  Multiplying and factoring are inverse (opposite) operations of each other.

Vocabulary: Greatest Common Factor, GCF

Sections Covered in Textbook:

9-2: Multiplying and Factoring (pages 462-465)

Resources & Tutorials:

1) How do you multiply a monomial by a polynomial?
2) How do you find the Greatest Common Factor (GCF) of monomials?
3) Factoring Monomials from Polynomials

Assignments:

Multiplying and Factoring worksheet

Adding and Subtracting Polynomials - March 2nd

Topics for Today:

Today we began our unit on polynomials with some definitions.  We also worked on adding and subtracting polynomials.  Like working with any variable expressions, we must always look for like terms when combining their components.  Variables raised to different powers cannot be combined by adding and subtracting.  One last concept to keep in mind is that when subtracting polynomials, you must subtract each piece of the polynomial; that is, the subtraction must be distributed to each piece of the polynomial and not just its first term.

Vocabulary:  monomial, degree of a monomial, polynomial, standard form of a polynomial, degree of a polynomial, binomial, trinomial

Sections Covered in Textbook:

9-1: Adding and Subtracting Polynomials (pages 456-461)

Resources & Tutorials:

1)  What is a monomial? 
2)  What is a polynomial? 
3)  How do you find the degree of a polynomial?
4)  How do you add polynomials? 
5)  How do you subtract polynomials? 

Assignments:

Adding and subtracting polynomials worksheet