Last-Class-Before-Break Edition...

Algebra I

Today we discussed
We continued our discussion about factoring, and the number of solutions (zeroes, roots) an equation has based upon its degree.  We moved into solving equations.

Remember:

IF  ab = 0, then either a=0 or b=0 or both must be equal to zero.

Sections Covered in Textbook
1)  7-9: Solving Equations by Factoring (pages 290-294)

Video Tutorials
1)  Zero Product Property
http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-strategy-solving-equations/solving-equations/zero-product-property-definition
2)  Solving Equations by Factoring

• http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-strategy-solving-equations/solving-equations/zero-product-property-for-solutions
• https://www.khanacademy.org/math/algebra-home/alg-quadratics/alg-solving-quadratic-equations-by-factoring/v/example-1-solving-a-quadratic-equation-by-factoring

Assignments
1)  No new assignment for break.  Complete semester exam if you haven't done so already.  Download the exam here.

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Pre-Algebra

Today we discussed
We worked on turning fractions into decimals (remember!  a fraction is just a division problem), and we reviewed multiplying fractions and mixed numbers.

Things to remember when multiplying fractions and mixed numbers:

• Turn mixed numbers into fractions first.
• Next, simply by dividing out the Greatest Common Factor (GCF)
• Multiply Numerators
• Multiply Denominators
• Simply, if necessary.

Sections Covered in Textbook
1) 6-1: Writing Fractions as Decimals (pages 204-207)
2) 6-3: Rationals: Multiplying Fractions (pages 211-214)

Video Tutorials
1) Writing Fractions as Decimals

• http://www.virtualnerd.com/middle-math/decimals/representing/fraction-as-decimal-example
• https://www.khanacademy.org/math/arithmetic-home/arith-review-decimals/decimals-to-fractions/v/converting-fractions-to-decimals

2)  Multiplying Fractions and Mixed Numbers

https://www.youtube.com/watch?v=zB7UTvg2VuM 

Assignments
1)  Complete game worksheet on Adding & Subtracting fractions.  Use this assignment as a warm up for Class on January 3rd.  Download worksheet here.

Class Concepts for December 13th

Algebra I

Today we discussed
Our work on factoring polynomials continued today with a discussion of factoring perfect squares.  We also summarized how to factor various types of polynomials and what strategies to use.

Sections Covered in Textbook
1) 7-7: Perfect Squares and Factoring (pages 281-284)
2) 7-8: Summary of Factoring (pages 286-289)

Video Tutorials
1) Shortcut for factoring perfect square trinomials.
http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-special-products/perfect-square-trinomials/perfect-square-trinomial-shortcut
2)  Factoring Polynomials all methods
https://www.youtube.com/watch?v=CATje5knF3k

Assignments
1)  Work on Division Quizlet!  Click here for Quizlet!
2)  Page 288 #'s 17-50 (only problems in the 1st column!)
3)  Review/look over semester exam and be prepared to ask questions in class on Thursday if you need reteaching, clarification or help.  Exam is due by December 31st.

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Today we put all the concepts we have been discussing so far together.  We first reviewed solving simple equations, and the discussed solving simple inequalities.  Finally, we put them all together and solved equations and inequalities using not only whole numbers, but rational numbers (decimals and fractions), too.

Important things to remember:

1. When adding and subtracting fractions, you must have a common denominator.
2. When adding and subtracting decimals, place value is important and you protect place value by lining up the decimal points before adding or subtracting.
3. When working with inequalities, in order to keep the truth of the inequality, you must reverse the sign when multiplying or dividing by a negative number, but only when multiplying or dividing by negatives.  

Sections Covered in Textbook
1)  5-7: Solving Equations and Inequalities (pages 184-187)

Video Tutorials
1)  Solving Equations
https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-one-step-add-sub-equations/v/examples-of-one-step-equations-with-fractions-and-decimals
2)  Solving Inequalities with Decimals
http://study.com/academy/lesson/inequalities-with-decimals.html
3)  Solving Inequalities with Fractions
https://www.youtube.com/watch?v=pwJ4MHwO2fo

Assignments
1)  Work on Division Quizlet!  Click here for Quizlet!
2)  Page 186 #'s 13-39 odd.

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

December 8th Concepts

Algebra I

Today we discussed
We reviewed factoring trinomials both with a leading coefficient of 1 and not 1 and then moved on to factoring the difference of squares.

Recall:

     a²- b² = (a + b)(a - b)

YOU CANNOT FACTOR a² + b²  using any of the methods we've discussed so far....

Sections Covered in Textbook
1) 7-6: Factoirng Difference of Squares (pages 276-280)

Video Tutorials
1) Factoring difference of squares

• http://www.virtualnerd.com/algebra-2/quadratics/solve-equations-by-factoring/factoring-strategies/difference-of-squares-example
• https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-factoring-polynomials-3-special-product-forms/v/factoring-difference-of-squares

Assignments
1) Page 279 #'s 15-39 odd
2)  Work on Division Practice Quizlet!
3)  Complete Semester 1 Exam.  You may turn it in prior to our break, or before we meet again in January.  DEADLINE IS DECEMBER 31st.  You may also submit electronically.  Please make sure your electronic copy is legible.  Email electronic copy to me when you are finished.  Download the exam here.

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We reviewed adding and subtracting rational number (both positive and negative fractions) for both fractions with like denominators and unlike denominators.  There are several cases, and we discussed regrouping and "borrowing/stealing" for some mixed number subtraction problems.

Sections Covered in Textbook
1)  5-6: Rationals:  Adding and Subtracting Unlike Fractions (pages 180-182)

Video Tutorials
1)  Subtracting Mixed Numbers by Regrouping
http://www.virtualnerd.com/middle-math/adding-subtracting-fractions/mixed-numbers/subtract-mixed-numbers-different-denominators-regrouping
2)  Adding Mixed Numbers with Regrouping
https://www.youtube.com/watch?v=_0cs5bHrKNw

Assignments
1) Page 182 #'s 15-29 odd; 36
2)  Work on Division Practice Quizlet!

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Topics for December 6th

Algebra I

Today we discussed
We began our discussion of  factoring trinomials using the "Product-Sum" game.  We covered both scenarios where the leading coefficient is 1 and also NOT 1.

**I encourage everyone to download and watch the Google Slides presentations and review how we work on factoring.  You will need to click on the links below to each presentation (there are TWO), and then open with Google Slides.  Once you have it open, click on the "Present" button near the top right of your computer or tablet screen.  From there, you will be taken through the presentations step-by-step with each mouse click.

** Product-Sum Game (leading coefficient of 1)
https://docs.google.com/presentation/d/1Cj5nsipVPKBWy_pfh1DuEj2PIZdImsE4jPvHwTB-Pcs/edit?usp=sharing
** Product-Sum Game (leading coefficient NOT 1)
https://docs.google.com/presentation/d/1Mgga8LCCofFsQCdYVdbeTTqI-C21FMG8zIWH9qzDR5Y/edit?usp=sharing

Example:  Leading Coefficient NOT 1

Sections Covered in Textbook
1) 7-5: Factoring Trinomials (pages 271-275)

Video Tutorials
1) Factoring Trinomials
http://www.virtualnerd.com/algebra-2/quadratics/solve-equations-by-factoring/factoring-strategies/trinomial-factorization-example
2)  Factoring Trinomials with a term greater than 1
http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/trinomial-factorization/leading-coefficient-not-1/factor-by-a-c-method
(This is not the method I taught in class, but it is a good way to work on these.  It's always good to have multiple ways to solve problems.....)

Assignments
1) Pages 274-275 #'s 23-53 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Today we broadened our discussion of rational number to adding and subtracting fractions.  We focused mainly on problems where the denominators were the same.

Here is an example of adding and subtracting fractions with like denominators:

For more examples, visit my Fractions Examples Page.

Sections Covered in Textbook
1) 5-5: Rationals: Adding and Subtracting Luke Fractions (pages 177-179)

Video Tutorials
1)  Adding and subtracting positive and negative fractions with common denominator:
https://www.youtube.com/watch?v=NYzQHc3rCfM

Assignments
1) Page 178 #'s 11-21 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

OPTIONAL!

Is It Already December? Topics for December 1st

Algebra I

Today we discussed
We discussed two different methods for factoring polynomials - using the GCF and factoring by grouping.  One tricky piece involved expressions that are opposites of one another.

Recall:  (5 - y) = -1(y - 5)

Sections Covered in Textbook
1) 7-2:  Factoring Using the Distributive Property (pages 261-264)
2) 7-3:  Factoring by Grouping (pages 265-268)

Video Tutorials
1)  Factoring by using Greatest Common Factor (GCF)
https://www.youtube.com/watch?v=Y1Vd5wb0rnM
http://www.virtualnerd.com/pre-algebra/factors-fractions-exponents/prime-factorization-greatest-common-factor/greatest-common-factor/factor-out-greatest-common-factor-example
2)  Factoring by Grouping
https://www.youtube.com/watch?v=9hSZEzBmG6M

Assignments
1) Pages 263-264 #'s 23-43 odd
2) Page 267 #'s 21-33 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We figured out how to turn a repeating decimal into a fraction.  Repeating decimals are actually rational numbers!  Also, we reviewed adding and subtracting rational numbers that are in the form of decimal numbers.  Remember, the rules for adding and subtracting integers apply to rationals:

* When adding Rational numbers:
            -->  If the signs are the same, add and keep the sign.
            -->  If the signs are different, subtract and keep the sign of the nubmer
                   with the greater absolute value!


Sections Covered in Textbook
1)  Rationals:  Adding and Subtracting Decimals (pages 174-176)

Video Tutorials
1)  Adding and Subtracting Rational Decimals
https://www.youtube.com/watch?v=WyXXDsRKlWg

Assignments
1)  Page 176 #'s 15-37 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK