Solving Equations with Variables on Both Sides

Topics for Today:

Our discussion about solving equations moved on to situations where there are variables on both sides of an equation.  The basic properties of equality still apply when dealing with variable terms.  We used the addition, subtraction, multiplication, and division properties of equality to get variables on one side, and constants on the other side of the equation.  For equations with variables on both sides, it is possible for the equation to have infinitely many solutions (identity) or no solution at all.  Students will need to be on the lookout for these special cases, which show themselves is interesting mathematical ways.

Sections Covered in Textbook:

2-4: Equations with Variables on Both Sides (pages 96-100)

Resources & Tutorials:

1) Solving Equations with Variables on Both Sides
2) Solving Equations with Variables on Both Sides and Grouping Symbols

Solving Multi-Step Equations

Topics for Today:

We moved on from two-step to multi-step equation solving.  Today's lesson focused on simplifying with grouping symbols, and multiplying through to eliminate fractions and decimals to make the equation easier to solve.

Sections Covered in Textbook:

2-3: Solving Multi-Step Equations (pages 88 - 93)

Resources & Tutorials:

1) Solving Multi-Step Equations using Distributive Property
2) Solving Multi-Step Equations by Clearing Fractions

Solving Two-Step Equations

Topics for Today:

Our discussion about solving equations moved on to solving 2-step equations.  The order of operations still figures in to this process, although since we are undoing operations, we go in reverse.

Sections Covered in Textbook:

2-2: Solving Two-Step Equations (pages 81- 86)

Resources & Tutorials:

1) How do you solve a 2-step equation?
2) Math Antics - How to solve 2-step equations.

Solving One-Step Equations

Topics for Today:

Today we reviewed solving one-step algebraic equations.  We discussed what inverse operations are, and also defined the term solution.  Students are reminded that all they are accountable for all the mathematics that came before this class, as well as any new learned material.  Mathematics is a cumulative subject, and the skills built in the past will continue to be used to solve new problems.  That means that we will continue to integrate fraction and decimal operations into our problem solving.  Equation operations will include all types of real numbers.

Sections Covered in Textbook:

2-1: Solving One-Step Equations (pages 74-79)

Resources & Tutorials:

1) Math Antics - How to Solve a 1-step Equation.
2) How to solve an equation using addition.
3) How to solve an equation using subtraction.
4) How to solve an equation using multiplication.
5) How to solve an equation using division.
6) How to solve a decimal equation using subtraction.
7) How to solve an equation when multiplying fractions. 

Chapter 1 Review

Topics for Today:

Today we played a game of Money Grab to finish up our review of Chapter 1.  Students should make sure their binders are fully organized prior to joining class on Thursday.  Binders will be collected at the beginning of class.  For a list of topics that need to be in the notebook, open the Chapter 1 Table of Contents Google Docs that I have shared with you from the Chapter 1 folder.  

Topics covered in Chapter 1:  Using variables, order of operations, classifications of real numbers, real number operations (adding, subtracting, multiplying, and dividing), as well as the properties of equality.  

Sections Covered in Textbook:

Chapter 1:  Tools of Algebra (pages 4-58) - Omit section 1-9

Resources & Tutorials:

The Distributive Property

Topics for Today:

Today we discussed the distributive property  of multiplication over addition and subtraction.  We also used the distributive property to multiply large numbers using mental math.  We also discussed how to combine algebraic like terms, and expanded our algebra vocabulary.  We revisited translating phrases into algebraic expressions with the addition of the distributive property.

Vocabulary: constant, like terms, distributive property, coefficient, term

Sections Covered in Textbook:

1-7: The Distributive Property (pages 47 - 52)

Resources & Tutorials:

1) What is the distributive property?

Multiplying and Dividing Real Numbers

Topics for Today:

Earlier this week we took our first quiz of the year.  How did it go?  Did you properly prepare?  If not, what improvements can you make for the future?  Students will be allowed and expected to complete quiz corrections for partial credit.  Quizzes are meant as assessment and learning tools.  Students should always be asking, "How can I do better?".

We moved on to multiplying and dividing real numbers today.

Some basic sign rules for multiplication and division:

+ · + = +      + / + = +
+ · - = -      + / - = -
- · + = -      - / + = -
- · - = +      - / - = +

Vocabulary: Identity property of Multiplication, Multiplication Property of Zero, Multiplication Property of -1, Inverse Property of Multiplication, multiplicative inverse, reciprocal

Sections Covered in Textbook:

1-6: Multiplying and Dividing Real Numbers (pages 37 - 44)

Resources & Tutorials:

1) How do you multiply and divide numbers with different signs?
2) What are Multiplicative Inverses?
3) What is a reciprocal?

Subtracting Real Numbers

Topics for Today:

We continued our discussion of adding real numbers (both positive and negative) using a number line and integer chips.  Our rules for addition are:

• If the signs are the same, add and keep the sign.
• If the signs are different, subtract and keep the sign of the number with the larger absolute value.  

Stated another way...

Subtraction is actually the addition of opposites!  

For subtraction problems, first change to addition by adding the opposite, then follow your addition rules!  

                  6 – 10 =

              6 + (-10) =  

Subtract 6 from 10 and keep the negative sign because |-10| > |6|

Therefore, the answer is – 4. 

Sections Covered in Textbook:

1-4: Adding Real Numbers (pages 24-31)
1-5: Subtracting Real Numbers (pages 32-36)

Resources & Tutorials:

1) How do you add two negative numbers?
2) Rules for Adding Integers
3)  How to rewrite a subtraction problem as addition