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

The Distributive Property Parts 1 and 2

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

Resources & Tutorials:

1) What is the distributive property?

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:

2-6: Solving Two-Step Equations (pages 98-101)

Resources & Tutorials:

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

Solving Equations Using Multiplication and Division

Topics for Today:

We continued our discussion today about inverse operations are, and also further defined the term solution.  We will continue to follow the same processes to solve equations, even as they become more complicated, with more operations and steps.  Because we have to "undo" operations to isolate our variable (get it by itself), we must follow the order of operations, but IN REVERSE!

Vocabulary:

division property of equality, multiplication property of equality, solution

Sections Covered in Textbook:

2-4: Solving Equations by Multiplying or Dividing (pages 88-92)

Resources & Tutorials:

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

Solving Equations Using Addition and Subtraction

Topics for Today:

We began our journey into solving algebraic equations today.  We also discussed what inverse operations are in the context of solving equations.  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 we will continue to integrate fraction and decimal operations into our problem solving.  Equation operations will include all types of real numbers.

Vocabulary:

addition property of equality, subtraction property of equality, inverse operations

Sections Covered in Textbook:

2-3: Solving Equations by Adding or Subtracting

Resources & Tutorials:

1) How to solve an equation using addition.
2) How to solve an equation using subtraction.
3) How to solve a decimal equation using subtraction.

Variables and Algebraic Expressions

Topics for Today:

Our lesson focused on some of the language of Algebra and how words can be translated into algebraic expressions.

Image Credit: https://www.pinterest.com/pin/651473902320727044/

Vocabulary:  variable, algebraic expression, evaluate, equation, open sentence, substitution property of equality

Sections Covered in Textbook:

2-1: Evaluating and Writing Algebraic Expressions (pages 71-76)

Resources & Tutorials:

1) What are numerical and algebraic expressions?
2) Translating mathematical expressions

Precision

Topics for Today:

Today we talked about precision in measurements.  Precision is the degree of exactness we can achieve when measuring something.  The smaller the unit of measurement we use, the more precise our measurement will be.  When we are combining (adding or subtracting) measurements, we can only report our answer using the precision of our least precise measurement.  

In the picture above, the most precise ruler is the last one, because inches are divided into the smallest pieces.  

Vocabulary:

precision

Sections Covered in Textbook:

4-9: Precision (pages 227-230)