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)

Changing Units in the Customary System

Topics for Today:

Today we discussed units of measurement in the customary system, and the various equivalent units.  We also used equivalent measurements to convert between measurements.  

When changing from one unit to another, we consider 3 things:

• Unit conversion (ex 1 foot = 12 inches)
• Are we converting from smaller units to larger units (inches to feet) --> Divide
  or are we converting from larger units to smaller units (feet to inches) --> Muliply
• Final step is to complete the arithmetic

Vocabulary:

customary system

Sections Covered in Textbook:

4-8:  Changing Units in the Customary System (pages 222-226)

Resources & Tutorials:

1) What are the customary units of length?

2) What are the customary units of capacity?

3) How do you convert cups to pints?

4) What are the customary units of weight?