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

Adding Real Numbers

Topics for Today:

We used models (number line and integer chips) and rules to add real numbers today.  We talked about the identity property of addition and also talked about inverses.  We also discussed how to use a number line to represent addition problems of both positive and negative integers.  


Vocabulary: identity property of equality, additive inverse, inverse property of addition

Sections Covered in Textbook:

1-4: Adding Real Numbers (pages 24-31)

Resources & Tutorials:

1) How do you add two negative numbers?
2) Rules for Adding Integers
3) What is the opposite of a number?
4) What are identities?

Exploring Real Numbers

Topics for Today:

We are still working on the language of Algebra and using precise words.  Today we discussed the different classifications for numbers and what sets various types of numbers belong to (Natural, Whole, Integers, Rational, Irrational, and Real).  We also reviewed the meaning of absolute value.

Vocabulary: natural numbers, whole numbers, integers, rational number, irrational number, real numbers, inequality, opposites, absolute value

Sections Covered in Textbook:

1-3: Exploring Real Numbers (Pages 17-23)

Resources & Tutorials:

1) What is a real number?
2) What is a rational number?
3) What are natural and whole numbers?

Exponents and Order of Operations

Topics for Today:

As with any language, algebra has some basic rules that must be followed to arrive at a correct answer.  Sometimes there are multiple ways to express an answer or number so we need a set of rules to follow so we always arrive at the same answer for any one particular problem.  The order of operations is a set of rules that tells problem solvers which operations to perform and in what order.

Vocabulary: simplify, exponent, base, power, order of operations (PEMDAS), evaluate 

Sections Covered in Textbook:

1-2: Exponents and Order of Operations (pages 9 - 16)

Resources & Tutorials:

1) What is the order of operations?
2) How do you use the order of operations

Writing Variable Expressions

Topics for Today:

Our Algebra 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, equation, open sentence

Sections Covered in Textbook:

1-1: Using Variables (Pages 4-8)

Resources & Tutorials:

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

Solving Radical Equations

Topics for Today:

We added to our equation solving tools today by working with equations containing radicals.  To solve these equations, we must isolate the variable on one side of the equation.  Once we do that, we can "undo" taking a square root by squaring both sides.  We must be careful when squaring equations so that our process does not result in extraneous (extra) solutions.  It's always best to check our solutions to make sure they satisfy the original equation.  As with many other equation types, we may have a situation where our equation has no solutions.  In Algebra I, we do not work with imaginary numbers (in our class they are the square roots of negative numbers), so if we encounter any of these, our equation has no real solution.

Vocabulary: radical equation, extraneous solution

Sections Covered in Textbook:

11-5: Solving Radical Equations (pages 607-612)

Resources & Tutorials:

1) How do you solve radical equations?
2) How to solve a radical equation with a binomial radicand.

Operations with Radicals and Other Roots

Topics for Today:

We finished our discussion of operations with radical expressions today with a method to simplify fractions with radical operations in the denominator.  We discussed the topic of conjugates to rationalize denominators that fall into this category.

We also discussed different roots other than square roots, and how to find them.

Vocabulary:  conjugate, cube root

Sections Covered in Textbook:

11-4:  Operations with Radical Expressions (pages 600-605)
**Other Root Functions are not in our book.

Resources & Tutorials:

1) Divide by Conjugate Method
2) Math is Fun: Cubes and Cube Roots (not a video).
3) How do you find the cube root of a perfect cube? 
4) Fourth Roots