Section 2.1 Operations with Numbers Objectives: Identify and use properties of Real Numbers.

Evaluate expressions using the Order of Operations expressions.

1) Warm-up on evaluating expressions and sentence readinga. Emphasize how there are grammar rules and the symbols (, ; .) have certain

roles, just like +, -, =. The order you do things is important.2) Classifying real Numbers via number sets (No Way I’m Rational)

a. Humans love to classify things: Animals, foods, cars.b. Mathematicians and humans so they do the same.c. Start with blank Venn diagram and vocab words and fill them in.d. Remind them that something can belong to more than one category.e. Do some examples.

3) Properties of numbers (Addition and Multiplication). They are important because they give us tools to use to solve equations.

a. Closure – You start and end in the real number setb. Commutative – You can move things around without changing the meaningc. Associative – You can move parentheses around without changing the meaningd. Identity – There is a number that won’t change the original value under the

operation (Multiplication has “*1” on one side. Addition has “+0” on one side).e. Inverse - There is a number that will change the original value to the identidy

number under the operation. (Multiplication has “1” or one side. Addition has “0” on one side.)

f. Distributive – Just show what it is4) Order of Operations. Start with demo of laws (gravity, Newton’s 1st Law). These are

indisputable facts that we have discovered. Go back to warm-up of interpreting sentences. Talk about conventions that are developed to understand the written word and how they can be different in different in different cultures. Responsible people got together to develop standards. Same was done with math and the Order of Operations.

a. Explain that languages have a set of rules we use to interpret them.b. Eastern cultures read right to left. Western reads left to right.c. No law of Order of Operations. Just a set of agreed to grammar rules.d. PEMDAS (It’s the grammar rules for reading a mathematical sentence so it

makes sense. So everyone gets the same meaning from it).e. There are a lot of different looking parentheses (grouping symbols). Absolute

value and divisor line are 2 unique ones. Also [ ], { }.f. There are 4 steps, not 6!!!!!!g. Remind them that MD are at the same level and go right to left.h. Remind them that AS are at the same level and go right to left.i. Do lots of examples.j. Go step by step or a few steps at a time. Don’t try and eat the elephant all at

once.k. Stress potential pitfalls with a calculator.l. Practice safe math, use parentheses.

5) Model procedure for solving problems! 6) Model what I expect for homework (what it should look like)7) Start HW as time permits.

HomeworkHW: Section 2.1 Pages 90 – 91: 16-22, 44-52 (even), 56-69, 73

Section 2.1 Operations with Numbers

Section 2.1 Operations with Numbers

TODAY’S GOALS: Identify and use properties of Real Numbers.Evaluate expressions using the Order of Operations.

Warm-up: Evaluate each expression

1) 15−13

2) −3+ 13

3) −3( 13 )

4) −3÷(−13 )

5) (-25)2

6) √25

Interpret these English sentencesTheraininspainfallsmainlyontheplane.

World the in people smartest the are math know who people.

Who two do four we six appreciate eight?

Section 2.1 Operations with Numbers

Classifying Numbers:

Natural Numbers: ______________________________

Whole Numbers: _______________________________

Integers: ______________________________________

Rational Numbers: ______________________________

Terminating Decimals:____________________________

Repeating Decimals:______________________________

Irrational Numbers:_______________________________

You can be more than one thing (Locate the number on the Venn Diagram and see what ovals it is in):

2/3 is ______________________________________

20 is ______________________________________

8888888888222222222222

Section 2.1 Operations with Numbers

Properties of Real Numbers:Property Words Addition MultiplicationClosure

Commutative

Associative

Identity

Inverse

Distributive

Section 2.1 Operations with Numbers

How do we read a Mathematical Sentence? - PEMDAS

Please

Excuse

MyDear

AuntSally

Section 2.1 Operations with NumbersHW

Show each step of Order of Operations

Section 2.1 Operations with NumbersHW Answers