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MJ3 Ch 1.2 – Variables, Expressions & Properties.

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1 MJ3 Ch 1.2 – Variables, Expressions & Properties

2 Bellwork Write the order of operations, then evaluate the following: 1. 15 – 5 + 9 – 2 = 2. 6 x 3  9 = 3. 12 + 20  4 – 5 =

3 Before we begin… Please put your bellwork away and take out your notebook About Notes – On a daily basis, you will begin writing notes with the date in the upper right hand corner. When you write the date you will copy it from the board verbatim! (word for word) Skip a line then write either the word Objective or OBJ – underline the word, then write today’s objective

4 Before we begin… Skip a line and indent and write the main heading of what we will discuss…you will find the main heading at the top of the PowerPoint page When taking notes you may abbreviate or paraphrase the concept. When abbreviating make sure you know what the abbreviation stands for… Always write the example…this will help you when you do your homework and study for tests

5 Before we begin… After all the notes are taken for the lesson…skip a line Write and underline the word Summary, then skip a line and indent. Here you will summarize, on a daily basis and in your own words, the concepts we covered in class. This is useful when studying…

6 How can the summary be useful when studying?  To review for a test read the summaries first. If you already know the material you can skip that section.  If you don’t know the material re-read your notes and choose some sample problems from the text section. Work on that until you are comfortable with the material.  To be effective when studying…you don’t spend time on what you know….you spend your time going over what you DON’T know!

7 Assignment Review None

8 Objective Students will evaluate expressions and identify properties

9 Vocabulary Variable – A symbol, usually a letter, used to represent a number. Example:4 x n (n is the variable) Algebraic Expression – An expression that contains a number, a variable and at least one operation (+, -, x,  ) Example:4 x n Numerical Expression – When you replace the variable with a number the algebraic expression becomes a numerical expression Example: n = 104 x 10 is a numerical expression

10 Vocabulary Evaluate – When you evaluate an expression you find its numerical value Example: n = 104 x n = 4 x 10 = 40 Order of Operations – To avoid confusion when evaluating expressions you use the order of operations.

11 Order of Operations It is expected that you already know the order of operations Please raise you hand if you can give me the order of operations.

12 Order of Operations The order of operations are as follows: 1. Do all operations within grouping symbols first; start with the innermost grouping symbols 2. Evaluate all powers 3. Multiply and divide in order from left to right 4. Add and subtract in order from left to right There is a device called a mnemonic that is used to remember the order of operations…its PEMDAS The mnemonic is:  Please Excuse My Dear Aunt Sally.

13 Strategy It is expected that you have already memorized the order of operations…If not, when taking tests or doing homework write the mnemonic for the order of operations on your paper and cross each item off as you complete it

14 Example Evaluate: 8 + 5 x ( 12 – 6  3) 8 + 5 x (12 – 2) 8 + 5 x 10 8 + 50 = 58 P E M D A S Write the mnemonic in this format 1. Do Parenthesis First, then cross off P 2. There are no exponents so you can cross it off 3. Multiply and cross off M. There is no division so just cross it off 4. All that’s left is to add. Then cross of A and S

15 Your Turn In the notes section of your notebook write and evaluate each of the following: 1. (9 + 6)  5 x 4 + (3 – 2) 2. 2 + 3 x (18 – 7)

16 Multiplication and Algebra If you don’t already know… there are 4 different ways to write multiplication in Algebra 8 ∙ 53(2)4n(x)(y) Notice that the x symbol is not used in algebra. That is to prevent confusion with the variable x At the 8 th grade level you are required to be able to recognize these multiplication formats AND know how to work with them.

17 Exponents Numbers with an exponents are called powers. The power or exponent represents repeated multiplication. The exponent tells the base how many times to multiply itself!

18 Example 7 2 (Seven squared) means to multiply seven (base) 2 times (exponent) Here is what it looks like: 7 2 = 7 ∙ 7 = 49 Here is what it DOES NOT look like: 7 2 = 7 ∙ 2 = 14

19 Comment Students seem to have a difficult time with exponents… For some reason (that I don’t get)…they always want to multiply the base time the exponent… If you do that I will mark the problem wrong! You need to figure a way for you to remember that exponents/powers are repeated multiplication!...If you come up with a way…please let me know!

20 Your Turn In the notes section of your notebook write and evaluate the following: 1. 8 2 2. 5 3 3. 10 5

21 Evaluating Algebraic Expressions To evaluate algebraic expressions use the following process: 1. Write the expression 2. Substitute 3. Do the math

22 Example Evaluate 4a – 3b + 1 where a = 5, b = 4 1. Write the expression4a – 3b + 1 2. Substitute4(5) – 3(4) + 1 3. Do the Math20 – 12 + 1 8 + 1 = 9 Note: In the 3 rd step you use the order of operations!

23 Your Turn In the notes section of your notebook write and evaluate the following when m = 9, n = 2 and p = 5 (Use the process and make sure that you show your work) 1. 25 – 5p 2. n 2 + 5n - 6

24 Equations A mathematical sentence that contains an equal sign (=) is called an equation. Examples: 7 + 5 = 153(6) = 18x + 2 = 5

25 Equations An equation that contains a variable is called an open sentence. When a number is substituted for a variable in an open sentence, the sentence is true or false

26 Example Consider the equation x + 2 = 5 If you substitute 2 for x you get 2 + 2 = 5, which is false 4 ≠ 5 If you substitute 3 for x you get 3 + 2 = 5, which is true 5 = 5

27 Comment The reason that you need to know about open sentences and true or false sentences is because when solving algebraic equation you are looking for the solution that makes the statement true.

28 Whew!…we are almost done…

29 Summary We have covered a lot of material today…hopefully this is a review for you… In the notes section of your notebook, in bullet fashion summarize the key concepts covered in today’s lesson. To help you with this I will do today’s summary…starting tomorrow you will do it…

30 Summary  Order of Operations (PEMDAS) tells the order in which to evaluate expressions  Reviewed different ways to show multiplication in algebra  Reviewed powers/exponents – repeated multiplication – the exponent tells the base how many times to multiply itself  Evaluated algebraic expressions with process: 1. Write expression 2. Substitute 3. Do the math  Solved equations to determine if true or false

31 Assignment Text p. 14 #14 – 39 Reminder  I do not accept answers only for assignments…you must write the problem and show how you got your answer…  Check your answers to the odd problems in the back of the book…  If you don’t know how to do something…at minimum you must write the problem and what you don’t understand…  This assignment is due tomorrow. I do not accept late assignments

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