Algebra! The area of mathematics that generalizes the concepts and rules of arithmetic using symbols to represent numbers

What is arithmetic?  Addition  Subtraction  Multiplication  Division  Exponents

What are some examples of symbols you see inside and outside of school?

In algebra, we use different symbols that we call variables  Many times, you will use letters as your symbol X, a, b, c, etc.  Sometimes you may see some Greek alphabet letters β = beta

How to set a problem up!  Add three to a number  A number plus 3  The sum of a number and 3  3 more than a number  A number increased by 3

How to set up a problem!  Subtract 12 from a number  A number minus 12  The difference of a number and 12  12 less than a number  A number decreased by 12  Take away 12 from a number  A number less 12

Set up the problem!  2 times a number  2 multiplied by a number  The product of 2 and a number

Set up the problem!  6 divided into a number  A number divided by 6  The quotient of a number and 6

What would the expression be?  Five less than a number  The product of three and a number  The sum of a number and 10  A number divided by 9

Try one on your own!  Make up an algebraic expression on your own. Write it on your whiteboard.  When your finished, pass it to a neighbor and see if they can figure it out!

Two step algebraic expressions  Three times a number decreased by two  Four more than five times a number  The sum of a number and four divided by two  The difference of a number and four added to nine

Write a verbal phrase for each algebraic expression

Write each sentence as an equation The product of four and a number is sixteen Three less than an number is twenty Nine more than “n” is eleven

To evaluate an algebraic expression, substitute a number for the variable!  Example: Evaluate n + 7 when n = 4

To evaluate an algebraic expression, substitute a number for the variable!  Example: Evaluate 5n + 3 when n = 6

To evaluate an algebraic expression, substitute a number for the variable!  Example: Evaluate 6n² + 2n when n = 3

Let’s try a few on our own!  1. p ÷ 2 + p when p = 4  2. 3a – 5when a = 5  3. 6/s + 4swhen s = 2

What about two variables?  Example: Evaluate a c when a = 9 b = 6

What about two variables?  Example: Evaluate 2n + 7b when n = 5 b = 2

Let’s try a few on our own!  1. p ÷ 2 + 3x when p = 6 and x = 7  2. 3a – 5twhen a = 6 and t = 2  3. 12/s + y²when s = 3 and y = 5

Try one on your own!  Make up an algebraic expression and assign the variable or variables values. Write it on your whiteboard.  When your finished, pass it to a neighbor and see if they can figure it out!

Definitions  Term: A term can be a number, a variable, or a product of numbers and variables.

Definitions  Please list all of the terms in this algebraic expression.

Definitions  Like terms: Terms that have the same variable raised to the same power. Examples

Definitions  Unlike terms: Terms that do not have the same variable raised to the same power. Examples

Definitions  Like terms: Terms that have the same variable raised to the same power.

Identify the like terms in the list:

You can only combine LIKE TERMS  Example: _s_ + 10s = 5  Example: 72c + 5b =  Example: 4x² + 53x =  Example: 7x + 5x =

Now let’s practice!  1. 3m + 4m =  2. 6t + 4 – 3t =  3. 17y + 3y – 2y²  r – 3 =

What about the more difficult ones? 3b² + 5b + 11b² - 4a² = Step 3 : solve and bring down the rest of the terms Step 2 : circle the numbers and the sign to the left of them Step 1 : underline like terms

What about the more difficult ones? 2(b + 2a²) + 2b Step 3 : solve and bring down the rest of the terms Step 2 : circle the numbers and the sign to the left of them Step 1 : distribute and underline like terms 2b + 4a² + 2b

Let’s try some on our own! 1. a + 2b + 2a + 3b + 4c d³ + d + 3d 3. a² + 9b + 5a² + 2b + 6c 4. 3(4x + z) – 4x

Try one on your own!  Make up an algebraic expression with several variables. Write it on your whiteboard.  When your finished, pass it to a neighbor and see if they can figure it out!

Lets try a few!  2 + x = 7 2 plus “some number” equals 7 Answer = 5 How did you know this?

2 + x = 7 subtract two from both sides x = 5 Additive inverse Step 1: Draw a line down the equal sign Step 2: Look at the number on the same side as the variable Step 3: Look at the sign next to the number you underlined (no sign = positive) Step 4: Do the opposite! Add or subtract that number from both sides

X + 14 = 27 subtract 14 from both sides X + 0 = 13 Additive inverse Step 1: Draw a line down the equal sign Step 2: Look at the number on the same side as the variable Step 3: Look at the sign next to the number you underlined (no sign = positive) Step 4: Do the opposite! Add or subtract that number from both sides

Now try on your own! x = X + 11 = X = X + 12 = X = 258

Problem #1  16 + x = 29

Problem #2  X + 11 = 34

Problem #3  18 + X = 86

Problem #4  X + 12 = 19

Problem #5  27 + X = 258