CHAPTER TWO

Variables Expressions and Properties

2-1 USING VARIABLES TO WRITE EXPRESSIONS  Objective: write numerical expressions with variables to represent relations  How: take notes, think pair share, read word phrases to convert to algebraic expressions

VARIABLE  a quantity (or amount) that can change, usually represented with a letter  Variable like the word vary meaning it changes or varies.  Example: 5a where a is a variable  Non-example: 4 2 there is no variable

COEFFICIENT  A number multiplied by a variable  Example: 5a (5xA)  Think of Co- like sharing so coefficients have to share multiplication with a variable  Think of Efficient- like achieving maximum productivity with minimum wasted effort or expense  Non-example: 5+a no multiplication

ALGEBRAIC EXPRESSION  Mathematical phrase having at least one variable and one operation  Example: 5+T or w/7  Non-example: w=8 or 6x8= 48

MEGAN BOUGHT SOCKS ON EBAY FOR \$10 A PAIR.

How can you represent the total cost of the socks bought?

4 A 2 3 Pairs of Socks Cost 1 \$10 x 1 \$10 x 2 \$10 x 3 \$10 x 4 \$10 x A When we don’t know how many pairs of socks Megan bought we can use the variable A to represent potential socks bought. That amount can change which is why we use a VARIable.

Word Phrase Operation five minutes more than time

t

ten erasers decreased by a number

n

six times a width

w n

nectarines divided by three eight more than four times an amount

x

Algebraic Expression

Word Phrase Operation five minutes more than time

t

ten erasers decreased by a number

n

six times a width

w

n

nectarines divided by three division eight more than four times an amount

x

multiplication and addition Algebraic Expression

Word Phrase Operation five minutes more than time

t

ten erasers decreased by a number

n

six times a width

w

n

nectarines divided by three division eight more than four times an amount

x

multiplication and addition Algebraic Expression

t

+ 5 10 -

n

6 x

W

or 6

w n

÷

3 or n

3 4

x

+ 8

NOW LET’S TRY SOME TOGETHER  12 times a number g  The difference of a number m and 18  Yuri walk p poodles and b bulldogs. Write an algebraic expression to represent how many dogs were walked.  P pennies added to 22 pennies

EXIT TICKET  Keeshon bought packages of pens. There are 4 pens in each package. Keeshon gave 6 pens to his friends. Write an expression that show this situation.

 (Hint- there are 2 operations that take place)

STARTER FOR 2-2 Juanita sells homemade jam at the farmers’ market. She sold 35 jars during the first hour and 85 jars during the second hour. Write an algebraic expression to show the number of jars Juanita has left to sell.

Explain how the expression relates to the problem.

2-2 PROPERTIES OF OPERATIONS  Objective: give missing addends and factors in equations and state the property used  How: discuss properties of addition and multiplication then use these properties to label equations and determine missing information

COMMUTATIVE PROPERTY OF ADDITION  The order numbers are added does not change the sum.

 a + b = b + a  8 + 18 = 18 + 8  6 + c = c + 6  Think about when you commute you can go different ways and still get to work.

COMMUTATIVE PROPERTY OF MULTIPLICATION  The order numbers are multiplied does not change the product.

 a x b = b x a  8 x 18 = 18 x 8  6 x c = c x 6  Think about when you commute you can go different ways and still get to work.

ASSOCIATIVE PROPERTY OF ADDITION  The way numbers are GROUPED does not affect the sum    a+(b+c)=(a+b)+c 2+(3+4)=(2+3)+4 3+(a+4)=(3+a)+4  Think my associates/friends: sometimes I hangout with one group sometimes another and they are all my friends

ASSOCIATIVE PROPERTY OF MULTIPLICATION  The way numbers are GROUPED does not affect the product  Think my associates/friends: sometimes I hangout with one group sometimes another and they are all my friends    a(bxc)=(axb)c 2(3x4)=(2x3)4 3x(ax4)=(3xa)x4

IDENTITY PROPERTY OF ADDITION  The sum of any number and zero is that number  a + 0 = a  24 + 0 = 24  Think about what you can do to a number that won’t change it’s value. Their “name tag”

IDENTITY PROPERTY OF MULTIPLICATION  The product of any number and one is that number  Think about what you can do to a number that won’t change it’s value. Their “name tag”  a x 1 = a  24 x 1 = 24

NOW LET’S PRACTICE  __ x (14x32) = (5x14) x 32  5 + 23 + 4 = 23 + 4 + __  25 + 0 + 3 = 25 + __  (7 + 12) + 4 = 7 + (12+__)  (5 x 7) x (3 x 8) = (5 x 3) x (8 x __)  (43 x 1) x 4 = ___ x 4  CHALLENGE  (41 x 43) x (3 x 19) = (41 x __) x (19 x 43)  (5 + 3) + __ = 5 + (8 + 3)

  328 x 1 8 + __ = 4 + 8 EXIT TICKET

STARTER 2-3

Can you use Associative, Commutative, or Identity Properties with subtraction or division? Explain.

2-3 ORDER OF OPERATIONS  Objective: Use the order of operations to evaluate expressions  How: Watch a video, learn a song, and evaluate numeric and algebraic expressions.

THERE IS AN AGREED UPON ORDER IN WHICH OPERATIONS ARE CARRIED OUT IN A NUMERICAL EXPRESSION.

ORDER OF OPERATIONS

ORDER OF OPERATIONS  The order to perform operations in calculations  Compute inside parentheses.

 Evaluate terms with exponents.

 Multiply and Divide from left to right.

 Add and Subtract from left to right.

PEMDAS

NOW LET’S PRACTICE!

 9 2 - 8 x 3  24 / 4 + 8 + 2  18 – 3 x 5 + 2  49 – 4 x (49 /7)  5 2 – 6 x 0  24 / (4+8) + 2

EXIT TICKET  Use parentheses to make each number sentence true.  8 x 9 – 2 – 3 = 53  6 2 + 7 + 9 x 10 = 133  2 2 + 4 x 6 = 48

2-4 STARTER  Mrs. Nerren is decorating her rectangular bulletin board by placing stars along the edges. It is 5 feet wide and 3 feet tall. She places stars every 6 inches. How many stars does she need? Explain your reasoning.

2-4 THE DISTRIBUTIVE PROPERTY  Objective: use the distributive property to evaluate expressions and to compute mentally.  How: take notes, video clip, work with a partner

DISTRIBUTIVE PROPERTY  Multiplying a sum (or difference) by a number gives the same result as multiplying each number in the sum (or difference) by the number and adding (or subtracting) products  WHITE BOARD

2-6 STARTER  Provide the missing information, then solve.

 Aki must take turns with his sisters mowing the lawn. One of them must mow the lawn every week. How many times in 12 weeks will Aki mow the Lawn?

2-6 EVALUATING EXPRESSIONS  Objective: Evaluate algebraic expressions using substitution.

 How: take notes on how to replace variables with given numbers and solving the expression.

EVALUATE  Find the value of an expression EXAMPLES:  5 3 = 125  2+8 = 10  SOLVE!  Get a number for an answer!!!

 NON-EXAMPLES:  5 3 = 5 x 5 x 5  2 + 8 = W

SUBSTITUTION  Replace the variable with a number EXAMPLE:  y + 9  Y = 10  10+9= 19 NON-EXAMPLE:  y + 9  Y = 10  W+9 =9

LET’S PRACTICE  Evaluate each expression for 2, 5, and 8.

 9x  3x+6  48 ÷ x  x(0)  1x  x(4) ÷ 2  X 2 + 1

EXIT TICKET  Evaluate the expression for the values of n.

N 3 5 8 12 25 2+3n

2-7/2-8 STARTER Max’s farm has 480 acres. His farm is divided into fields of n acres each. Write an expression that shows the number of fields on Max’s farm. EXPLAIN YOUR THINKING.

2-7/2-8 USING EXPRESSIONS TO DESCRIBE PATTERNS AND MAKING A TABLE TO SOLVE PROBLEMS  Objective: identify missing numbers in a pattern and write algebraic expressions to describe the pattern, make and use tables to solve word problems.

 How: take notes, read and create tables, discuss patterns with a partner, write expressions.

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