Chapter 5 Expressions (Part 1)

Day….. Order of Operations w/ Exponents Solving Numerical Expressions Writing Numerical Expressions Algebraic Properties

Day 1

Please complete the Provided Pages 111-112 In your bell ringer book. Bell Work Please complete the Provided Pages 111-112 In your bell ringer book.

Homework Check

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Expressions that have the same value. Equivalent Expressions- Evaluate- To find the value of an algebraic expression by replacing variables with numbers. Exponent- The shorthand way to represent repeated multiplication. Numerical Expression - A combination of numbers and operations. Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Variable - A letter or symbol used to represent an unknown number.

Properties Commutative- states that the order in which numbers are added or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7 Associative- states that the way in which numbers are grouped does not change the sum or product. Ex: 1 + (2+3) = 6 or (1+2) +3= 6 Identity- states that any number added to 0 or multiplied by 1 will be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4 Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis. Ex: 4(2 + 3) = 8 +12

Today’s Standard Write and evaluate numerical expressions involving whole-number exponents.

Exponents Essential Understanding: Exponents are a shorthand way to show how many times a number, called the base, is multiplied times itself. Example: A number with an exponent is said to be "raised to the power" of that exponent. The "Laws of Exponents” come from three ideas: The exponent says how many times to use the number in a multiplication equation.   A negative exponent means divide, because the opposite of multiplying is dividing A fractional exponent like 1/n means take the nth root

Laws of Exponents Law: Examples: x1 = x 61 = 6 x0 = 1 70 = 1 xmxn = xm+n x2x3 = x2+3 = x5 xm/xn = xm-n x6/x2 = x6-2 = x4 (xm)n = xmn (x2)3 = x2×3 = x6 (xy)n = xnyn (xy)3 = x3y3 (x/y)n = xn/yn (x/y)2 = x2 / y2 x-n = 1/xn x-3 = 1/x3

Order of Operations Essential Understanding: Examples: 4+6*8-6(12-9) = Order of operation is the rule that states the order in which an expression or equation is solved. You can remember this order with simple mnemonic devices such as “Please Excuse My Dear Aunt Sally”. Where as: P stands for parenthesis E stands for Exponents M stands for multiply D stands for divide A stands for addition S stands for subtraction Examples: 4+6*8-6(12-9) = 14-8+5*5+102=

Your Turn Orange Book pages 148-149 https://drive.google.com/open?id=0B39oLT9Jr3WDVTM2am1CdlF5UTg Green Book page 97

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Day 2

Please complete pages 150- 151 in your orange book. Bell Work Please complete pages 150- 151 in your orange book.

Homework Check

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Expressions that have the same value. Equivalent Expressions- Evaluate- To find the value of an algebraic expression by replacing variables with numbers. Exponent- The shorthand way to represent repeated multiplication. Numerical Expression - A combination of numbers and operations. Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Variable - A letter or symbol used to represent an unknown number.

Properties Commutative- states that the order in which numbers are added or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7 Associative- states that the way in which numbers are grouped does not change the sum or product. Ex: 1 + (2+3) = 6 or (1+2) +3= 6 Identity- states that any number added to 0 or multiplied by 1 will be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4 Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis. Ex: 4(2 + 3) = 8 +12

Today’s Standard Write and evaluate numerical expressions involving whole-number exponents.

Numerical Expressions Essential Understanding: When you look at a problem with numbers, you are most likely looking at a numerical expression. A numerical expression is a mathematical sentence involving only numbers and one or more operation symbols. Examples of operation symbols are the ones for addition, subtraction, multiplication, and division Numerical Expressions that have more than one operation must be solved using the order of operations.

As a group work together to complete page 104 in the Green Book.

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Day 3

Please complete pages 152-153 in your orange book. Bell Work Please complete pages 152-153 in your orange book.

Homework Check

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Expressions that have the same value. Equivalent Expressions- Evaluate- To find the value of an algebraic expression by replacing variables with numbers. Exponent- The shorthand way to represent repeated multiplication. Numerical Expression - A combination of numbers and operations. Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Variable - A letter or symbol used to represent an unknown number.

Properties Commutative- states that the order in which numbers are added or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7 Associative- states that the way in which numbers are grouped does not change the sum or product. Ex: 1 + (2+3) = 6 or (1+2) +3= 6 Identity- states that any number added to 0 or multiplied by 1 will be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4 Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis. Ex: 4(2 + 3) = 8 +12

Today’s Standard Write and evaluate numerical expressions involving whole-number exponents.

Writing Numerical Expressions Essential Understanding: word problems are just expressions written in word form. They are used to describe real life situations and to solve real life problems. Example: The key to successfully solving an algebraic word problem is to translate the expression from word form to numerical form. To do this, we follow a few very simple steps. Step 1: Know your vocabulary. Step 2: Read the problem CAREFULLY. Step 3: Code the problem. Step 4: Determine what is known (what numbers are given) Step 5: Determine what is unknown (what variables are given) Step 6: Determine what operation(s) to used based on what the question is asking/telling. Step 7: Translate expression/equation Step 8: Solve if necessary Examples:

https://drive.google.com/open?id=0B39oLT9Jr3WDYldnOTE5clJpX0k Your Turn https://drive.google.com/open?id=0B39oLT9Jr3WDYldnOTE5clJpX0k

Math Menu Directions: As a group you will work to complete pages 7-9 of your math menu packet. https://drive.google.com/open?id=0B39oLT9Jr3WDUmJiUjlGRlFscGs

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Day 4

Bell Work  

Homework Check

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Expressions that have the same value. Equivalent Expressions- Evaluate- To find the value of an algebraic expression by replacing variables with numbers. Exponent- The shorthand way to represent repeated multiplication. Numerical Expression - A combination of numbers and operations. Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Variable - A letter or symbol used to represent an unknown number.

Properties Commutative- states that the order in which numbers are added or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7 Associative- states that the way in which numbers are grouped does not change the sum or product. Ex: 1 + (2+3) = 6 or (1+2) +3= 6 Identity- states that any number added to 0 or multiplied by 1 will be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4 Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis. Ex: 4(2 + 3) = 8 +12

Apply the properties of operations to generate equivalent expressions. Today’s Standard Apply the properties of operations to generate equivalent expressions.

Algebraic Properties Essential Understanding: Algebraic properties can be used to rewrite expressions/generate equivalent expressions. For instance, the expression 3+4+2 can be rewritten as 4+3+2 using commutative property of addition to rearrange the numbers. Examples of other algebraic properties: 1 x 4 x 3 = 4 x 3 x 1 -_____________________ (6 + 3) +8 = (8 +3) + 6-____________________ 9 x (3 x 2) = (9 x 3) x 2-____________________ 4(3 – 2)-______________________

Watch This Associative property: http://learnzillion.com/lessons/137-combine-parts-of-an-expression-using-the-associative-property ( 5 mins) Commutative property: http://learnzillion.com/lessons/2357-the-commutative-property (3 mins)

Your Turn Property Sort https://drive.google.com/open?id=0B39oLT9Jr3WDcm11eU9mYlBsZDg

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Day 5

Please complete green book page 98 in your bell ringer book. Bell Work Please complete green book page 98 in your bell ringer book.

pOp Quiz Clear EVERYTHING from your desk

Homework Check

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Expressions that have the same value. Equivalent Expressions- Evaluate- To find the value of an algebraic expression by replacing variables with numbers. Exponent- The shorthand way to represent repeated multiplication. Numerical Expression - A combination of numbers and operations. Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Variable - A letter or symbol used to represent an unknown number.

Properties Commutative- states that the order in which numbers are added or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7 Associative- states that the way in which numbers are grouped does not change the sum or product. Ex: 1 + (2+3) = 6 or (1+2) +3= 6 Identity- states that any number added to 0 or multiplied by 1 will be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4 Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis. Ex: 4(2 + 3) = 8 +12

Today’s Standard Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

Distributive Property Essential Understanding: Distributive property can be used to rewrite algebraic expressions by multiplying the number outside the parenthesis by each number, term, or variable inside. For instance the expression 3(p+2) can be rewritten as 3p + 6 Examples: 2(3+7) (6-3)3 5(3+6d) (4-a)8 (5b+6c)8 9(ab + 4c)

Watch This Distributive property: http://learnzillion.com/lessons/2338-create-an-equivalent-expression-using-the-standard-algorithm ( 5 mins)

Puzzle Time Before we begin……. Spend your tickets, if you have any. Pack up everything else, except for a pencil. Sit quietly unit everyone is ready.

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