Mastering Algebra: Combining Like Terms with Exponents

1. Chapter 5Expressions

2. Day….. • Combining Like Terms (with Exponents) • Field Trip • Combining Like Terms (with Distributive Property) • Evaluating Algebraic Expressions • Translating Verbal Expressions

3. Day 1

4. Bell Work • What is the value of the expression 32 + 33? • Choose all the expressions equivalent to 4(9+3). • 4(12) • 36+3 • 36+12 • 4+(9+3) • (9+3) + (9+3) + (9+3) + (9+3) • What is the value of 1500/ (62 + 43 ) * 37 ?

5. Homework Check Please turn in your Facing Math projects.

6. Vocabulary A combination of variables, numbers, and at least one operation. Algebraic Expressions - The numerical part of a term followed by a variable. Coefficient- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable. Constant- Expressions that have the same value. Equivalent Expressions- To find the value of a mathematical statement. To solve or find a solution. Evaluate- Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base. Numerical Expression - A combination of numbers and operations.

7. Vocabulary The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Order of Operations- Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Simplify- To make smaller or easier. Substitution- To replace one thing with another. Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ). Translate- To change from one form or place to another. Variable - A letter or symbol used to represent an unknown number.

8. 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

9. I Can…. combine like terms to simplify algebraic expressions.

10. Combining Like Terms Essential Understandings: Expressions that can not be solved , can often be simplified by combining the terms that are alike. • To simplify like terms, you must begin by identifying the types of terms you have. Terms are defined by their variables or lack of one. They must have the exact same variable with exact same exponent to be considered like terms. Example: • To give your self a visual, you can use shapes to code expressions before attempting to combine the like terms. Remember the sign belongs to the term that follows. Example: • After you have coded the terms, you can rearrange them using your knowledge of commutative property. This will make combing the like terms easier in the next step. Example: • Once you have rearranged the terms, you can simply combine (add) the like terms. You should have the same number of terms in your final answer as the number of shapes you used to code the expression. Example:

11. Wrap it Up • Review • Questions • Exit Tickets

12. Day 2

13. Homework Check

14. Vocabulary A combination of variables, numbers, and at least one operation. Algebraic Expressions - The numerical part of a term followed by a variable. Coefficient- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable. Constant- Expressions that have the same value. Equivalent Expressions- To find the value of a mathematical statement. To solve or find a solution. Evaluate- Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base. Numerical Expression - A combination of numbers and operations.

15. Vocabulary The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Order of Operations- Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Simplify- To make smaller or easier. Substitution- To replace one thing with another. Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ). Translate- To change from one form or place to another. Variable - A letter or symbol used to represent an unknown number.

16. 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

17. Wrap it Up • Review • Questions • Exit Tickets

18. Day 3

19. Bell Work • Write a numerical expression that is equal to 10, using at least four different numbers, parentheses, exponents, division, multiplication, and addition. • Factor 6x – 9 • 2(3x-9) • 3(2x-3) • 3(3x-2) • 6(x-9)

20. Homework Check

21. Vocabulary A combination of variables, numbers, and at least one operation. Algebraic Expressions - The numerical part of a term followed by a variable. Coefficient- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable. Constant- Expressions that have the same value. Equivalent Expressions- To find the value of a mathematical statement. To solve or find a solution. Evaluate- Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base. Numerical Expression - A combination of numbers and operations.

22. Vocabulary The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Order of Operations- Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Simplify- To make smaller or easier. Substitution- To replace one thing with another. Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ). Translate- To change from one form or place to another. Variable - A letter or symbol used to represent an unknown number.

23. 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

24. I Can…. combine like terms to simplify algebraic expressions.

25. Combining Like Terms Essential Understanding: • You can simplify an expression by combining like terms. Example: • Only like terms can be combined (added). To be considered alike they must have the exact same variable with the exact same exponent. Terms without variable are called constants, and can be combined with other constants. Example: • Terms can be coded and rearranged using commutative property to make simplifying easier. Remember to make a key. Examples: • When simplifying an expression you must follow the order of operations. PEMDAS Examples: • Unlike like terms cannot be combined, but they can be multiplied by other unlike terms. Often this appears in the form of distributive property. Example:

26. Distributive Property Essential Understanding: Distributive property can be used to rewrite algebraic expressions. This is done by multiplying the term on the outside of the parenthesis by Everyterm on the 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)

27. Wrap it Up • Review • Questions • Exit Tickets

28. Day 4

29. Bell Work • What is the value of 6(x + 15) – 12 when x=12 ? • Does n=3 make the following equations true? Yes or No • 8n=512 • 0.5n = 1.25 • 2n = 6 • 4n – 30 = 34 • At a bake sale, plates of cookies , p, are sold for $5 each. The amount of money from the sale of cookies is expressed as dollars, d. Which equation represents the earnings of the bake sale? • P =5d • d = p+5 • d= p/5 • d=5p

30. Homework Check

31. Vocabulary A combination of variables, numbers, and at least one operation. Algebraic Expressions - The numerical part of a term followed by a variable. Coefficient- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable. Constant- Expressions that have the same value. Equivalent Expressions- To find the value of a mathematical statement. To solve or find a solution. Evaluate- Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base. Numerical Expression - A combination of numbers and operations.

32. Vocabulary The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Order of Operations- Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Simplify- To make smaller or easier. Substitution- To replace one thing with another. Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ). Translate- To change from one form or place to another. Variable - A letter or symbol used to represent an unknown number.

33. 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

34. I Can…. evaluate algebraic expressions involving substitution.

35. Evaluating Expressions Essential Understanding: Substitution is used to evaluate an algebraic expression, when the value of the variables is given. • To do this, you simply replace the variable(s) with the given value. Example: • Then simply evaluate the expressions following the standard procedure. PEMDAS Example: Additional Examples: • 3x + 5 when x=2 • 4w +5w when w=8 • 2abc when a=3, b=4, and c=5 • 7y – 3p when y=7 and p =2

36. Wrap it Up • Review • Questions • Exit Tickets

37. Day 5

38. Bell Work • Solve the expression if y=8. ((y3 – 212) *2) + (12 + 22 + 32)2 • Which numerical expression is equivalent to add seven and seven, then multiply by seven, then divide by seven? • (7*7)+7/ 7 • 7*7+(7 / 7) • ( 7*7*7)/ 7 • 7*(7+7)/ 7

39. Homework Check

40. Vocabulary A combination of variables, numbers, and at least one operation. Algebraic Expressions - The numerical part of a term followed by a variable. Coefficient- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable. Constant- Expressions that have the same value. Equivalent Expressions- To find the value of a mathematical statement. To solve or find a solution. Evaluate- Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base. Numerical Expression - A combination of numbers and operations.

41. Vocabulary The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Order of Operations- Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined. Simplify- To make smaller or easier. Substitution- To replace one thing with another. Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ). Translate- To change from one form or place to another. Variable - A letter or symbol used to represent an unknown number.

42. 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

43. I Can…. Identify key terms for addition, subtraction, multiplication, division, etc...

44. Key Terms for Addition • Increased + • Added + • Combine + • Plus + • And + • Climbed + • Rose + • Together + • Sum ( + ) • Average ( + ) then ÷

45. Key Terms for Subtraction • Subtracted - • Decreased – • Reduced - • Minus - • Less - • Lower - • Dropped - • Difference ( - )

46. Key Terms for Multiplication • Times x • Each x • Of x • Multiply x • Half x½ • Double x2 • Twice x2 • Triple x3 • Product ( x )

47. Key Terms for Division

48. Key Terms for Exponents

49. Key Terms for Order • Than switch • Sum ( + ) • Difference ( - ) • Product ( x ) • Quotient ( ÷ ) • First • Then • Next • Last

50. Key Terms for Equations • Is = • Equals = • Equivalent =