1. Expressions and Equations
EE Learning
targets
Math 6
Expressions and Equations
EE.D1 Model and solve problems involving whole number exponents.
EE.D2 Use mathematical properties to generate and identify equivalent expressions.
EE.D3 Write expressions using variables from contextual problems.
EE.D4 Solve real-world problems by writing and solving equations.
Write inequalities from contextual problems and graph or describe the solution.
Use variables to represent two quantities in a contextual problem.
Analyze the relationship between variables using graphs and tables.

2. Vocabulary of this unit
EE.D1
Term, Expression, Equation, Variable, Variable Structure, Coefficient, Exponent, Factors, Simplify, Solve

3. Term Terms: Parts of an expression or series separated by + or -
Algebra Vocabulary
EE.D1
Term
Parts of an expression or series separated by + or -
Expression:
Terms:

4. More Vocabulary
EE.D1
Coefficient
exponent

5. What’s a factor?
EE.D1
What are the factors of: 80
125 w3

6. 5x + 3x = 10 An Expression - An Equation -
Expressions vs Equations
EE.D1
An Expression -
A group of terms added or subtracted
An Equation -
5x + 3x = 10
What’s the difference between an expression and an equation?

7. Example: Solve for n when 3 + n = 5
Solving vs Simplifying
EE.D1
Solve – Make a true statement, find a value that makes a true statement.
Example: Solve for n when 3 + n = 5
Simplify - Rewrite an expression so it is more simply put.
Example: => or 2n + 3n => 5n

8. You try….
EE.D1

9. How many ways can you write these numbers using exponents?
EE.D1
How many ways can you write these
numbers using exponents?
125 27 81 48

10. Simplify: Write out factors then recombine
EE.D1
Simplify: Write out factors then recombine

11. Simplify: Write out factors then recombine
EE.D1
Simplify: Write out factors then recombine

12. Simplify: Write out factors then recombine
EE.D1
Simplify: Write out factors then recombine

13. U3D1
Independent Practice
ICP GM U3D1

14. Must Do:
*Please set yesterday’s assignment on your desk so I can check off that you did it!
In your notebook on the vocabulary page, write a definition and give an example of the
vocabulary we discussed so far.
Term, Expression, Equation, Variable, Coefficient, Exponent, Factors, Simplify, Solve

15. EE.D2
Use mathematical properties to generate and identify equivalent expressions.

16. What does an equal sign mean?
EE.D2
Let’s discuss
What does an equal sign mean?

17. 8 6 + 4 n + 2 What is an equivalent Expression?
EE.D2
What is an equivalent Expression?
Write an expression equivalent to: 8
6 + 4
n + 2

18. Let’s review and discuss
EE.D2
Let’s review and discuss
Order of Operations
1. Calculations must be done from left to right.
2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first.
3. Exponents (or radicals) must be done next.
4. Multiply and divide in the order the operations occur.
5. Add and subtract in the order the operations occur.

19. (y + y + y) 9(3y + n) 3(3f + g) EE.D2 Practice
Let’s Create some Equivalent Expressions
Expression
Equivalent Expression
Simplest Expression
(y + y + y)
9(3y + n)
3(3f + g)

20. What’s the difference between
EE.D2
What’s the difference between
n + n + n
and
n x n x n
How would you simplify each? Are they equivalent?

21. n + 4 4n + 4 4n + n EE.D2 What terms can you simplify?
How do you know if you can combine terms?
n + 4
4n + 4
4n + n

22. EE.D2
Simplify expressions by combining like terms

23. EE.D2
Challenging

24. EE.D2
Independent Practice
EE.D2

25. EE.D3
Review and Continue:
Use mathematical properties to generate and identify equivalent expressions.
EE.D3 Write expressions using variables from contextual problems.

26. EE.D3
Write an equivalent equation
3 + x = 5
2n + 5 = 15

27. 3n + 4 = 16 What does it mean to solve an equation? EE.D3
Let’s solve it…. Using a bar model, and algebra

28. EE.D3
Solving simple equations using a bar model and algebraic manipulation
4n + 6 = 14
Let’s do bar model first.
How can we write equivalent equations to help us solve?

29. EE.D3
Solve this one
Discuss: Is this the same as 10/4 + 6/4? Talk about misconceptions in reducing…..

30. EE.D3
Writing Expressions and equations from contextual problems

31. Tom is 12 years old. Find his age after
EE.D3
Write an expression
Tom is 12 years old. Find his age after
a) 4 years b) 7 years c) x years

32. EE.D3
Write an expression
A worker’s salary is $200 less than one-third of a manager’s salary. Find the worker’s salary when the manager’s salary is
$7, b) $m

33. EE.D3
Write an expression
The price of a papaya is $2 and the price of a mango is $1. Find the total price of
4 papayas and 5 mangos
x papayas and y mangos

34. EE.D3
Write an expression
The price of a cup is $5 and the price of a plate is $12. Find the total price of
5 cups and 6 plates
N cups and M plates

35. Report on conclusions and the reasoning behind them
Do you agree? Prove and explain why you agree or disagree
EE.D3

36. EE.D3
Independent Practice
EE.D3

37. Mathematical PracticesEE
Learning Targets
I can solve equations arising from a context by first drawing a model and then writing an equation to represent the context.
Mathematical Practices
Make sense of problems and persevere in solving them
Model with mathematics
Resource: Singapore 3.3-7a
EE.D4

38. Review
The price of a cup is $5.50 and the price of a plate is $ Find the total price of
5 cups and 6 plates
N cups and M plates
EE.D4

39. Concept Review
EE.D4
Order of operations
Solve when x = 3 and n = 2

40. EE.D4
Problem solving.. Use any method to solve
The average score a student earned on 11 tests was 90. He averaged a score of 88 on the first 5 tests he took, and the average of his final 5 test scores was 94. What score did the student earn on his 6th test?

41. Draw a model, write an equation
EE.D4
Draw a model, write an equation
Solve
At birth, baby George weighs 2 pounds lighter than his twin brother Harry.
Suppose Harry’s weight is x pounds, what is George’s weight in terms of x?
If the sum of their weight is 15 pounds, how much does each weigh?

42. Draw a model, write an equation
Solve
A store is selling a notebook computer at $90 more than 4 times the price of a mobile phone.
Suppose the price of the mobile phone is $m. Express the price of the notebook in terms of m.
Given that the notebook computer costs $n, write a formula connecting m and m
EE.D4

43. Draw a model, write an equation
EE.D4
Draw a model, write an equation
Solve
Stella has $11 more than Roland. Together they have $159. How much money does Stella have? How much money does Roland have?

44. Draw a model, write an equation
EE.D4
Draw a model, write an equation
Solve
Jared has twice as many DVDs as Eric. Together they have 51 DVDs. How many DVDs does Jared have? How many DVDs does Eric have?

45. Draw a model, write an equation
Solve
EE.D4
The sum of three consecutive integers is What are the three numbers?

46. Write an equation and solve
EE.D4
YOU TRY!
Write an equation and solve
A corn plant was 4 inches tall. It grew 1.5 inches a day and is now 22 inches tall. How many days did it take?

47. Mathematical Practices
Learning Targets
I can differentiate between like and unlike terms
I can use the distributive law and add and subtract linear equations
Mathematical Practices
Make sense of problems and persevere in solving them
Model with mathematics
Resources: Singapore 4.1 & 4.2 – 7a
EE.D5

48. Bell Work
Let x = 4, y = -2, z = 0
EE.D5

49. Warm Up
EE.D5

50. Draw a model, write an equation
Kylie is addressing invitations to her party. She has already addressed 17 of them. She finishes the rest of them in 4 hours. If she addressed a total of 81 invitations, how many invitations did she address per hour?
EE.D5

51. Like and unlike terms
EE.D5
Review vocab: Terms, Coefficient
Like terms have the same variable structure: same variables with same exponents, but the coefficient need not be the same.
Constants are always “Like Terms”: 5, 24, -73

52. Simplifying by adding or subtracting like terms
EE.D5
Simplifying by adding or subtracting like terms
If two terms are “like” (have the same variable structure), you can add or subtract them, but add the coefficient in front of the variables. Any numbers without a variable (a constant), can just be added or subtracted.
Examples

53. EE.D5
You Try

54. Solve 3(4 + 5) using an area model
EE.D5
The Distributive law of multiplication over addition
Demonstrate using area models
Solve 3(4 + 5) using an area model
Solve 2(4x + 5y) using an area model
Solve -x(4y + 5y) using an area model

55. The Distributive Law in general
EE.D5
The Distributive Law in general
a(x + y) = ax + ay
a(x - y) = ax - ay
a(x + y + z) = ax + ay + az

56. You Try; use the distributive property to remove parenthesis
EE.D5

57. (2x + 3y) – (3x + 2y) 4x – x(3 + 2y) + xy
EE.D5
Harder… use distributive property and collect like terms
(2x + 3y) – (3x + 2y)
4x – x(3 + 2y) + xy

58. EE.D5
Independent Practice
ICP EE.D5

59. Mathematical Practices
Learning Targets
I can solve equations in one variable
Mathematical Practices
Make sense of problems and persevere in solving them
Model with mathematics
Resources: Singapore 5.1 – 7a
EE.D6

60. 15 minute Skill Check EE.SC1
EE.D6
15 minute Skill Check EE.SC1

61. sum of their ages is 47, how old are Sam, Bill & Jack?
Model and write an equation
Solve
EE.D6
Sam is 4 less than twice Bill’s age. Jack is 3 years older than Bill. If the
sum of their ages is 47, how old are Sam, Bill & Jack?

62. Solving Equations Using Algebra
When we solve an equation using algebra, we want to undo the operations on the unknown in order to find out what it is.
Remember! Keep the equation balanced by doing the same thing on both sides!!!
Example:
Solve
EE.D6
Explain the opposite of multiplication is division, etc…

63. Solving Equations Using Algebra Solve each equation 1.2. 3.
EE.D6
Do first problem with class, have students do 2 & 3.

64. Solving Two-Step Equations
What’s the first step in solving this equation? Why?
How about this one? Why?
EE.D6

65. Solving Two-Step Equations
Solve each equation 1. 2. 3.
EE.D6
Do first problem with class, have students do 2 & 3.

66. A word about notation
Are these equivalent?
What about these?
EE.D6

67. EE.D6
Independent Practice
EE.D6

68. Mathematical Practices
EE.D7
Learning Targets
I can solve equations involving parenthesis in one variable
I can rearrange equations to solve.
Mathematical Practices
Make sense of problems and persevere in solving them
Model with mathematics
Resources: Singapore 5.2 – 7a

69. Bell work The sum of 3 consecutive numbers is 234. Find the numbers
EE.D7
The sum of 3 consecutive numbers is 234. Find the numbers
The sum of 3 consecutive even numbers is Find the numbers
The sum of 3 consecutive odd numbers is Find the numbers

70. Review
Let x = 5, y = -3, z = 0
EE.D7

71. Problem Solving
EE.D7
Kylie is addressing invitations to her graduation party. She has already addressed 17 of them. She finishes the rest of them in 4 hours. If she addressed a total of 81 invitations, how many invitations did she address per hour?

72. Can us solve with algebra, a model, or some other method?
Problem Solving
Can us solve with algebra, a model, or some other method?
EE.D7
104 chickens and goats in a farm have 246 legs altogether. How many of each type of animal are there?

73. Solving Multi-Step Equations
Let’s review the Distributive Property for a moment…
The Distributive Property says
Simplify
EE.D7

74. Solving Equations with the Distributive Property
What should we do first to solve this equation? Why?
EE.D7
Explain we need both sides of equation as simplified as possible to make solving easier…

75. Solving Equations with the Distributive Property
Solve each equation 1. 2. 3.
EE.D7
Do first problem with class, have students do 2 & 3.

76. How does the distributive property apply here?
EE.D7
A little more challenging examples….
How does the distributive property apply here?

77. U4D8

78. Independent Practice
EE.D7
EE.D7

79. Mathematical Practices:
EE.D8
Standards Assessed:
I can solve equations using algebraic manipulation
I can create and solve equations arising from a context
Mathematical Practices:
Make sense of problems and persevere in solving them
Model with mathematics

80. EE.D8
U4D8

81. Practice
Solving proportions
EE.D8

82. Keep practicing!

83. Write an equation and solve. Draw a model if necessary.
EE.D8
Write an equation and solve. Draw a model if necessary.
The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width of the rectangle.

84. You Try! Write an equation and solve. Draw a model if necessary.
EE.D8
You Try!
Write an equation and solve. Draw a model if necessary.
Twelve decreased by 8 times a number is Find the number.

85. Write an equation and solve. Draw a model if necessary.
EE.D8
You Try!!
Write an equation and solve. Draw a model if necessary.
JoGrandpa is 75 years old. This is nine years less than seven times the age of Jo. How old is Jo?

86. Write an equation and solve. Draw a model if necessary.
EE.D8
You Try!!
Write an equation and solve. Draw a model if necessary.
JoGrandpa is 75 years old. This is nine years less than seven times the age of Jo. How old is Jo?

87. EE.D8
Write an equation and solve
A-1 Plumbing company pays Sam $45 per day, plus for each hour he works. If he earned last week, how many hours a day did he work.
(Sam works a 5 day week, and each day he works the same number of hours)

88. EE.D8
Write an equation and solve
Lisa is bored, riding in the backseat of her parent’s SUV on their family vacation. She notices the mile markers on the interstate. She adds up three consecutive mile markers and discovers the sum is Which three mile marker signs did her family just pass?

89. Independent Practice
EE.D8

90. EE.D9
Continue developing algebraic manipulation skills by solving inequalities
Expressing a solution to an inequality

91. EE.D9
Solutions to equations vs solutions to inequalities
How do we express a solution to the equations:
2n = 10
2n + 1 = 2n + 10
2n = 2n

92. EE.D9
Inequalities!
Vocab: An Inequality is a comparison of two values that may or may not be equal.

93. The Symbols and Their Meanings
EE.D9
The Symbols and Their Meanings
Symbol
Meaning
a > b
a is greater than b
a ≥ b
a is greater than or equal to b
a < b
a is less than b
a ≤ b
a is less than or equal to b

94. What does it all mean!? Examples!
EE.D9
What does it all mean!?
Examples!
Graph each inequality on a number line using or
properties ws

95. Solutions to an Inequality
EE.D9
Solutions to an Inequality
Remember that the solution to an equation gave us a single, unique result… but for inequalities…
The solution to an inequality is a range of possibilities.
Example: The solution of allows every real number that is bigger than 2. So we get to use any possible number we can think of as long as it is greater than 2.

96. Let’s try some…. Examples!
EE.D9
Examples!
Solve each inequality and graph the solution on a number line.

97. EE.D9
You Try!
Solve each inequality and graph the solution on a number line.

98. EE.D10
Standards Addressed Today:
Attend to Precision
Reason Abstractly and Quantitatively
Solve Inequalities Using Algebraic Manipulation
Explain the Multiplication Property by Negative Integers for Inequalities

99. EE.D10
Concept Review
Solve each inequality and graph the solution on a number line.

100. Now for the tricky part…
EE.D10
Now for the tricky part…
Consider the inequality 4 < 12
Divide both sides by 2. Is the inequality still true?
Now divide both sides by –2. Is the inequality still true?
Divide by 4.
Divide by –4.
Complete questions 1-4 on your half sheet.

101. EE.D10
Solve each inequality

102. EE.D10
Challenge!

103. EE.D10
Describe a situation
… that could be modeled by the inequality

104. EE.D10
Work with a partner
You are building a patio. You want to cover the patio with Spanish Tile that costs $5 per square foot. You budget for the tile is $1700. How wide can you make the patio without going over budget?

105. EE.D10
Independent Practice
EE.D10

106. Reason Abstractly and Quantitatively
EE.D11
EE.D11
Standards:
Attend to Precision
Reason Abstractly and Quantitatively
Solve Inequalities Using Algebraic Manipulation
Solve Inequalities Arising From a Context

107. Concept Review Solve each equation or inequality.
EE.D11
Concept Review
Solve each equation or inequality.
Graph the solution to the inequality.

108. Concept Review Write an inequality and solve.
EE.D11
Concept Review
Write an inequality and solve.
Four times a number is at least –48. What is the number?

109. Problem Solving Write an inequality and solve.
EE.D11
Problem Solving
Write an inequality and solve.
Ilona is saving up to buy a digital camera that costs $ So far, she has $175 saved. She would like to buy the camera 5 weeks from now. At least how much must she save every week to have enough money to purchase the camera?

110. Use the definition of mean to write an inequality and solve
You need a mean score of at least 90 to advance to the next round of the trivia game. What score do you need on the fifth game to advance?

111. EE.D11
Problem Solving
For what values of x will the area of the blue region be greater than 12 square units?

112. EE.D11
Try this on your own
For what values of y will the area of the trapezoid be less than or equal to 10 square units?

113. EE.D11
In Class Practice
EE.D11 – ICP

114. Unit Review
Solving equations and inequalities