Unit 2 Lesson 1 Warm Up Problem of the Day Lesson Presentation

Unit 2 Lesson 1 Warm Up Problem of the Day Lesson Presentation
Lesson Quizzes

Warm Up 1. 7x + 4 for x = 6 2. 8y – 22 for y = 9
Evaluate each algebraic expression for the given value of the variables. 1. 7x + 4 for x = 6 2. 8y – 22 for y = 9 3. 12x + for x = 7 and y = 4 4. y + 3z for y = 5 and z = 6 46 50 8 y 86 23

Problem of the Day A farmer sent his two children out to count the number of ducks and cows in the field. Jean counted 50 heads. Charles counted 154 legs. How many of each kind were counted? 23 ducks and 27 cows

Learn to translate words into numbers, variables, and operations.

Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua. An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua. When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

Turn composition notebook sideways and divide page into 4 sections:
ADD Subtract Multiply Divide

Algebraic Expressions
Operation Verbal Expressions Algebraic Expressions • add 3 to a number • a number plus 3 + • the sum of a number and 3 n + 3 • 3 more than a number • a number increased by 3 • subtract 12 from a number • a number minus 12 • the difference of a number and 12 - x – 12 • 12 less than a number • a number decreased by 12 • take away 12 from a number • a number less than 12

Algebraic Expressions
Operation Verbal Expressions Algebraic Expressions • 2 times a number • 2 multiplied by a number 2m or 2 • m + • the product of 2 and a number • 6 divided into a number ÷ a 6 ÷ 6 or • a number divided by 6 • the quotient of a number and 6

Additional Example 1: Translating Verbal Expressions into Algebraic Expressions
Write each phrase as an algebraic expression. A. the quotient of a number and 4 quotient means “divide” n 4 B. w increased by 5 increased by means “add” w + 5

Additional Example 1: Translating Verbal Expressions into Algebraic Expressions
Write each phrase as an algebraic expression. C. the difference of 3 times a number and 7 the difference of 3 times a number and 7 3 • x – 7 3x – 7 D. the quotient of 4 and a number, increased by 10 the quotient of 4 and a number, increased by 10 4 n + 10

Check It Out: Example 1 Write each phrase as an algebraic expression. A. a number decreased by 10 decreased means “subtract” n – 10 B. r plus 20 plus means “add” r + 20

Check It Out: Example 1 Write each phrase as an algebraic expression. C. the product of a number and 5 the product of a number and 5 n • 5 5n D. 4 times the difference of y and 8 4 times the difference of y and 8 4 • y – 8 4(y – 8)

When solving real-world problems, you may need to determine the action to know which operation to use. Action Operation Put parts together Add Put equal parts together Multiply Find how much more Subtract Separate into equal parts Divide

Additional Example 2A: Translating Real-World Problems into Algebraic Expressions
Mr. Campbell drives at 55 mi/h. Write an algebraic expression for how far he can drive in h hours. You need to put equal parts together. This involves multiplication. 55mi/h · h hours = h miles

Additional Example 2B: Translating Real-World Problems into Algebraic Expressions
On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly. The total points include 2 points for each short-answer question. Multiply to put equal parts together. 2q In addition to the points for short-answer questions, the total points included 50 points on the essay. Add to put the parts together: q

Check It Out: Example 2A Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours. You need to put equal parts together. This involves multiplication. 8 units/h · h hours = h

Check It Out: Example 2B At her job Julie Ann is paid $8 per hour. In addition, she is paid $2 for each unit she produces. Write an expression for her total hourly income if she produces u units per hour. Her total wage includes $2 for each unit produced. Multiply to put equal parts together. 2u In addition the pay per unit, her total income includes $8 per hour. Add to put the parts together: 2u + 8.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Write each phrase as an algebraic expression. 1. 18 less than a number 2. the quotient of a number and 21 3. 8 times the sum of x and 15 4. 7 less than the product of a number and 5 x – 18 x 21 8(x + 15) 5n – 7 5. The county fair charges an admission of $6 and then charges $2 for each ride. Write an algebraic expression to represent the total cost after r rides at the fair. 6 + 2r

Lesson Quiz for Student Response Systems
1. Which of the following is an algebraic expression that represents the phrase ‘15 less than a number’? A. x – 15 B. x + 15 C. 15 – x D. 15x

2. Which of the following is an algebraic expression that represents the phrase ‘the product of a number and 36’? A. 36x C. B D. x + 36 36 x x 36

3. Which of the following is an algebraic expression that represents the phrase ‘5 times the sum of y and 17’? A. 5(y + 17) B. y + 17 C. 5y + 17 D. 5(y – 17)

4. Which of the following is an algebraic expression that represents the phrase ‘9 less than the product of a number and 7’? A. 7x + 9 B. 7x – 9 C. 9x + 7 D. 9x – 7

5. A painter charges $675 for labor and $30 per gallon of paint. Identify an algebraic expression that represents the total cost of painting, if the painter used x gallons of paint. A x B. 675x C x D. 30x

Unit 2 Lesson 2 Warm Up Problem of the Day Lesson Presentation
Lesson Quizzes

Warm Up Evaluate each expression for y = 3. 1. 3y + y 2. 7y 3. 10y – 4y 4. 9y 5. y + 5y + 6y 12 21 18 27 36

Problem of the Day Emilia saved nickels, dimes, and quarters in a jar. She had as many quarters as dimes, but twice as many nickels as dimes. If the jar had 844 coins, how much money had she saved? $94.95

Learn to simplify algebraic expressions.

Vocabulary term coefficient

In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms
In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by + and –. x 3 7x – 3y y + term term term term term Coefficient Variable 7 In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y. x

Like terms are terms with the same variables raised to the same exponents. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms. 1 2 Like Terms Unlike Terms w 7 3x and 2x w and 5 and 1.8 5x2 and 2x 6a and 6b 3.2 and n Only one term contains a variable The exponents are different. The variables are different

Additional Example 1: Identifying Like Terms
Identify like terms in the list. 3t 5w2 7t 9v w2 8v Look for like variables with like powers. 3t 5w2 7t 9v w2 8v Like terms: 3t and 7t 5w2 and 4w2 9v and 8v Use different shapes or colors to indicate sets of like terms. Helpful Hint

Check It Out: Example 1 Identify like terms in the list. 2x 4y3 8x 5z y3 8z Look for like variables with like powers. 2x y x 5z y3 8z Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

+ = Combining like terms is like grouping similar objects. x x x x x x
To combine like terms that have variables, add or subtract the coefficients.

Additional Example 2: Simplifying Algebraic Expressions
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 6t – 4t 6t – 4t 6t and 4t are like terms. 2t Subtract the coefficients. B. 45x – 37y + 87 In this expression, there are no like terms to combine.

Additional Example 2: Simplifying Algebraic Expressions
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 Identify like terms. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 Group like terms. (3a2 + 2a2) + (5b – 4b) + 11b2 – 6 5a2 + b + 11b2 – 6 Add or subtract the coefficients.

Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 5y + 3y 5y + 3y 5y and 3y are like terms. 8y Add the coefficients.

Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 4x2 + 4y + 3x2 – 4y + 2x2 + 5 4x2 + 4y + 3x2 – 4y + 2x2 + 5 Identify like terms. (4x2 + 3x2 + 2x2)+ (4y – 4y) + 5 Group like terms. Add or subtract the coefficients. 9x2 + 5

Additional Example 3: Geometry Application
Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 3 3x + 2 x Write an expression using the side lengths. 2x x x (x + 3x + 2x) + (2 + 3) Identify and group like terms. 6x + 5 Add the coefficients.

Write an expression using the side lengths. x + 2x + 1 + 2x + 1
Check It Out: Example 3 Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 1 2x + 1 x Write an expression using the side lengths. x + 2x x + 1 (x + 2x + 2x) + (1 + 1) Identify and group like terms. 5x + 2 Add the coefficients.

Lesson Quiz: Part I Identify like terms in the list. 1. 3n2 5n 2n3 8n 2. a5 2a2 a3 3a 4a2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 3. 4a + 3b + 2a 4. x2 + 2y + 8x2 5n, 8n 2a2, 4a2 6a + 3b 9x2 + 2y

Lesson Quiz: Part II 5. Write an expression for the perimeter of the given figure. 2x + 3y x + y x + y 2x + 3y 6x + 8y

1. Identify the like terms in the list. 6a, 5a2, 2a, 6a3, 7a A. 6a and 2a B. 6a, 5a2, and 6a3 C. 6a, 2a, and 7a D. 5a2 and 6a3

2. Identify the like terms in the list. 16y6, 2y5, 4y2, 10y, 16y2 A. 16y6 and 16y2 B. 4y2 and 16y2 C. 16y6 and 2y2 D. 2y5 and 10y

Identify an expression for the perimeter of the given figure.
A. (4x + 5y)(x + 2y) C. 10x + 14y B D. 5x + 7y 4x + 5y x + 2y

Unit 2 Lesson 3 Part A

How do you write equivalent expressions using the Distributive Property?

LearnZillion Notes: --This is our lesson objective. Keep it as short and student-friendly as possible. Put what they will learn in green and then how they’ll learn it in blue. For example, “In this lesson you will learn how to compare fractions with different denominators by using a number line.”

For example, how do you expand
How do you expand linear expressions that involve multiplication, addition, and subtraction? For example, how do you expand 3(4 + 2x)? Hook How do you expand linear expressions that involve multiplication, addition, and subtraction? For example, how do you expand 3(4 + 2x)? Coach’s Commentary I chose this example because it is easy to demonstrate with an area model, which gives students a concrete way to visualize the distributive property of multiplication over addition.

Vocabulary: Linear expression Rational coefficient Combine like terms
Let’s Review Vocabulary: linear expression, rational coefficient, combine like terms

LearnZillion Notes: --We’ve included a second “Core Lesson” slide for you. If you don’t need this, just delete it, and if you need more you can copy and paste the entire slide or add a blank “Core Lesson” template slide by clicking on arrow below “New Slide” menu.

Distributive Property Steps:
S1: Identify the term outside the ( ). S2: Multiply the outside term by the 1st inside term. S3: Bring down the correct operation. S4: Multiply the outside term by the 2nd inside term. S5: Continue multiplying the outside term by any other inside terms. S6: Combine like terms to simplify.

Forgetting to distribute to the second term (number). For example,
3(2 + 4) ≠ (3 • 2) + 4 LearnZillion Notes: --For some lessons it may be best to include a slide or two about “A Common Mistake.” These slides show students what mistakes to avoid so that they can follow the Core Lessons more easily. --Feel free to move or resize the blue text box to fit your content. --Remember that you can add multiple “A Common Mistake” slides if you need them or you can just delete this slide!

x 1 x 1 Core Lesson How do we expand 3(2x + 4)? One way to visualize this is by using an area model. Let a rectangle of no particular size represent the value x, and 4 small squares, each with an area of 1, represent the value 4. Placing them side by side results a rectangle with an area of 2x + 4. Since we are given 3 groups of 2x + 4, we simply use three of these rectangles. Now we can see that there are 3 groups of 2x and 3 groups of 4, or 2x + 2x + 2x plus , so the result is 6x + 12. Coach’s Commentary Using an area model gives students a concrete way to visualize the abstract concept of distribution. x 1

33a -22 Core Lesson Sometimes we have to use the distributive property on two quantities, then simplify by combining like terms. The commutative property can help us gather like terms. When subtraction is involved, you are simply distributing a negative number rather than a positive number. It is helpful to change subtraction to addition of a negative. For example, 11(3a – 2) – 6(8a – 9) = 11(3a + (–2)) + (–6)(8a + (–9)) = 33a + (–22) + (–48a) + 54 = –15a + 32. Coach’s Commentary Some students forget to distribute the negative to every term in parentheses.

Guided Practice Simplify: 9(5k – 8) – 4(7 – 2k) Answer: 53k – 100

Use a diagram to show why 4(3y + 2) = 12y + 8.
Extension Activities For a struggling student who needs more practice: Use a diagram to show why 4(3y + 2) = 12y + 8. Coach’s Commentary Asking a student to explain the reason why a mathematical procedure works will help the student to solidify his or her reasoning.

Extension Activities For a student who gets it but needs more practice: Simplify 5(7y + 1) – 2(9y – 10) + 3(18 – 4y) Answer: 5y + 79

Quick Quiz 1. Simplify: 7(3x – 4) + 2(5 + 6x) 2. Simplify: 11(4 – 8w) – 6(–9w – 5) Answers: 33x – 18; 74 – 34w

Unit 2 Lesson 3 Part B

when there is a negative term?
How do you simplify when there is a negative term? -3(2x -5) LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific. For example, the hook could be “How do you know if 2/3 is greater than 5/8?” rather than something more generic such as “How do you compare fractions?” --You can fill in an example using the blue text or you can delete that text box and include some other image that explains what you’re talking about.

Simplified Expression
Original Expression Simplified Expression -4(x + 2) -4x – 8 -3(2x – 5) -6x + 15

LearnZillion Notes: --This is the lesson conclusion. On this slide you’ll change your original lesson objective to past tense and explain what the student has just learned. You can retype it here or you can delete the text on this slide and then just copy and paste the text box from the original Lesson Objective slide and then edit it to make it past tense!

LearnZillion Notes: --The “Guided Practice” should include 1 practice problem that targets the skill that was used in the Core Lesson. Use the same vocabulary and process you used in the original lesson to solve this problem. You’ll be making a video in which you solve this question using your tablet and pen, so all you need to do is write the question on this slide.

A student simplified the following expression but made a mistake in the process. Identify the mistake and then explain why it was incorrect. -4(x + y) = -4x + 4y

LearnZillion Notes: --”Quick Quiz” is an easy way to check for student understanding at the end of a lesson. On this slide, you’ll simply display 2 problems that are similar to the previous examples. That’s it! You won’t be recording a video of this slide and when teachers download the slides, they’ll direct their students through the example on their own so you don’t need to show an answer to the question.

Unit 2 Lesson 4

2(2x – 3) + 3(x + y) + 4(-4x – y) ½(6x – 12) Solve (-23)(4) Solve 2/3 + (-5/8)

How do you reverse the distributive property?
-4x + 12 = ?(? +?) LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific. For example, the hook could be “How do you know if 2/3 is greater than 5/8?” rather than something more generic such as “How do you compare fractions?” --You can fill in an example using the blue text or you can delete that text box and include some other image that explains what you’re talking about.

The distributive property tells us that
5(x + 2) = 5x + 10 LearnZillion Notes: --Some lessons may build off of previous lessons. In those cases, it may be helpful to include one or more review slides. Use these slides to remind students of previous concepts you’ve taught in other lessons. --Feel free to move or resize the blue text box to fit your content. --Remember that you can add multiple “Let’s Review” slides if you need them or you can just delete this slide!

_____ _______ _____

What is wrong with this one?
6x + 24 Correct: 6x + 24 = 6(x + 4) What is wrong with this one? 6x + 24 = 3(2x + 8)

LearnZillion Notes: --This is the lesson conclusion. On this slide you’ll change your original lesson objective to past tense and explain what the student has just learned. You can retype it here or you can delete the text on this slide and then just copy and paste the text box from the original Lesson Objective slide and then edit it to make it past tense!

LearnZillion Notes: --The “Guided Practice” should include 1 practice problem that targets the skill that was used in the Core Lesson. Use the same vocabulary and process you used in the original lesson to solve this problem. You’ll be making a video in which you solve this question using your tablet and pen, so all you need to do is write the question on this slide.

LearnZillion Notes: --”Quick Quiz” is an easy way to check for student understanding at the end of a lesson. On this slide, you’ll simply display 2 problems that are similar to the previous examples. That’s it! You won’t be recording a video of this slide and when teachers download the slides, they’ll direct their students through the example on their own so you don’t need to show an answer to the question.

Unit 2 Lesson 5

Learn to solve one-step equations with integers.

Inverse Property of Addition
Words Numbers Algebra The sum of a number and its opposite, or additive inverse, is 0. 3 + (–3) = 0 a + (–a ) = 0

Additional Example 1A: Solving Addition and Subtraction Equations
Solve each question. Check each answer. –6 + x = –7

Additional Example 1B: Solving Addition and Subtraction Equations
Solve each equation. Check each answer. p + 5 = –3

Additional Example 1C: Solving Addition and Subtraction Equations
Solve each equation. Check each answer. y – 9 = –40

Check It Out: Example 1A Solve each equation. Check each answer. –3 + x = –9

Check It Out: Example 1B Solve each equation. Check each answer. q + 2 = –6

Check It Out: Example 1C Solve each equation. Check each answer. y – 7 = –34

Additional Example 2A: Solving Multiplication and Division Equations
Solve each equation. Check each answer. b –5 = 6

Additional Example 2B: Solving Multiplication and Division Equations
Solve each equation. Check each answer. –400 = 8y

Check It Out: Example 2A Solve each equation. Check each answer. c 4 = –24

Check It Out: Example 2B Solve each equation. Check each answer. –200 = 4x

Additional Example 3: Business Application
In 2003, a manufacturer made a profit of $300 million. This amount was $100 million more than the profit in What was the profit in 2002? Let p represent the profit in 2002 (in millions of dollars). This year’s profit 300 is = 100 million 100 More than Last year’s profit p 300 = p –100 –100 200 = p The profit was $200 million in 2002.

Let x represent the money they made last year.
Check It Out: Example 3 This year the class bake sale made a profit of $243. This was an increase of $125 over last year. How much did they make last year? Let x represent the money they made last year. This year’s profit 243 is = 125 million 125 More than Last year’s profit x 243 = x –125 –125 118 = x The class earned $118 last year.

Solve each equation. Check your answer. 1. –8y = –800 2. x – 22 = –18
Lesson Quiz Solve each equation. Check your answer. 1. –8y = –800 2. x – 22 = –18 3. – = 7 4. w + 72 = –21 5. Last year a phone company had a loss of $25 million. This year the loss is $14 million more last year. What is this years loss? 100 4 y 7 –49 –93 $39 million

1. Solve the equation. y + 65= –20 A. y = 45 B. y = 85 C. y = –45 D. y = –85

2. Solve the equation. x – 25= –15 A. x = 10 B. x = 20 C. x = 35 D. x = 45

3. Solve the equation. –10y = –1000 A. y = –200 B. y = –100 C. y = 100 D. y = 200

4. Solve the equation. – — = 6 A. a = 54 B. a = 15 C. a = –15 D. a = –54 a 9

5. In an online test, Dick scored –34 points. This was 20 points less than his previous score. What was his previous score? A. 54 points B. 14 points C. –14 points D. –54 points

Unit 2 Lesson 6

Solving Two-Step Equations

Examples of Two-Step Equations
y/4 + 3 = 12 5n + 4 = 6 n/2 – 6 = 4

Steps for Solving Two-Step Equations
Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.

Opposite Operations Addition  Subtraction Multiplication  Division

Helpful Hints? Identify what operations are on the variable side. (Add, Sub, Mult, Div) “Undo” the operation by using opposite operations. Whatever you do to one side, you must do to the other side to keep equation balanced.

Ex. 1: Solve 4x – 5 = 11 4x – 5 = 15 +5 +5 (Add 5 to both sides)
4x = 20 (Simplify) (Divide both sides by 4) x = 5 (Simplify)

Try These Examples 2x – 5 = 17 3y + 7 = 25 5n – 2 = 38 12b + 4 = 28

Check your answers!!! x = 11 y = 6 n = 8 b = 2

Ready to Move on?

Ex. 2: Solve x/3 + 4 = 9 x/3 + 4 = 9 - 4 - 4 (Subt. 4 from both sides)
x/3 = (Simplify) (x/3)  3 = 5  3 (Mult. by 3 on both sides) x = (Simplify)

Try these examples! x/5 – 3 = 8 c/7 + 4 = 9 r/3 – 6 = 2 d/9 + 4 = 5

Check your answers!!! x = 55 c = 35 r = 24 d = 9

Time to Review! Make sure your equation is in the form Ax + B = C
Keep the equation balanced. Use opposite operations to “undo” Follow the rules: Undo Addition or Subtaction Undo Multiplication or Division

Unit 2 Lesson 7

Inequalities and their Graphs
2 3 4 5 6 7 8

Objective: To write and graph simple inequalities with one variable

What is a good definition for Inequality? An inequality is a statement that two expressions are not equal 2 3 4 5 6 7 8

Terms you see and need to know to graph inequalities correctly < less than Notice open circles > greater than

Terms you see and need to know to graph inequalities correctly ≤ less than or equal to ≥ greater than or equal to Notice colored in circles

Let’s work a few together Notice: when variable is on left side, sign shows direction of solution 3

Let’s work a few together Notice: when variable is on left side, sign shows direction of solution 7

Let’s work a few together Notice: when variable is on left side, sign shows direction of solution Color in circle -2

Let’s work a few together Notice: when variable is on left side, sign shows direction of solution 8 Color in circle

Try this one on your own

On your Own

Answer 1 through 5 1.

On your Own 2.

On your Own 3.

On your Own 4.

On your Own 5.

Answers: 1 through 5 5. 10 -6 25 -15 13

Answer 6 through 10 6. b ≤ -7

On your Own 7. a > 8

On your Own 8. q ≥ -5

On your Own 9. s < 14

On your Own 10. m ≥ 8

Answers: 6 through 10 10. -7 8 -5 14 8

Graphing Inequalities
Excellent Job !!! Well Done

Unit 2 Lesson 1 Warm Up Problem of the Day Lesson Presentation

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Unit 2 Lesson 1 Warm Up Problem of the Day Lesson Presentation

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