6th Grade Math: Chapter 2 LEARNING GOALStudents will understand variables, expressions, and equations by being able to do the following:

•Identify and Evaluate Expressions (2-1)

•Translate between Words and Math (2-2)

•Determine Whether a Number is a Solution of an Equation (2-3)

•Solve Whole-Number Addition Equations (2-4)

•Solve Whole-Number Subtraction Equations (2-5)

•Solve Whole-Number Multiplication Equations (2-6)

•Solve Whole-Number Division Equations (2-7)

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2-3 Equations and Their Solutions

HW: Pg. 54 #8-23 ANSWERS

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2-3 Equations and Their Solutions

6th Grade Math HW

Page 60 #8-20 all

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2-3 Equations and Their Solutions

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2-3 Equations and Their Solutions

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

29

169

16

Warm UpEvaluate each expression for x = 8.

1. 3x + 52. x + 83. 2x – 74. 8x 45. 7x – 16. x – 3

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2-3 Equations and Their Solutions

55

5

Problem of the Day

Complete the magic square so that every row, column, and diagonal add up to the same total.

Solving Subtraction Equations

10

7

4

9 2

8 6

12 5

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2-3 Equations and Their Solutions

Today’s Learning Goal

Learn to determine whether a number is a solution of an equation.

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2-3 Equations and Their Solutions

equationsolution

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2-3 Equations and Their Solutions

Vocabulary

An equation is a mathematical statement that two quantities are equal. You can think of a correct equation as a balanced scale.

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2-3 Equations and Their Solutions

3 + 2 5

Equations may contain variables. If a value for a variable makes an equation true, that value is a solution of the equation.

Course 1

2-3 Equations and Their Solutions

12 + 15 27

s + 15 = 27

s = 12 s = 1010 + 15

27

s = 12 is a solution because 12 + 15 = 27.

s = 10 is not a solution because 10 + 15 27.

Determine whether the given value of the variable is a solution.

Additional Example 1A: Determining Solutions of Equations

b — 447 = 1,203 for b = 1,650

Because 1,203 = 1,203, 1,650 is a solution tob — 447 = 1,203.

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2-3 Equations and Their Solutions

b — 447 = 1,203

Substitute 1,650 for b.

1,203 = 1,203?

1,650 — 447 = 1,203 ?

1,203 1,203

Subtract.

Determine whether the given value of the variable is a solution.

Additional Example 1B: Determining Solutions of Equations

27x = 1,485 for x = 54

Because 1,458 1,485, 54 is not a solution to27x = 1,485.

Course 1

2-3 Equations and Their Solutions

27x = 1,485

Substitute 54 for x.

1,458 = 1,485?

27 54 = 1,485?

1,4581,485

Multiply.

Determine whether the given value of the variable is a solution.

u + 56 = 139 for u = 73

Because 129 139, 73 is not a solution tou + 56 = 139.

Course 1

2-3 Equations and Their Solutions

u + 56 = 139

Substitute 73 for u.

129 = 139?

73 + 56 = 139?

Try This: Example 1A

129139

Add.

Determine whether the given value of the variable is a solution.

45 g = 3 for g = 15

Because 3 = 3,15 is a solution to45 g = 3.

Course 1

2-3 Equations and Their Solutions

45 g = 3

Substitute 15 for g.

3 = 3?

45 15 = 3?

Try This: Example 1B

3 3

Divide.

Paulo says that his yard is 19 yards long. Jamie says that Paulo’s yard is 664 inches long. Determine if these two measurements are equal.

Additional Example 2

Because 684 664, 19 yards are not equal to 664 inches.

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2-3 Equations and Their Solutions

Substitute 19 for y

684 = 664?

Multiply.

36 yd = in.

36 19 = 664 ?36 y = 664

Anna says that the table is 7 feet long. John says that the table is 84 inches long. Determine if these two measurements are equal.

Because 84 = 84, 7 feet is equal to 84 inches.

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2-3 Equations and Their Solutions

12f = 84

Substitute 7 for f.

84 = 84 ?

12 7 = 84?

Try This: Example 2

12 ft. = in.

Multiply.

Determine whether the given value of the variable is a solution.

1. 85 = 13x for x = 5

2. w + 38 = 210 for w = 172

3. 8y = 88 for y = 11

4. 16 = w 6 for w = 98

Lesson Quiz

no

yes

yes

no

no

5. The local pizza shop charged Kylee $172 for 21 medium pizzas. The price of a medium pizza is $8. Determine if Kylee paid the correct amount of money. (Hint: $8 • pizzas = total cost.)

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2-3 Equations and Their Solutions