THREE DAYTHREE DAYUnit Topic/Title: Unit Topic/Title:

EQUATIONS: EQUATIONS: AN INTRODUCTION / AN INTRODUCTION / PROBLEM SOLVINGPROBLEM SOLVING

THREE DAYTHREE DAYLESSON OBJECTIVESLESSON OBJECTIVES

To solve equations using the To solve equations using the Addition, Subtraction, Division Addition, Subtraction, Division and Multiplication Properties for and Multiplication Properties for Equations. Equations.

To solve equations of the form To solve equations of the form x +b =cx +b =c

To solve equations of the form To solve equations of the form ax = c ; x/a =c ax = c ; x/a =c

To solve equations of the form To solve equations of the form ax + b =c ; x/a +b =c ax + b =c ; x/a +b =c

THREE DAYTHREE DAYINDIANA STANDARDSINDIANA STANDARDS

TECHNOLOGYTECHNOLOGY BMS.T.5.1 ---- Technology as a Communication Tool: BMS.T.5.1 ---- Technology as a Communication Tool:

Students use telecommunications to collaborate, publish, Students use telecommunications to collaborate, publish, and interact with peers, teachers, and other audiences. and interact with peers, teachers, and other audiences. Students use a variety of technologies to convey information Students use a variety of technologies to convey information such as e-mail, e-learning, video conferencing, and such as e-mail, e-learning, video conferencing, and telephonytelephony

BMS.T.6.1 ----- Technology as an information Research Tool: BMS.T.6.1 ----- Technology as an information Research Tool: Students use technology to access, review, evaluate, and Students use technology to access, review, evaluate, and select information from multiple resources for reporting select information from multiple resources for reporting purposes. Students write appropriate research reports.purposes. Students write appropriate research reports.

BMS.T.7.1 ---- Technology as a Problem-Solving and Data BMS.T.7.1 ---- Technology as a Problem-Solving and Data Driven Decision- Making Tool: Students use technology to Driven Decision- Making Tool: Students use technology to develop strategies for solving problems.develop strategies for solving problems.

STUDENT ACADEMIC STUDENT ACADEMIC STANDARDSSTANDARDS

A1.2.1A1.2.1 Solve linear equationsSolve linear equations A1.2.2 Solve equations and A1.2.2 Solve equations and

formulas for a specified formulas for a specified variablevariable

A1.2.6 Solve word problems A1.2.6 Solve word problems that involve linear equations, that involve linear equations, formulas, and inequalities. formulas, and inequalities.

KEY DEFINITIONSKEY DEFINITIONS

ADDITION PROPERTY FOR EQUATIONS:ADDITION PROPERTY FOR EQUATIONS: For all real numbers a, b, and c, if a = b, then a + c = b + c.For all real numbers a, b, and c, if a = b, then a + c = b + c.

SUBTRACTION PPROPERTY FOR EQUATIONS:SUBTRACTION PPROPERTY FOR EQUATIONS: For all real numbers a, b, and c, if a = b, then a – c = b – c.For all real numbers a, b, and c, if a = b, then a – c = b – c.

DIVISION PROPERTY FOR EQUATIONS:DIVISION PROPERTY FOR EQUATIONS: For all real numbers a, b, and c, (c For all real numbers a, b, and c, (c ≠ 0), if a = b,≠ 0), if a = b, then a/c = b/c.then a/c = b/c.

MULTIPLICATION PROPERTY FOR EQUATIONS:MULTIPLICATION PROPERTY FOR EQUATIONS: For all real numbers a, b, and c, (c ≠ 0), if a = b, For all real numbers a, b, and c, (c ≠ 0), if a = b, then c · a = c · b.then c · a = c · b.

EQUATION: A mathematical statement that contains an = sign that is EQUATION: A mathematical statement that contains an = sign that is used between two numerical or algebraic expressions. An equation used between two numerical or algebraic expressions. An equation is also a statement in which the item on the left is equal to the item is also a statement in which the item on the left is equal to the item on the right. on the right.

Example: 15 = 15Example: 15 = 15

DAY ONEDAY ONEPROCEDURE / ACTIVITIESPROCEDURE / ACTIVITIES

Students will solve equations with Students will solve equations with variables on both sides.variables on both sides.

To solve equations of the form To solve equations of the form x = b = cx = b = cExample: Solve x - 7 = 6Example: Solve x - 7 = 6X – 7 = 6X – 7 = 6X – 7 + 7 = 6 + 7 X – 7 + 7 = 6 + 7 X = 13X = 13

PROCEDUREPROCEDURE

To solve equations of the form ax = cTo solve equations of the form ax = c

Solve: 7x = -21Solve: 7x = -21

7x = -21 (solve for x)7x = -21 (solve for x)

7x 7x = = -21-21 (divide both sides by 7) (divide both sides by 7)

7 77 7

1x = -3 1x = -3

X = -3X = -3

Website to visit: yourteacher.comWebsite to visit: yourteacher.com

PROCEDUREPROCEDURE

To solve equations with the form :To solve equations with the form : x x = c= c aaSolve:Solve: x x = 5= 5 -3-3-3 -3 ·· x x = -3 · 5 Multiply both sides by –3.= -3 · 5 Multiply both sides by –3. -3-3 check: check: x x = 5 = 5 -15 -15 = =

55X = -15 -3 -3 X = -15 -3 -3

5 = 55 = 5

DAY TWODAY TWOPROCEDUREPROCEDURE

To solve equations of the form To solve equations of the form ax + b = cax + b = cSolve: 2x + 6 = 14 Solve: 2x + 6 = 14 2x + 6 = 142x + 6 = 142x + 6 – 6 = 14 – 62x + 6 – 6 = 14 – 62x + 0 = 82x + 0 = 8 2x2x = = 88 2 22 2 x = 4x = 4

DAY THREEDAY THREEPROCEDURE / ACTIVITIESPROCEDURE / ACTIVITIES

Students will solve equations with variables on both Students will solve equations with variables on both sides.sides.

Solve 5x – 8 = 3x + 12Solve 5x – 8 = 3x + 12

-3x +5x – 8 = -3x +3x +12 -3x +5x – 8 = -3x +3x +12 ↔ Add -3x to each side.↔ Add -3x to each side.

2x – 8 = 0 + 12 ↔ Combine like terms.2x – 8 = 0 + 12 ↔ Combine like terms.

2x – 8 = 12 ↔ Now we have one variable 2x – 8 = 12 ↔ Now we have one variable term.term.

2x – 8 + 8 = 12 + 8 ↔ Add 8 to each side.2x – 8 + 8 = 12 + 8 ↔ Add 8 to each side.

2x 2x = = 2020 ↔ Divide each side by 2 ↔ Divide each side by 2

2 22 2

x = 10x = 10

Therefore, the solution is 10.Therefore, the solution is 10.

DAY FOURDAY FOURWORD PROBLEMWORD PROBLEM

Word problems can lead to equations with the variable on Word problems can lead to equations with the variable on both sides. Solve:both sides. Solve:

Twenty more than 4 times Jack’s age is the same as 6 times Twenty more than 4 times Jack’s age is the same as 6 times his age.his age.

Read > The problem asks for Jack’s age.Read > The problem asks for Jack’s age.

Plan > Use a variable to represent Jack’s age. Let a = his Plan > Use a variable to represent Jack’s age. Let a = his age.age.

(20 more than (20 more than 4 times Jack’s age) (4 times Jack’s age) (is the same as) (6 times is the same as) (6 times his age).his age).

Solve > 4a + 20 = 6aSolve > 4a + 20 = 6a -4a + 4a + 20 = -4a + 6a-4a + 4a + 20 = -4a + 6a 20 20 = = 2a2a 2 22 2 10 = a10 = a

DAY FIVEDAY FIVEWORD PROBLEMWORD PROBLEM

20 MORE THAN 4 Times Jack’s age is the same as 6 times 20 MORE THAN 4 Times Jack’s age is the same as 6 times is age.is age.

4 4 · 10 + 20 | 6 · 10· 10 + 20 | 6 · 10

40 + 20 | 6040 + 20 | 60

60 = 60 True60 = 60 True

Therefore, Jack is 10 years Therefore, Jack is 10 years old.old.

Supplemental Website:Supplemental Website:

SOLVE THESE PROBLESSOLVE THESE PROBLES

1.1. 6X + 7 = 3X + 166X + 7 = 3X + 16

2.2. 6 + 10X = 8X + 126 + 10X = 8X + 12

3. 6P + 13 = 9P – 53. 6P + 13 = 9P – 5

Answer to Problem #1Answer to Problem #1

6x + 7 + 3x + 166x + 7 + 3x + 16 6x – 6x +7 = 3x -6x +166x – 6x +7 = 3x -6x +16 0 + 7 = -3X + 160 + 7 = -3X + 16 7 – 16 = -3X + 16 – 167 – 16 = -3X + 16 – 16 -9-9 = = -3X-3X

-3 = -3-3 = -3

3 = X 3 = X

Answer to ProblemAnswer to Problem#1(same problem)#1(same problem) 6X + 7 = 3X + 166X + 7 = 3X + 16 6X -3X + 7 = 3X – 3X +166X -3X + 7 = 3X – 3X +16 3X + 7 = 0 + 163X + 7 = 0 + 16 3X + 7 - 7 = 16 – 73X + 7 - 7 = 16 – 7 3X + 0 = 93X + 0 = 9 3X3X = = 9 9 3 33 3 X = 3X = 3

HOMEWORK HOMEWORK WILL BE WILL BE

ASSIGNEDASSIGNED

WEB SITES TO VISIT FOR WEB SITES TO VISIT FOR ADDITIONAL HELPADDITIONAL HELP

http://www.yourteacher.com http://www.facebook.com/pages/

yourteachermath/13

POST - TESTPOST - TEST

EQUATIONSEQUATIONS

THREE DAYTHREE DAYUnit Topic/Title: Unit Topic/Title:

EQUATIONS: EQUATIONS: AN INTRODUCTION / AN INTRODUCTION / PROBLEM SOLVINGPROBLEM SOLVING

THREE DAYTHREE DAYLESSON OBJECTIVESLESSON OBJECTIVES

To solve equations using the To solve equations using the Addition, Subtraction, Division Addition, Subtraction, Division and Multiplication Properties for and Multiplication Properties for Equations. Equations.

To solve equations of the form To solve equations of the form x +b =cx +b =c

To solve equations of the form To solve equations of the form ax = c ; x/a =c ax = c ; x/a =c

To solve equations of the form To solve equations of the form ax + b =c ; x/a +b =c ax + b =c ; x/a +b =c

THREE DAYTHREE DAYINDIANA STANDARDSINDIANA STANDARDS

TECHNOLOGYTECHNOLOGY BMS.T.5.1 ---- Technology as a Communication Tool: BMS.T.5.1 ---- Technology as a Communication Tool:

Students use telecommunications to collaborate, publish, Students use telecommunications to collaborate, publish, and interact with peers, teachers, and other audiences. and interact with peers, teachers, and other audiences. Students use a variety of technologies to convey information Students use a variety of technologies to convey information such as e-mail, e-learning, video conferencing, and such as e-mail, e-learning, video conferencing, and telephonytelephony

BMS.T.6.1 ----- Technology as an information Research Tool: BMS.T.6.1 ----- Technology as an information Research Tool: Students use technology to access, review, evaluate, and Students use technology to access, review, evaluate, and select information from multiple resources for reporting select information from multiple resources for reporting purposes. Students write appropriate research reports.purposes. Students write appropriate research reports.

BMS.T.7.1 ---- Technology as a Problem-Solving and Data BMS.T.7.1 ---- Technology as a Problem-Solving and Data Driven Decision- Making Tool: Students use technology to Driven Decision- Making Tool: Students use technology to develop strategies for solving problems.develop strategies for solving problems.

STUDENT ACADEMIC STUDENT ACADEMIC STANDARDSSTANDARDS

A1.2.1A1.2.1 Solve linear equationsSolve linear equations A1.2.2 Solve equations and A1.2.2 Solve equations and

formulas for a specified formulas for a specified variablevariable

A1.2.6 Solve word problems A1.2.6 Solve word problems that involve linear equations, that involve linear equations, formulas, and inequalities. formulas, and inequalities.

KEY DEFINITIONSKEY DEFINITIONS

ADDITION PROPERTY FOR EQUATIONS:ADDITION PROPERTY FOR EQUATIONS: For all real numbers a, b, and c, if a = b, then a + c = b + c.For all real numbers a, b, and c, if a = b, then a + c = b + c.

SUBTRACTION PPROPERTY FOR EQUATIONS:SUBTRACTION PPROPERTY FOR EQUATIONS: For all real numbers a, b, and c, if a = b, then a – c = b – c.For all real numbers a, b, and c, if a = b, then a – c = b – c.

DIVISION PROPERTY FOR EQUATIONS:DIVISION PROPERTY FOR EQUATIONS: For all real numbers a, b, and c, (c For all real numbers a, b, and c, (c ≠ 0), if a = b,≠ 0), if a = b, then a/c = b/c.then a/c = b/c.

MULTIPLICATION PROPERTY FOR EQUATIONS:MULTIPLICATION PROPERTY FOR EQUATIONS: For all real numbers a, b, and c, (c ≠ 0), if a = b, For all real numbers a, b, and c, (c ≠ 0), if a = b, then c · a = c · b.then c · a = c · b.

EQUATION: A mathematical statement that contains an = sign that is EQUATION: A mathematical statement that contains an = sign that is used between two numerical or algebraic expressions. An equation used between two numerical or algebraic expressions. An equation is also a statement in which the item on the left is equal to the item is also a statement in which the item on the left is equal to the item on the right. on the right.

Example: 15 = 15Example: 15 = 15

DAY ONEDAY ONEPROCEDURE / ACTIVITIESPROCEDURE / ACTIVITIES

Students will solve equations with Students will solve equations with variables on both sides.variables on both sides.

To solve equations of the form To solve equations of the form x = b = cx = b = cExample: Solve x - 7 = 6Example: Solve x - 7 = 6X – 7 = 6X – 7 = 6X – 7 + 7 = 6 + 7 X – 7 + 7 = 6 + 7 X = 13X = 13

PROCEDUREPROCEDURE

To solve equations of the form ax = cTo solve equations of the form ax = c

Solve: 7x = -21Solve: 7x = -21

7x = -21 (solve for x)7x = -21 (solve for x)

7x 7x = = -21-21 (divide both sides by 7) (divide both sides by 7)

7 77 7

1x = -3 1x = -3

X = -3X = -3

Website to visit: yourteacher.comWebsite to visit: yourteacher.com

PROCEDUREPROCEDURE

To solve equations with the form :To solve equations with the form : x x = c= c aaSolve:Solve: x x = 5= 5 -3-3-3 -3 ·· x x = -3 · 5 Multiply both sides by –3.= -3 · 5 Multiply both sides by –3. -3-3 check: check: x x = 5 = 5 -15 -15 = =

55X = -15 -3 -3 X = -15 -3 -3

5 = 55 = 5

DAY TWODAY TWOPROCEDUREPROCEDURE

To solve equations of the form To solve equations of the form ax + b = cax + b = cSolve: 2x + 6 = 14 Solve: 2x + 6 = 14 2x + 6 = 142x + 6 = 142x + 6 – 6 = 14 – 62x + 6 – 6 = 14 – 62x + 0 = 82x + 0 = 8 2x2x = = 88 2 22 2 x = 4x = 4

DAY THREEDAY THREEPROCEDURE / ACTIVITIESPROCEDURE / ACTIVITIES

Students will solve equations with variables on both Students will solve equations with variables on both sides.sides.

Solve 5x – 8 = 3x + 12Solve 5x – 8 = 3x + 12

-3x +5x – 8 = -3x +3x +12 -3x +5x – 8 = -3x +3x +12 ↔ Add -3x to each side.↔ Add -3x to each side.

2x – 8 = 0 + 12 ↔ Combine like terms.2x – 8 = 0 + 12 ↔ Combine like terms.

2x – 8 = 12 ↔ Now we have one variable 2x – 8 = 12 ↔ Now we have one variable term.term.

2x – 8 + 8 = 12 + 8 ↔ Add 8 to each side.2x – 8 + 8 = 12 + 8 ↔ Add 8 to each side.

2x 2x = = 2020 ↔ Divide each side by 2 ↔ Divide each side by 2

2 22 2

x = 10x = 10

Therefore, the solution is 10.Therefore, the solution is 10.

DAY FOURDAY FOURWORD PROBLEMWORD PROBLEM

Word problems can lead to equations with the variable on Word problems can lead to equations with the variable on both sides. Solve:both sides. Solve:

Twenty more than 4 times Jack’s age is the same as 6 times Twenty more than 4 times Jack’s age is the same as 6 times his age.his age.

Read > The problem asks for Jack’s age.Read > The problem asks for Jack’s age.

Plan > Use a variable to represent Jack’s age. Let a = his Plan > Use a variable to represent Jack’s age. Let a = his age.age.

(20 more than (20 more than 4 times Jack’s age) (4 times Jack’s age) (is the same as) (6 times is the same as) (6 times his age).his age).

Solve > 4a + 20 = 6aSolve > 4a + 20 = 6a -4a + 4a + 20 = -4a + 6a-4a + 4a + 20 = -4a + 6a 20 20 = = 2a2a 2 22 2 10 = a10 = a

DAY FIVEDAY FIVEWORD PROBLEMWORD PROBLEM

20 MORE THAN 4 Times Jack’s age is the same as 6 times 20 MORE THAN 4 Times Jack’s age is the same as 6 times is age.is age.

4 4 · 10 + 20 | 6 · 10· 10 + 20 | 6 · 10

40 + 20 | 6040 + 20 | 60

60 = 60 True60 = 60 True

Therefore, Jack is 10 years Therefore, Jack is 10 years old.old.

Supplemental Website:Supplemental Website:

SOLVE THESE PROBLESSOLVE THESE PROBLES

1.1. 6X + 7 = 3X + 166X + 7 = 3X + 16

2.2. 6 + 10X = 8X + 126 + 10X = 8X + 12

3. 6P + 13 = 9P – 53. 6P + 13 = 9P – 5

Answer to Problem #1Answer to Problem #1

6x + 7 + 3x + 166x + 7 + 3x + 16 6x – 6x +7 = 3x -6x +166x – 6x +7 = 3x -6x +16 0 + 7 = -3X + 160 + 7 = -3X + 16 7 – 16 = -3X + 16 – 167 – 16 = -3X + 16 – 16 -9-9 = = -3X-3X

-3 = -3-3 = -3

3 = X 3 = X

Answer to ProblemAnswer to Problem#1(same problem)#1(same problem) 6X + 7 = 3X + 166X + 7 = 3X + 16 6X -3X + 7 = 3X – 3X +166X -3X + 7 = 3X – 3X +16 3X + 7 = 0 + 163X + 7 = 0 + 16 3X + 7 - 7 = 16 – 73X + 7 - 7 = 16 – 7 3X + 0 = 93X + 0 = 9 3X3X = = 9 9 3 33 3 X = 3X = 3

HOMEWORK HOMEWORK WILL BE WILL BE

ASSIGNEDASSIGNED

WEB SITES TO VISIT FOR WEB SITES TO VISIT FOR ADDITIONAL HELPADDITIONAL HELP

http://www.yourteacher.com http://www.facebook.com/pages/

yourteachermath/13

POST - TESTPOST - TEST

EQUATIONSEQUATIONS