1.
THREE DAYTHREE DAY
Unit Topic/Title:Unit Topic/Title:
EQUATIONS:EQUATIONS:
AN INTRODUCTION /AN INTRODUCTION /
PROBLEM SOLVINGPROBLEM SOLVING
2.
THREE DAYTHREE DAY
LESSON OBJECTIVESLESSON OBJECTIVES
To solve equations using theTo solve equations using the
Addition, Subtraction, DivisionAddition, Subtraction, Division
and Multiplication Properties forand Multiplication Properties for
Equations.Equations.
To solve equations of the formTo solve equations of the form
x +b =cx +b =c
To solve equations of the formTo solve equations of the form
ax = c ; x/a =cax = c ; x/a =c
To solve equations of the formTo solve equations of the form
ax + b =c ; x/a +b =cax + b =c ; x/a +b =c
3.
THREE DAYTHREE DAY
INDIANA 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 informationStudents use a variety of technologies to convey information
such as e-mail, e-learning, video conferencing, andsuch 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, andStudents use technology to access, review, evaluate, and
select information from multiple resources for reportingselect 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 DataBMS.T.7.1 ---- Technology as a Problem-Solving and Data
Driven Decision- Making Tool: Students use technology toDriven Decision- Making Tool: Students use technology to
develop strategies for solving problems.develop strategies for solving problems.
4.
STUDENT ACADEMICSTUDENT ACADEMIC
STANDARDSSTANDARDS
A1.2.1A1.2.1 Solve linear equationsSolve linear equations
A1.2.2 Solve equations andA1.2.2 Solve equations and
formulas for a specifiedformulas for a specified
variablevariable
A1.2.6 Solve word problemsA1.2.6 Solve word problems
that involve linear equations,that involve linear equations,
formulas, and inequalities.formulas, and inequalities.
5.
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, (cFor 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 isEQUATION: A mathematical statement that contains an = sign that is
used between two numerical or algebraic expressions. An equationused between two numerical or algebraic expressions. An equation
is also a statement in which the item on the left is equal to the itemis 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
6.
DAY ONEDAY ONE
PROCEDURE / ACTIVITIESPROCEDURE / ACTIVITIES
Students will solve equations withStudents will solve equations with
variables on both sides.variables on both sides.
To solve equations of the formTo solve equations of the form
x = b = cx = b = c
Example: Solve x - 7 = 6Example: Solve x - 7 = 6
X – 7 = 6X – 7 = 6
X – 7 + 7 = 6 + 7X – 7 + 7 = 6 + 7
X = 13X = 13
7.
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)
7x7x == -21-21 (divide both sides by 7)(divide both sides by 7)
7 77 7
1x = -31x = -3
X = -3X = -3
Website to visit: yourteacher.comWebsite to visit: yourteacher.com
8.
PROCEDUREPROCEDURE
To solve equations with the form :To solve equations with the form : xx = c= c
aa
Solve:Solve: xx = 5= 5
-3-3
-3-3 ·· xx = -3 · 5 Multiply both sides by –3.= -3 · 5 Multiply both sides by –3.
-3-3 check:check: xx = 5= 5 -15-15 = 5= 5
X = -15 -3 -3X = -15 -3 -3
5 = 55 = 5
9.
DAY TWODAY TWO
PROCEDUREPROCEDURE
To solve equations of the formTo solve equations of the form
ax + b = cax + b = c
Solve: 2x + 6 = 14Solve: 2x + 6 = 14
2x + 6 = 142x + 6 = 14
2x + 6 – 6 = 14 – 62x + 6 – 6 = 14 – 6
2x + 0 = 82x + 0 = 8
2x2x == 88
2 22 2
x = 4x = 4
10.
DAY THREEDAY THREE
PROCEDURE / ACTIVITIESPROCEDURE / ACTIVITIES
Students will solve equations with variables on bothStudents 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 variable2x – 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.
2x2x == 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.
11.
DAY FOURDAY FOUR
WORD PROBLEMWORD PROBLEM
Word problems can lead to equations with the variable onWord 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 6Twenty more than 4 times Jack’s age is the same as 6
times his age.times 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 =Plan > Use a variable to represent Jack’s age. Let a =
his age.his age.
(20 more than(20 more than 4 times Jack’s age) (4 times Jack’s age) (is the same as) (6is the same as) (6
times his age).times his age).
Solve > 4a + 20 = 6aSolve > 4a + 20 = 6a
-4a + 4a + 20 = -4a + 6a-4a + 4a + 20 = -4a + 6a
2020 == 2a2a
2 22 2
10 = a10 = a
12.
DAY FIVEDAY FIVE
WORD PROBLEMWORD PROBLEM
20 MORE THAN 4 Times Jack’s age is the same as 620 MORE THAN 4 Times Jack’s age is the same as 6
times is age.times is age.
44 · 10 + 20 | 6 · 10· 10 + 20 | 6 · 10
40 + 20 | 6040 + 20 | 60
60 = 60 True60 = 60 True
Therefore, Jack is 10 yearsTherefore, Jack is 10 years
old.old.
Supplemental Website:Supplemental Website:
16.
HOMEWORKHOMEWORK
WILL BEWILL BE
ASSIGNEDASSIGNED
17.
WEB SITES TO VISIT FORWEB SITES TO VISIT FOR
ADDITIONAL HELPADDITIONAL HELP
http://www.yourteacher.comhttp://www.yourteacher.com
http://www.facebook.com/pages/yohttp://www.facebook.com/pages/yo
19.
THREE DAYTHREE DAY
Unit Topic/Title:Unit Topic/Title:
EQUATIONS:EQUATIONS:
AN INTRODUCTION /AN INTRODUCTION /
PROBLEM SOLVINGPROBLEM SOLVING
20.
THREE DAYTHREE DAY
LESSON OBJECTIVESLESSON OBJECTIVES
To solve equations using theTo solve equations using the
Addition, Subtraction, DivisionAddition, Subtraction, Division
and Multiplication Properties forand Multiplication Properties for
Equations.Equations.
To solve equations of the formTo solve equations of the form
x +b =cx +b =c
To solve equations of the formTo solve equations of the form
ax = c ; x/a =cax = c ; x/a =c
To solve equations of the formTo solve equations of the form
ax + b =c ; x/a +b =cax + b =c ; x/a +b =c
21.
THREE DAYTHREE DAY
INDIANA 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 informationStudents use a variety of technologies to convey information
such as e-mail, e-learning, video conferencing, andsuch 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, andStudents use technology to access, review, evaluate, and
select information from multiple resources for reportingselect 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 DataBMS.T.7.1 ---- Technology as a Problem-Solving and Data
Driven Decision- Making Tool: Students use technology toDriven Decision- Making Tool: Students use technology to
develop strategies for solving problems.develop strategies for solving problems.
22.
STUDENT ACADEMICSTUDENT ACADEMIC
STANDARDSSTANDARDS
A1.2.1A1.2.1 Solve linear equationsSolve linear equations
A1.2.2 Solve equations andA1.2.2 Solve equations and
formulas for a specifiedformulas for a specified
variablevariable
A1.2.6 Solve word problemsA1.2.6 Solve word problems
that involve linear equations,that involve linear equations,
formulas, and inequalities.formulas, and inequalities.
23.
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, (cFor 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 isEQUATION: A mathematical statement that contains an = sign that is
used between two numerical or algebraic expressions. An equationused between two numerical or algebraic expressions. An equation
is also a statement in which the item on the left is equal to the itemis 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
24.
DAY ONEDAY ONE
PROCEDURE / ACTIVITIESPROCEDURE / ACTIVITIES
Students will solve equations withStudents will solve equations with
variables on both sides.variables on both sides.
To solve equations of the formTo solve equations of the form
x = b = cx = b = c
Example: Solve x - 7 = 6Example: Solve x - 7 = 6
X – 7 = 6X – 7 = 6
X – 7 + 7 = 6 + 7X – 7 + 7 = 6 + 7
X = 13X = 13
25.
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)
7x7x == -21-21 (divide both sides by 7)(divide both sides by 7)
7 77 7
1x = -31x = -3
X = -3X = -3
Website to visit: yourteacher.comWebsite to visit: yourteacher.com
26.
PROCEDUREPROCEDURE
To solve equations with the form :To solve equations with the form : xx = c= c
aa
Solve:Solve: xx = 5= 5
-3-3
-3-3 ·· xx = -3 · 5 Multiply both sides by –3.= -3 · 5 Multiply both sides by –3.
-3-3 check:check: xx = 5= 5 -15-15 = 5= 5
X = -15 -3 -3X = -15 -3 -3
5 = 55 = 5
27.
DAY TWODAY TWO
PROCEDUREPROCEDURE
To solve equations of the formTo solve equations of the form
ax + b = cax + b = c
Solve: 2x + 6 = 14Solve: 2x + 6 = 14
2x + 6 = 142x + 6 = 14
2x + 6 – 6 = 14 – 62x + 6 – 6 = 14 – 6
2x + 0 = 82x + 0 = 8
2x2x == 88
2 22 2
x = 4x = 4
28.
DAY THREEDAY THREE
PROCEDURE / ACTIVITIESPROCEDURE / ACTIVITIES
Students will solve equations with variables on bothStudents 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 variable2x – 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.
2x2x == 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.
29.
DAY FOURDAY FOUR
WORD PROBLEMWORD PROBLEM
Word problems can lead to equations with the variable onWord 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 6Twenty more than 4 times Jack’s age is the same as 6
times his age.times 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 =Plan > Use a variable to represent Jack’s age. Let a =
his age.his age.
(20 more than(20 more than 4 times Jack’s age) (4 times Jack’s age) (is the same as) (6is the same as) (6
times his age).times his age).
Solve > 4a + 20 = 6aSolve > 4a + 20 = 6a
-4a + 4a + 20 = -4a + 6a-4a + 4a + 20 = -4a + 6a
2020 == 2a2a
2 22 2
10 = a10 = a
30.
DAY FIVEDAY FIVE
WORD PROBLEMWORD PROBLEM
20 MORE THAN 4 Times Jack’s age is the same as 620 MORE THAN 4 Times Jack’s age is the same as 6
times is age.times is age.
44 · 10 + 20 | 6 · 10· 10 + 20 | 6 · 10
40 + 20 | 6040 + 20 | 60
60 = 60 True60 = 60 True
Therefore, Jack is 10 yearsTherefore, Jack is 10 years
old.old.
Supplemental Website:Supplemental Website:
34.
HOMEWORKHOMEWORK
WILL BEWILL BE
ASSIGNEDASSIGNED
35.
WEB SITES TO VISIT FORWEB SITES TO VISIT FOR
ADDITIONAL HELPADDITIONAL HELP
http://www.yourteacher.comhttp://www.yourteacher.com
http://www.facebook.com/pages/yohttp://www.facebook.com/pages/yo
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