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Date, October 5th, 2010
AIM: How do we solve one- and two- step equations?
Objectives: SWBAT
-solve equations of the type x + a = b, where a and b are rational numbers, by isolating the variable using inverses, by guess and
check, by manipulating algebra tiles
- check the solutions and write the solution set
- solve equations of the type ax = b, where a and b are rational signed numbers, by isolating the variable using reciprocals, guess and
check.
- investigate the connections between solving equations of the form ax=b and x+a=b
- select and apply the appropriate isolation method for solving equations of the form ax=b as compared to solving equations of the
form x+a=b
- isolate the variable using properties of inverses and identities
- solve equations of the type ax + b = c where a, b, and c are rational signed numbers
Standards:
A.A.21 Determine whether a given value is a solution to a given linear equation in one variable
A.A.22 Solve all types of linear equations in one variable (including 1-step, 2-step )
A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equations (only linear for now)
Quiz: Choose 2. 1. 5x  35 2. 35= 3 + 5x
Key Points
Common
Mistakes
1.
2.
3.
1.
2.
3. 4d  2  6
To solve equations, use inverse operations in the reverse order of operations
5-x=10 is actually a two-step equation.
–x is the same as -1*x.
Students will solve an equation “4-b=10” by adding 4.
Students are afraid when they do not get integers as answers
3. Students forget what to do when they see
Do Now
Minilesson
d
 6.
4
Substitution into equations, inverse operations.
One way to find the solution of an equation is to get the variable _alone_on one side of the equal sign.
We can do this using ___Inverse operations_, which are operations that undo one another.
Since we use the inverse (opposite) operation to undo, we perform these operations in the opposite order from the _order of operation.
First undo ___addition and subtraction. Then, undo multiplication and division.
One way to find the solution of an equation is to get the variable _________on one side of the equal sign.
We can do this using ______________________________, which are operations that undo one another.
Since we use the inverse (opposite) operation to undo, we perform these operations in the opposite order from the
_____________________________________.
The inverse of addition is ____________________________; subtraction is ___________________________;
Multiplication is ________________________; division is _____________________________.
Note: -x is the same as _____________________.
To Solve Two-Step Equations:
First undo _______________________________. Then, undo ___________________________________.
Guided
Practice
Think, Pair,
Share
( group
work)
Independent
Practice
Processing
Questions
Summary
Demonstrate solving one and two steps equations
See attached.
9 problems dealing with one and two steps equations and proportions.
1) 3x-2 = 4 2) 10=
m
+2
4
In example 1 and 2 what operation do we undo first, why and how do we do it?
How is solving a two step equation like working the order of operations backwards?
MATH MASTER: ____________________________________________________
ALGEBRA
DATE:_____________________________________________________________
PAGE: _______
AIM:_____________________________________________________________________________________
_________________________________________________________________________________________
DO NOW( 5 MINUTES)
1. Substitute the given value into the equation and see if it makes the sentence true or false.
a)  3x  5  3
( x  0)
b) 2x  4  2
( x  1)
2. What is the difference between #1 and #2?
3. Can you find a solution for each equation? If so, how do you know?
a) g+7 = 11
b) 4c = -96
4.What is the sum of
75 and
48 ? [A.N.3]
(1) 123
(3) 9 6
(2) 9 3
(4) 41 3
MINI-LESSON( 3 minutes)
Frayer Model
1) 3x-2 = 4
2) 10=
m
+2
4
Procedure:
GUIDED PRACTICE( 5 MINUTES)
Check:
Procedure:
Check:
MEDIAL SUMMARY ( 3 MINUTES)
In examples 1 and 2 what operations do we undo first? Why? How did we do this?
THINK( 5 MINUTES ) , PAIR AND SHARE( 3 MINUTES)
Solve each equation. Show all your steps. Choose two equations to check.
1) 3x  21
3) 4  2x  10
x
2)  2
4
4)
x
5 1
3
5) 7  x  8
Check
6)
x2
5
9
Check
INDEPENDENT PRACTICE( 15 MINUTES)
1) x -15 = 20
4) 7- 3k = -14
7) -8-c = 11
2)
x
 12
4
5) -8-c = 11
8)
4 m

6 9
3) 3x-15 =33
6)
a
 15  30
5
9) 2x  3  10
( Summary Reflection 4 minutes) Quiz ( 7 minutes)
REFLECTION: WHAT DID YOU LEARN TODAY? On a
SUMMARY: How is solving a two step equation like
working the order of operations backwards?
scale of 1 to 10, how well do you think you met
___________________________________________ today’s objective? What questions do you still have?
___________________________________________ ___________________________________________
___________________________________________ ___________________________________________
___________________________________________ ___________________________________________
TOTAL
POINTS