GRADE 7 EXPRESSIONS AND EQUATIONS.

CCSS.Math.content.7.EE.7

OBJECTIVES AND DEPTH OF THE LESSON.By the end of this lesson students should know,

• Use the Addition and Multiplication property of equality to transform equations.

• Solve problems involving linear equations in one variable.

• Determine the accuracy of solutions.

A + B = B + C A . B = B . A

LINEAR EQUATIONS WITH ONE VARIABLE

PRIOR KNOWLEDGE for one variable LINEAR equation lesson

1. What is a equation?.

ax + b = 0

Two expressions set equal to each other

VARIABLE

WHAT IS A VARIABLE

X,Y,5X,4Y,8A

SOLVE LINEAR EQUATIONS WITH ONE VARIABLE

Linear Equation• Ex: X + 5 = 10

Step 1:

Constant

X + 5 = 10STEP 1:-

Identify the variable in

the equation.

Variable

CCSS.MATH.CONTENT.8.E.E.7.A

X + 5 = 10Constant

IDENTIFY THE CONSTANTSTEP 2

CONSTANT = 5,10

BALANCE THE EQUATION

X +

Not balanced

X + 5 = 10

Step 3

10X 105+

USE ADDITION BALANCE THE PROPERTY EQUATIONA + B = B + A

X + 5 = 10 -5 -5X = 5

ISOLATE THE VARIABLE X

Ex : X + 5 = 10

- 5 -5

SOLVE FOR X

X = 5

SOLVING MORE LINEAR EQUATIONS

X + 2 = 3 -2 -2X =

1

REVIEW ONE VARIABLE EQUATIONS

An equation will always contain an equal sign with an expression on each side.

Ex: X + 4 = 6 1. A Equation has to be balanced.

X + 4 = 6 - 4 -4

SOLVE FOR X

X = 2

LINEAR EQUATION ONE VARIABLE ADDITION AND MULTIPLICATION PROPERTY

2X +8 = 18

USE ADDITION PROPERTY

2X + 8 = 18 - 8 -

82X = 10

STEP 1

2X = 10

USE THE MULTIPLICATION PROPRETY

STEP 2: DIVIDE BOTH SIDES BY 2 TO GET X

2X = 102 2 X = 5

ONE VARIABLE LINEAR EQUATION WITH NO SOLUTION

X + 10 = x + 18

STEP 1

ISOLATE THE VARIABLES (X)

X + 10 = X + 18X -X 10 = 18NO SOLUTION

ONE VARIABLE WITH MANY SOLUTIONS

7X +2 = 2X +2 + 5X

7X + 2 = 2X + 5X +2

-2 -2

STEP 1: IDENTIFY THE CONSTANT.

7X + 2 = 2X +2 +5X STEP 2: USE THE ADDITION

PROPERTY TO GET RID OF THE CONSTANT 2

7X = 2X +5X

COMBINE LIKE TERMS

EX: VARIABLES ARE APPLES

X

CONSTANTS AS HORSES

2,10,5

COMBINE LIKE TERMS IN THE PROBLEM

7X = 2X + 5X

VARIABLE = APPLES

X

7X = 7X

2X 5X+ 7X=

USE THE MULTIPLICATION PROPERTY

7X = 7X7 7

X = X INFINITELY MORE SOLUTIONS

STUDENTS WILL KNOWONE VARIABLE LINEAR EQUATION WITH ONE SOLUTION,NO SOLUTION AND MORE SOLUTIONS.

DISTRIBUTIVE PROPERTY IN ONE VARIALBE LINEAR EQUATIONSWITH RATIONAL NUMBERS.

CCSS.Math.Content.7EE.7B

PRIOR KNOWLEDGE

RATIONAL NUMBERS

(3/4,5/7,9/18)DISTRIBUTIVE PROPERTY A(B + C) = AC + AC

DRISTIBUTIVE PROPERTY

A (B + C) = AB + AC

2(X+5)=20

DISTRIBUTING 2 INTO THE PARENTHESES

2 (X + 5) = 20

2X + 10 = 20

USE THE ADDITION PROPERTY

2X + 10 = 20 - 10 -102X = 10

2X 10

USE THE MULTIPLICATION PROPERTY

2X = 102 2

X = 5

X 5

SOLVE ONE VARIABLE RATIONAL NUMBERS EQUATIONS-DISRTIBUTIVE PROPERTY

1 (2X + 3) = 82

STEP 1

STEP 2:

STEP 3:USE THE ADDITION PROPERTY

X + 2 = 8 3 - 2 - 2 3 = 3 X = 22/3

X = 22/3

APPLICATIONS OF EQUATIONS IN REAL LIFE

Force, speed and distance a foot ball travels.

BUILDING SHELVES

LINEAR EQUATIONS APPLICATION

BUILDING A FOOTBALL STADIUM

Linear Equations- dimensions of the stadium.

Linear Equations –how many people sit.