Solving Two Step Solving Two Step EquationsEquations

August 19,2013August 19,2013

WELCOME!WELCOME!Math is used in everyday life activities consciously Math is used in everyday life activities consciously

and unconsciously.and unconsciously.

Objective: The student will solve two step equations Objective: The student will solve two step equations using the addition, subtraction, multiplication, using the addition, subtraction, multiplication, and division properties of equality. and division properties of equality.

Students will identify the Commutative and Students will identify the Commutative and Associative Property.Associative Property.

All students will be able to solve real-world All students will be able to solve real-world application:application:

There are 26 students in Ms. Bean's class. The There are 26 students in Ms. Bean's class. The number of boys is equal to seven fewer than number of boys is equal to seven fewer than twice the number of girls. How many boys and twice the number of girls. How many boys and how many girls are in the class?how many girls are in the class?

Monday, Aug. 19Monday, Aug. 19

Round the decimals to the underlined Round the decimals to the underlined place value.place value.

1)1) 4.94.988772)2) 3.3.1134343)3) 7799.85.854)4) 55442.912.915)5) 12.1012.105522

4.99

3.1

80

540

12.105

Properties of MathProperties of MathCommutative Properties of Addition and Commutative Properties of Addition and MultiplicationMultiplication

For any numbers a For any numbers a and b,and b,

a + b = b + aa + b = b + a

The order in which The order in which numbers are added numbers are added does not change the does not change the sum.sum.

9 + 2 = 2 + 99 + 2 = 2 + 9

For any numbers a For any numbers a and b,and b,

a a ** b = b b = b ** a a

The order in which The order in which numbers are numbers are multiplied does not multiplied does not change the product. change the product.

6 6 ** 5 = 5 5 = 5 ** 6 6

Properties of MathProperties of MathAssociative Properties of Addition and Associative Properties of Addition and MultiplicationMultiplication

For any numbers a, For any numbers a, b, and c,b, and c,

(a + b) + c = a + (b (a + b) + c = a + (b + c)+ c)

The way in which The way in which addends are grouped addends are grouped does not change the does not change the sum.sum.

(5 + 3) + 1 = 5 + (3 (5 + 3) + 1 = 5 + (3 + 1)+ 1)

For any numbers a, b For any numbers a, b and c, and c,

(a (a ** b) b) ** c = a c = a ** (b (b ** c) c)

The way in which The way in which numbers are numbers are grouped does not grouped does not change the product. change the product.

(2 (2 ** 6) 6) ** 7 = 2 7 = 2 ** (6 (6 ** 7) 7)

InstructionInstruction

It takes two steps to solve an equation that It takes two steps to solve an equation that has more than one operation.has more than one operation.

1.1. Simplify by using the addition or Simplify by using the addition or subtraction property of equality. (use the subtraction property of equality. (use the inverse of addition or subtraction)inverse of addition or subtraction)

2.2. Simplify further by using the Simplify further by using the multiplication or division property of multiplication or division property of equality. (use the inverse of equality. (use the inverse of multiplication or division)multiplication or division)

Consider the problem:Consider the problem:

2x-15=52x-15=5

Practice ProblemsPractice Problems

Let’s practice these problems as a Let’s practice these problems as a group – check answers with your group – check answers with your

table grouptable group

• 11n + 1 = 6711n + 1 = 67• -2y + 4 = 8-2y + 4 = 8• 5x – 2 = 35x – 2 = 3

StepsSteps

11n + 1 = 6711n + 1 = 67 - 1 - 1 - 1 - 1 Subtraction Property Subtraction Property

of Equalityof Equality

11n11n = = 6666 Division Property of Division Property of EqualityEquality

11 1111 11

n = 6n = 6

StepsSteps

-2y + 4 = 8-2y + 4 = 8 - 4 - 4 - 4 - 4 Subtraction Property of Subtraction Property of

EqualityEquality

--2y2y = = 44 Division Property of Division Property of EqualityEquality

-2 -2-2 -2

y = -2y = -2

StepsSteps

5x – 2 = 35x – 2 = 3 +2 +2 +2 +2 Addition Property of Addition Property of

EqualityEquality

5x5x = = 55 Division Property of Division Property of EqualityEquality

5 55 5

x = 1x = 1

Challenging Practice Challenging Practice ProblemsProblems

Practice these problems with your Practice these problems with your table group table group

• 6 – 3y = -36 – 3y = -3• 7 = 4 – 2y7 = 4 – 2y• 3/2 = 5/2 + 7x3/2 = 5/2 + 7x

StepsSteps

6 – 3y = -36 – 3y = -3-6 -6 -6 -6 Subtraction Property of Subtraction Property of

EqualityEquality

--3y3y = = -9-9 Division Property of Division Property of EqualityEquality

-3 -3-3 -3

y = 3y = 3

StepsSteps

7 = 4 – 2y7 = 4 – 2y -4 -4 -4 -4 Subtraction Property of Subtraction Property of

EqualityEquality

33 = = -2y-2y Division Property of Division Property of EqualityEquality

-2 -2-2 -2

-3/2 = y-3/2 = y

StepsSteps

3/2 = 5/2 + 7x3/2 = 5/2 + 7x-5/2 -5/2 -5/2 -5/2 Subtraction Property of Subtraction Property of

EqualityEquality

-2/2 = 7x -2/2 = 7x

-1-1 = = 7x7x Division Property of Division Property of

EqualityEquality

7 77 7

-1/7 = x-1/7 = x

Real World Real World SituationsSituations

There are 26 students in Ms. Bean's class. There are 26 students in Ms. Bean's class. The number of boys is equal to seven fewer The number of boys is equal to seven fewer than twice the number of girls. How many than twice the number of girls. How many boys and how many girls are in the class? boys and how many girls are in the class?

You are ordering tulip bulbs from a flowering You are ordering tulip bulbs from a flowering catalog. The cost is .75 cents per bulb. catalog. The cost is .75 cents per bulb. You have $14 to spend. If the shipping cost You have $14 to spend. If the shipping cost is $3 for any size order, determine the is $3 for any size order, determine the number of bulbs you can order. number of bulbs you can order.

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1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

East

WestNorth

StepsSteps

x + 2x – 7 = 26 x + 2x – 7 = 26 x is # of girls; 2x-7 is # of boysx is # of girls; 2x-7 is # of boys

3x – 7 = 263x – 7 = 26 +7 +7 +7 +7 Addition Property of EqualityAddition Property of Equality

3x3x = = 3333 Division Property of EqualityDivision Property of Equality

3 33 3

x = 11x = 11

So there are 11 girls and 15 boys.So there are 11 girls and 15 boys.

StepsSteps

.75b + 3 = 14.75b + 3 = 14 - 3 - 3 - 3 - 3 Addition Property of EqualityAddition Property of Equality

.75b.75b = = 1111 Division Property of EqualityDivision Property of Equality

.75 .75.75 .75

b = 14.667b = 14.667

So you can purchase about 14 bulbs. So you can purchase about 14 bulbs. If you purchase 15 bulbs you will go If you purchase 15 bulbs you will go over your $14 budget.over your $14 budget.

What have you learned!!What have you learned!!

Math is used in everyday life activities Math is used in everyday life activities consciously and unconsciously.consciously and unconsciously.

Objective: The student will solve two step Objective: The student will solve two step equations using the addition, subtraction, equations using the addition, subtraction, multiplication, and division properties of multiplication, and division properties of equality.equality.

All students will be able to solve:All students will be able to solve: