One Step Equations

Solving problems ONE STEP at a time

One Step Equations

What am I Learning Today?

How will I show that I learned it?Use order of operations to solve mathematical

equations

Write and evaluate algebraic expressions, including those with exponents

Solve simple one step equations using the four basic operations and rational numbers

VocabularyEquation: A mathematical sentence that contains an equal signVariable: A letter or symbol used to represent a numberAlgebraic Expression: A mathematical phrase involving one or more variables and operation symbolsEvaluate: Perform operations to obtain a single value for a numerical or algebraic expressionOrder of Operations: The rules that must be followed when simplifying expressionsExponent: Tells how many times the base is used as a factor

Who is right?

How did the boy solve this problem?

How did the girl solve this problem?

When performing arithmetic operations there can be only one correct answer. We need a set of rules in order to

avoid this kind of confusion. Mathematicians have devised a standard order of operations for calculations

involving more than one arithmetic operation.

Questions AnswersWhat are the

Order of Operations?

How can I remember the

Order of Operations?

What if there are several

multiplication and division or addition

and subtraction operations?

- Parentheses: Simplify the inside of all parentheses first - Exponents: Simplify the exponent of every number

- Multiplication and Division: Simplify one at a time

- Addition and Subtraction: Simplify one at a time

Please Excuse My Dear Aunt Sally (PEMDAS)

** Always keep things in order- Solve operations as they appear from left to right - Multiplication DOES NOT have to be solved before division- Addition DOES NOT have to be solved before subtraction

**Rewrite the equation after solving each part from left to right

Let’s Talk about Exponents

A number is in exponential form when it is written with a base and an exponent.

Base 73Exponent

= 7 7 7= 343

Find the value.

26 = 2 2 2 2 2 2

4 x 2 x 2 x 2 x 2

8 x 2 x 2 x 2

16 x 2 x 2

32 x 2 = 64

Let’s Talk about Parentheses Parentheses ( ) or brackets [ ] or { } are like

a cocoon…what is inside must be complete before it can leave the cocoon.

Order of operations MUST be used inside parentheses or brackets if there is more than one operation being used.

Always complete the operations in the parentheses or brackets the furthest inside

For Example: {[24 ÷ (2 x 3)] + 9} – 7 = ?

Order of Operations: PEMDASEvaluate the expressions.

[7 + (24 ÷ 6)] 3

42 + (3 7)

[7 + 4] 3

11 x 12

132

Perform operations within parentheses.

Multiply.

Add.

42 + (21)

16 + 21

37

Find the value of the number with the exponent.

Multiply.

Add.

Now Try This!Evaluate the expression.

[24 ÷ (9 – 6)] (33 – 10)

Perform operations within brackets and parentheses.

Multiply.

8 (27 – 10)

8 x 17

Perform operation in parentheses.

136

Find the value of the number with the exponent.

[24 ÷ (9 – 6)] (33 – 10)

[8] (33 – 10)

[24 ÷ 3] (33 – 10)

Order of Operation Practice

1. 35 ÷ 7 – 5 =2. 80 x 2 ÷ 40 – 1 =3. 2 + 2² x (5 + 4) ÷ (2³ + 4)

=4. 8 + (2 x 5) x 18 ÷ 9 = 5. 12 x [2² x(4 • 3)] ÷ 6 – 9 =

0

35

28 8

7

Dice Substitution Find a partner.

Designate each color dice #1 and #2

Roll dice #1. Substitute the value for the variable and evaluate.

Roll dice #2. Substitute the value for the variable and evaluate.

Find the sum of the determined values. This is your score.

The person with the highest score wins!

Paired DiscussionTurn to someone around you and discuss the

following:Why do you have to use the order of operations toevaluate each expression?

What would happen if there were no orderof operations rules?

When performing arithmetic operations there can be only one correct answer. We need a set of rules in order to avoid

confusion and help us evaluate the expression in the same way each time.

People might perform operations in different orders and arrive at different solutions. The purpose of the order of operations is to guarantee that every numerical expression has a unique value.