warm-up interpreting and simplifying multistep expressions

8
© Edgenuity, Inc. 1 Warm-Up Interpreting and Simplifying Multistep Expressions Lesson Question ? W K 2 Words to Know Write the letter of the definition next to the matching word as you work through the lesson. You may use the glossary to help you. brackets operation expression evaluate order of operations parentheses A. to determine the value of B. a pair of rounded symbols used to group items together C. the set of rules that are followed to find the value of a mathematical expression D. a pair of symbols used to group items together, usually found outside parentheses E. a mathematical phrase that combines numbers and/or variables using mathematical operations F. an action or process such as addition or subtraction Lesson Goals Solve problems with more than one operation. Evaluate expressions using the order of . Write expressions to solve problems with one operation.

Upload: others

Post on 03-Dec-2021

10 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Warm-Up Interpreting and Simplifying Multistep Expressions

© Edgenuity, Inc. 1

Warm-Up Interpreting and Simplifying Multistep Expressions

Lesson Question

?

WK2 Words to Know

Write the letter of the definition next to the matching word as you work through the lesson. You may use the glossary to help you.

brackets

operation

expression

evaluate

order of operations

parentheses

A. to determine the value of

B. a pair of rounded symbols used to group items together

C. the set of rules that are followed to find the value of a mathematical expression

D. a pair of symbols used to group items together, usually found outside parentheses

E. a mathematical phrase that combines numbers and/or variables using mathematical operations

F. an action or process such as addition or subtraction

Lesson Goals

Solve problems with more than one operation.

Evaluate expressions using the order of

.

Write expressions to solve problems

with one operation.

Page 2: Warm-Up Interpreting and Simplifying Multistep Expressions

© Edgenuity, Inc. 2

Warm-Up Interpreting and Simplifying Multistep Expressions

Evaluating Simple Expressions

Evaluate these expressions.

• 42 + 24

42  +24

• 56 − 47

56 −47

• 6 × 12

12 ×6

• 65 ÷ 5

)−

5 65

5

15

15

Page 3: Warm-Up Interpreting and Simplifying Multistep Expressions

© Edgenuity, Inc. 3

Interpreting and Simplifying Multistep ExpressionsInstruction

2Slide

Reviewing Expressions

EXAMPLE

Evaluate these expressions.

• 3 + 5 + 6Work left to right.

8 + 6

Add 3 and 6 first.

9 + 14

• 2 × 4 × 5Work left to right.

8 × 5

Multiply 4 × 5 first.

× 2040

Addition and multiplication have associative and commutative properties. In subtraction and division, we do not have associative and commutative properties.

• 30 − 20 − 710 − 7 30 − 20 − 7

30 − 1317

• 18 ÷ 6 ÷ 33 ÷ 3

With subtraction and division, it is important to work from left to .

Page 4: Warm-Up Interpreting and Simplifying Multistep Expressions

© Edgenuity, Inc. 4

Interpreting and Simplifying Multistep ExpressionsInstruction

4Slide

Understanding the Order of Operations

What is the order of operations?

• Evaluate within parentheses.

• Multiply and

from left to right.

• Add and subtract from left to right.

• 2 operations: 3 + 10 × 5 Multiply first, then add.

3 + 50 =

• 3 operations: 30 − 15 ÷ 3 + 2 Divide first. Then add and subtract from left to right.

30 − 5 +

+ 2 = • 4 operations: 40 ÷ 5 + 12 − 3 × 3

+ 12 − 9

20 − = 11

Understanding the Importance of Order

Find the value of each expression.

• 4 + 5 × 10 ÷ 2

Perform the operations from left to right.

9 × 10 ÷

÷ 245

• 4 + 5 × 10 ÷ 2

Do the multiplication and division first.

+ 50 ÷ 2

4 + 25

We got two different answers. How do we know which way is correct? We need to use the agreed upon order of operations.

Page 5: Warm-Up Interpreting and Simplifying Multistep Expressions

© Edgenuity, Inc. 5

Interpreting and Simplifying Multistep ExpressionsInstruction

7Slide

Parentheses and Brackets in the Order of Operations

Simplify inside parentheses first.

(7 − 2) × (1 + 6)

5 × =

Parentheses ( ) are a pair of

symbols used to group

items together.

Brackets [ ] are a of symbols

used to group items together, usually found outside parentheses.

If there are multiple sets of grouping symbols, you will complete the innermost first, then work your way outward.

Multiply first.

7 − 2 × 1 + 6

7 − 2 +

+ 6 =

What is the order of operations?

1. Evaluate within parentheses.

2. Multiply and divide from left to right.

3. Add and subtract from left to right.

• 30 ÷ [(7 − 5) × 5]

÷ ×

30 5

÷ 10 = 3

• [(3 + 2) × (4 − 2) − 1] × 3

× − ×

5 2 3

− ×

1 3

9 × 3 =

Page 6: Warm-Up Interpreting and Simplifying Multistep Expressions

© Edgenuity, Inc. 6

Interpreting and Simplifying Multistep ExpressionsInstruction

11Slide

Using Order of Operations inside Parentheses and Brackets

MISCONCEPTIONS

The order of should be followed inside the parentheses and brackets.

(20 - 14 ï 2) + 4

(6 ï 2) + 4

3 + 4

7

The student did not simplify correctly within the parentheses. They should have divided first.

(20 - 14 ï 2) + 4

(20 - 7) + 4

+ 4

This is simplified correctly.

Use the same order of operations within the parentheses and brackets until all of

the operations have been completed. Then move the parentheses and brackets and continue.

Page 7: Warm-Up Interpreting and Simplifying Multistep Expressions

© Edgenuity, Inc. 7

Interpreting and Simplifying Multistep ExpressionsInstruction

14Slide

Creating Expressions

What is 10 times the between 18 and 12?

10 × 18 − 12

When we think about the order of operations, we would multiply first and then subtract.

We want to find the difference between 18 and 12, so we have to put the

around 18 − 12.

10 × (18 −  )

× 6 =

Creating Expressions

Eight classes recently donated 30 books each to the school library. The books will be placed in a new bookcase. If each shelf in the bookcase holds 20 books, how many shelves are needed?

(  × 30) ÷ 20

240 ÷

shelves

Did we really need parentheses in this problem? If we remove the parentheses and work from left to right, we get the same answer.

16

Page 8: Warm-Up Interpreting and Simplifying Multistep Expressions

© Edgenuity, Inc. 8

Summary Interpreting and Simplifying Multistep Expressions

Answer

Use this space to write any questions or thoughts about this lesson.

Lesson Question How can I solve a problem that requires more than one operation??