warm-up interpreting and simplifying multistep expressions
TRANSCRIPT
© 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.
© 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
© 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 .
© 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.
© 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 =
© 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.
© 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
© 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??