1. Find your seat and be ready for your Do Now
Good Morning !!
Find your seat and be ready for your Do Now

2. Estimation of the Day (EOTD)
What is Peter’s height?
What is too low?
What is too high?
Your estimate.

3. Estimation of the Day (EOTD)
Too Low
Too High

4. Estimation of the Day (EOTD)
Peter’s is 6 feet and 4 inches tall.
Were you close?

5. Do Now
Evaluate in order from left to right.
1. 18 ÷ 3 + 7
÷ 4 – 8
– 8 + 7
4. 8  2 –
5. 81 ÷ 9  13 17 32 37 42

6. SWBAT use the order of operations to simplify numerical expressions.
Objective:
SWBAT use the order of operations to simplify numerical expressions.

7. Vocabulary
numerical expression
order of operations

8. A numerical expression is made up of numbers and operations.
Numerical Expressions
4 + 8 ÷ 2  6
371 –
5,006  19
When you simplify a numerical expression, you find its value.

9. Let’s compare these two examples
Student Student 2
5 + 9 • 3 – 12 ÷ 2
14 • 3 – 12 ÷ 2
42 – 12 ÷ 2
30 ÷ 2 15
5 + 9 • 3 – 12 ÷ 2
– 12 ÷ 2
– 6
32 – 6 26
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:

10. Let’s put some meaning behind it…
5 + 9 • 3 – 12 ÷ 2
First, there were 5 students in class.
Next, 9 groups of 3 students walked in.
Then, half of 12 students walked out. 5
+ 9 • 3
– 12 ÷ 2

11. When simplifying a numerical expression, rules must be followed so that everyone gets the same answer. These rules are called the order of operations.
They are rules used to clarify which procedures should be performed first in a given numerical expression.

12. ORDER OF OPERATIONS 1. Perform operations within Grouping symbols.
2. Evaluate powers.
3. Multiply and Divide in order from left to right.
4. Subtract and Add in order from left to right.

13. The first letters of these words can help you remember the order of operations.
Please Parentheses
Excuse Exponents
My Multiply/
Dear Divide
Aunt Add/
Sally Subtract
Helpful Hint

14. Order of Operations
G Simplify within Grouping Symbols like ( ), { }, [ ]
E Simplify Exponents
M Perform multiplications and divisions in order from left to right
S Perform subtractions and additions in order from left to right

15. Ex. 1: Using the Order of Operations
Simplify the expression. Use the order of operations to justify your answer.
÷ 5

16. TOYO 1
Simplify the expression. Use the order of operations to justify your answer.
· 4

17. Ex. 2: Using the Order of Operations
Simplify the expression. Use the order of operations to justify your answer.
44 – 14 ÷ 2 · 4 + 6

18. TOYO 2
Simplify the expression. Use the order of operations to justify your answer.
28 – 21 ÷ 3 · 4 + 5

19. Ex. 3: Using the Order of Operations
Simplify the expression.
42 – (3 · 4) ÷ 6

20. TOYO 3
Simplify the expression.
24 – (4 · 5) ÷ 4

21. Find your seat and be ready for your Do Now
Good Morning !!
Find your seat and be ready for your Do Now

22. Do Now
Simplify the expression. Use the order of operations to justify your answer.
90−36×2
1.)
2.)
3.)
4.)
16+14÷2−7
64÷
(9−4) 2 −12×2

23. Estimation of the Day (EOTD)
What is Peter’s wife’s height?

24. Estimation of the Day (EOTD)
Too Low
Too High

25. Estimation of the Day (EOTD)
She is 5 feet and 5 inches tall.
Were you close?

26. Ex. 4: Using the Order of Operations
Simplify the expression.
[(26 – 4 · 5) + 6]2

27. When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set.
Helpful Hint

28. TOYO 4
Simplify the expression.
[(32 – 4 · 4) + 2]2

29. Communicator Activity

30. Find your seat and be ready for your Do Now
Good Morning !!
Find your seat and be ready for your Do Now

31. Do Now
Simplify the expression. Use the order of operations to justify your answer.
8−2∙3 3 ÷2
[ 16−3∙4 +7] 2
1.) )

32. What is Peter’s son’s height?
Estimation of the Day (EOTD)
What is Peter’s son’s height?

33. Estimation of the Day (EOTD)
Too Low
Too High

34. He is 3 feet and 7 inches tall.
Estimation of the Day (EOTD)
He is 3 feet and 7 inches tall.
Were you close?

35. Ex. 5: Application
Sandy runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks.
Week
Days
Week 1 5
Week 2 3
Week 3
Week 4
TWAP!
Create a numerical expression that represents this situation.
Simplify the expression (5 + 3 · 3) · 4 to find how many miles she ran last month.

36. TWAP 2
Jill is learning vocabulary words for a test. From the list, she already knew 30 words. She is learning 4 new words a day for 3 days each week.
Day
Words
Initially 30
Day 1 4
Day 2
Day 3
Create a numerical expression that represents this situation.
Evaluate the expression 3 · 4 · to find out how many words will she know at the end of seven weeks.

37. Exit Ticket
Simplify each expression.
÷ 7
2. [ 𝟐 ]×2
3. (28 – 8) ÷ 4
– 102 ÷ 5
5. (9 – 5)3 – (7 + 1)2 ÷ 4

38. Order of Operations BINGO!

40. Lesson Quiz: Part II
Evaluate.
6. Denzel paid a basic fee of $35 per month plus $2 for each phone call beyond his basic plan. Simplify the expression (2) to find how much Denzel paid for a month with 8 calls beyond the basic plan.
$51

41. Lesson Quiz for Student Response Systems
1. Simplify the expression ÷ 9.
A. 11
B. 36
C. 27
D. 43

42. Lesson Quiz for Student Response Systems
2. Simplify the expression 3  6 – 12.
A. 12
B. 36
C. 24
D. 42

43. Lesson Quiz for Student Response Systems
3. Simplify the expression (36 – 6) ÷ 15.
A. 15
B. 10
C. 12
D. 2

44. Lesson Quiz for Student Response Systems
4. Simplify the expression
(8 – 3)3  (9 + 1)2 ÷ 5.
A. 1,000
B. 1,500
C. 2,000
D. 2,500

45. Lesson Quiz for Student Response Systems
5. Robert paid a $200 basic fee plus $70 a day to get his house painted. Simplify the expression (7) to find how much it cost him if it took 9 days to complete the painting.
A. $830
B. $1260
C. $1740
D. $2030