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9.7.14. Learning Objectives. We will evaluate 1 numerical expressions involving rational numbers.
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Learning Objectives
What are we going to learn?
What does evaluate mean?
Evaluate means __________.
CFU
Common Core Standard 7.NS.1 & 7.NS.2 Prerequisite Skills
Apply and extend previous understandings of addition, subtraction, multiplication, and division of integers (AND other rational numbers); Students will reinforce skills learned in 6th grade.
99
18
–
81
Students, you already know how to evaluate simple expressions. Now, we will evaluate numerical expressions that include grouping symbols.
Make Connection
Activate Prior Knowledge
Evaluate from left to right.
1. 4 12 + 38
2. 10 × 6 + 8
1 find the value
Vocabulary
48
+ 38
60
+ 8
86
68
( )
parentheses
Grouping Symbols
CFU
3 + (42 – 16)
To evaluate the numerical expression above, which operation would be calculated first? How do you know?
A 3+ 42
B 42 – 16
In your own words, what do grouping symbols mean in a numerical expression?
“Grouping symbols mean _______.”
Evaluating Numerical Expressions
Without Grouping Symbols
With Grouping Symbols
10 6 + 8
10 (6 + 8)
60 + 8
10 14
4 12–10
48–8 + 2
[
]
68
140
4 2
40 + 2
8
42
What is the correct order of operations?
1. ___________ 2.____________ 3._____________ 4.____________
Skill Development/Guided Practice
How did I/you know which operation to calculate first?
CFU
Evaluate numerical expressions.
1
Calculate the operation in the grouping symbols. (Evaluate)
Continue to evaluate to get a final value.
1
2
1. (28 + 36) 4
2. 28 + (36 4)
28
+ 9
64
4
37
16
64
4
28
9
+
16
37
When there are two separate grouping symbols, either one can be evaluated first.
3. (28+ 32) (48 – 18)
4. (72 9) (63 – 13)
60
×
30
8
×
50
1800
400
Skill Development/Guided Practice (continued)
How did I/you know which operation to calculate first?
CFU
Evaluate numerical expressions.
1
Calculate the operation in the grouping symbols. (Evaluate)
Continue to evaluate to get a final value.
1
2
98
11
7
3
–
10 × (3 + 5) and (10 × 3) + (10 × 5)
87
21
10 ×
8
+
30
50
× (40 + 60)
and ( × 40) + ( × 60)
1
2
1
2
1
2
1
2
80
80
+
20
30
×
100
50
50
80 marbles
$50
Evaluating numerical expressions will help you when purchasing items.
1
Sam’s Electronics is having a special on their Blaze music players. What is the total price for 3 music players?
(50 3) – 20
150
20
–
130
The total price is $130.
Evaluating numerical expressions will help you do well on tests.
2
Sample Test Question:
18. Select the numerical expressions that have a value of 52 when evaluated. Choose Yes or No for A and B.
A (10 + 3) 4 O Yes O No
B 10 + (3 4) O Yes O No
Does anyone else have another reason why it is relevant to evaluate numerical expressions? (PairShare) Why is it relevant to evaluate numerical expressions? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?
CFU
A numerical expression is made up of numbers connected by operations (+, –, , ).
Skill Closure
Evaluate numerical expressions.
Calculate the operation in the grouping symbols. (Evaluate)
Continue to evaluate to get a final value.
1
2
1. (27 – 13) 5
2. (34+ 15) (62 – 55)
÷
14
× 5
49
7
Word Bank
14
5
49
7
Word Bank
7
evaluate
calculate
first
parentheses
70
70
7
Access Common Core
Place grouping symbols in the numerical expression so that 10 + 25 is calculated first. Then evaluate. How would the value of the expression change if grouping symbols were placed around 25 5 instead?
The value of the expression would change because we would have to calculate 255 first. The answer would be 15.
( )
10 + 25 5
5
35
7
Summary Closure
What did you learn today about evaluating numerical expressions? (PairShare)
Use words from the word bank.
Evaluate numerical expressions.
Calculate the operation in the grouping symbols. (Evaluate)
Continue to evaluate to get a final value.
1
2
1. (56 + 28) 7
2. (56 7) + (28 7)
3. 9 (50 + 7)
4. (9 60) – (9 3)
+

84
7
9 ×
57
8
4
540
27
12
513
12
513
84
7
56
4
+
12
60
× (12 + 10)
1
2
1
2
×
22
17 × (12 + 10)
11
17 ×
22
374
11 water bottles
374 fluid ounces of water
1. (13 + 20) × 4
2. (30 7) – (54 6)
3. (14 ½) + (24 ½)
33 × 4
132
210 – 9
201
7 + 12
19
264
540
Access Common Core
1. Decide if the value of the expression is less than, equal to, or greater than 52. Write a check mark in the correct column.
2. Decide if the value of the expression is less than, equal to, or greater than 27. Write a check mark in the correct column.
1. (14+ 36) (77 – 17)
2. 40(58 – 23)
3. (32 ¼) + (40 ¼)
50 × 60
3000
40 × 35
1400
8 + 10
18
3000
1400
Access Common Core
Place ( ) in the numerical expression to get the value.
( )
( )
( )
1. 32 + 15 4 = 188
2. 56 8 – 4 = 14
3. 32 + 15 4 = 92
( )
( ) ( )
( )
( )
4. 20 – 10 10 + 7 = 170
5. 56 8 – 4 = 3
6. 5 10 + 5 7 = 85
1. (72 6) + (86 – 59)
3. 250
2. (200 ) + (50 )
12 + 27
39
100 + 25
125
125
39
1200
Access Common Core
1. Fill in the blanks to create numerical expressions that have a value of 32 when evaluated.
4
2
6
10
2
4
×( + ) = 42
×( – ) = 32
×( + ) = 32
×( – ) = 42
( × ) + ( × ) = 42
( × ) + ( × ) = 32
Use INTEGERS. You may use the same one more than once if needed.
4
4
5
3
1
2
1
2
1
2
2. Fill in the blanks to create numerical expressions that have a value of 42 when evaluated.
7
3
3
10
4
7
Use INTEGERS. You may use the same one more than once if needed.
7
7
5
1