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9.7.14. Learning Objectives. We will evaluate 1 numerical expressions involving rational numbers.

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What are we going to learn? What does evaluate mean? Evaluate means __________.

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What are we going to learn what does evaluate mean evaluate means

9.7.14

Learning Objectives

  • We will evaluate1 numerical expressions involving rational numbers.

  • Students will be able to group symbols dictating the order of applying calculations and how the absence or different placement of these symbols can lead to different results given the same numbers and operations.

  • Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

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


What are we going to learn what does evaluate mean evaluate means

Concept Development

  • A numerical expression is made up of numbers connected by operations (+, –, , ).

  • The operation in the grouping symbols is calculated first.

( )

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.____________


What are we going to learn what does evaluate mean evaluate means

Skill Development/Guided Practice

  • A numerical expression is made up of numbers connected by operations (+, –, , ).

  • The operation in the grouping symbols is calculated first.

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


What are we going to learn what does evaluate mean evaluate means

Skill Development/Guided Practice (continued)

  • A numerical expression is made up of numbers connected by operations (+, –, , ).

  • The operation in the grouping symbols is calculated first.

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


What are we going to learn what does evaluate mean evaluate means

Relevance

  • A numerical expression is made up of numbers connected by operations (+, –, , ).

  • The operation in the grouping symbols is calculated first.

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)  4O 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? (Pair-Share) 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


What are we going to learn what does evaluate mean evaluate means

  • A numerical expression is made up of numbers connected by operations (+, –, , ).

  • The operation in the grouping symbols is calculated first.

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 255 first. The answer would be 15.

( )

10 + 25  5

 5

35

7

Summary Closure

What did you learn today about evaluating numerical expressions? (Pair-Share)

Use words from the word bank.


What are we going to learn what does evaluate mean evaluate means

Independent Practice

  • A numerical expression is made up of numbers connected by operations (+, –, , ).

  • The operation in the grouping symbols is calculated first.

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


What are we going to learn what does evaluate mean evaluate means

Periodic Review 1

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.


What are we going to learn what does evaluate mean evaluate means

Periodic Review 2

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


What are we going to learn what does evaluate mean evaluate means

Periodic Review 3

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


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