1-1 Numerical Expressions

1-1 Numerical Expressions

by Larry Lawson

​Numerical Expressions Rap​

https://www.youtube.com/watch?v=FCSD8AQS27g

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​Turn to someone and discuss:

​What is a numerical expression?

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​What does it mean to evaluate?

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​In what order do we do the operations?

Review:

• ​The sum of 1 and 2 ---> ( 1 + 2 )

• ​The difference of 8 and 4 ---> ( 8 - 4 )​

• The product of 3 and 5 ---> (3 x 5)

• The quotient of 6 and 3 --> (6 / 3)​

• ​7 less than the sum of 8 and 5 ---> ( 8 + 5 ) - 7

• ​

Multiple Choice

Which numeric expression matches this written expression?

The sum of fifteen and six

• 15 - 6

• 6 + 15

• 15 x 6

Multiple Choice

Which numeric expression matches this written expression?

Two times the sum of eight and seven

• 2 x 87

• 2 + (8 + 7)

• 2 x 8 + 7

• 2 x (8 + 7)

Multiple Choice

Which numeric expression represents the written expression?

4 times the sum of 20 and 5

• 4 + ( 20 x 5)

• 4 x ( 20 + 5)

• 4 x ( 20 - 5)

• 4 + 20 + 5

Multiple Choice

Which numeric expression matches this written expression?

fifteen less than the product of eight and four

• 15 - 8 x 4

• 15 - (8 x 4)

• (8 x 4) -15

• 8 x (4 - 15)

​Reveal Online Textbook

Go to google.com

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​Click on the waffle and click McGraw Hill

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​There should be an assignment titled "1-1 Numerical Expressions"

​Notebooks!

Open to the second page in your notebook and title it:

1-2 Algebraic Expressions

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​We will alternate between taking notes, practicing, and discussing

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​When the slide says "Notes", take notes.

Notes - Order of Operations

Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.

Multiple Choice

Which operation is performed FIRST? (13 - 1) + 4

• addition

• subtraction

• multiplication

Multiple Choice

Which operation should be done first? $$3\ \times\ 4\ +\ 8\ -\ 2$$  

• addition

• subtraction

• multiplication

• division

Multiple Choice

Which operation would you do first?

( 12 + 10) ÷ 10 · 14 - 6

• Division

• Multiplication

• Addition

• Subtraction

​Notes: Lesson 1-2 Algebraic Expressions

​Lesson 1-2 Algebraic Expressions

Goal: ​I can write and evaluate algebraic expressions.

Vocabulary:

• ​variable - a letter used to represent a number or value

• ​algebraic expression - an expression that contains at least one variable

• ​term - a number, variable, or product of numbers and variables

Multiple Choice

Identify the constant in the expression.

2y + x + 8 + 7p

• 7

• 2

• 1

• 8

Multiple Choice

Identify the coefficient in the expression.

6y + 7

• 6y

• 7

• 6

• 1

Multiple Choice

Identify the Variable in the expression 5y+7?

• x

• 5y

• y

• 7

Multiple Choice

How many terms are in the algebraic expression?

2y + x + 4 + y²

• 4

• 3

• 5

• 2

​Notes - Example 1

​Write a verbal expression for 5x³ + 2

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​Notes - Example 1

​Write a verbal expression for 5x³ + 2

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• ​five times x to the third power, plus two

Multiple Choice

Which expression represents: "the product of 3 and x increased by 5"? 

• 5x - 3

• 3 - 5x

• 3x + 5

• 3x(5)

Multiple Choice

Choose the algebraic expression that matches the verbal phrase.

​Notes - Example 2

​Notes - Example 2

Multiple Choice

Which verbal expression represents the given expression?  3(4-x)

• four minus the number x divided by 3

• three times four less than a number x

• three times the quantity x less than four

• four subtracted from x times three

Multiple Choice

Which expression represents "x cubed less than 7"? 

• x³ - 7

• 3x - 7

• 7 - x³

• 7 - 3x

Notes - ​Example 3

​Write an algebraic expression for each:

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​2 times the sum of y and 11

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​n cubed increased by 5

Notes - ​Example 3

​Write an algebraic expression for each:

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​2 times the sum of y and 11 ---> 2 ( y + 11 )

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​n cubed increased by 5 ---> n³ + 5

Multiple Choice

Twenty decreased by x

• 20+x

• 20/x

• x-20

• 20-x

Multiple Choice

The number h decreased by eight

• h-8

• 8h

• h+8

• 8-h

Multiple Choice

The sum of seven and x

• 7-x

• x-7

• 7x

• 7+x

​Notes - Example 4

​Write an expression:

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​A team scores 3 points per win, 1 point per tie, and 0 points per loss.

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Use w for win, t for tie, and l for loss

​Notes - Example 4

​Write an expression:

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​A team scores 3 points per win, 1 point per tie, and 0 points per loss.

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Use w for win, t for tie, and l for loss

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​3w + 1t + 0l

Since 0 doesn't change anything, we can rewrite as: 3w + t

​To evaluate an expression:

​Plug in the number for each variable and solve

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​Example:

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Evaluate ​5x + 4y - x³ if x = 2 and y = 3

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​5(2) + 4(3) - (2)³

​10 + 12 - 8

​22 - 8

​14

Multiple Choice

Evaluate when a = 15:

2(a - 5) + 2

• 22

• 27

• 14

• 7

Multiple Choice

2x + 3 + x²; for x = 4

• 17

• 27

• 19

• 25

Multiple Choice

3(2x + z) when x=8 and z=2

• 12

• 30

• 54

• 60

​Notes - Example 5

​Reveal 1-2 HW

• ​Complete Reveal 1-2 online (check your answers too)

• ​Write your work on a separate sheet of paper and turn it in for credit

Have a great day!​

Thank you!​