Operations with Integers/Linear Expressions

Operations with Integers/Linear Expressions

Lesson Intro

Do Now

1. Simplify the following integers.
a. -19 + 17 =
b. 15 - 16 =
c. 32 +(-6) =
d. -6 -(-5) =

2. What are different ways of writing 33 using various operations?

Lesson Objectives

• I can apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

• I can apply the properties of operations to solve real world problems.

Open Ended

What are integers? Give some examples of integers.

Open Ended

What is a linear expression? Give some examples of linear expression.

Definition

Integers are set of numbers that include whole numbers, positive and negative numbers.

Linear expression is the one that has variable in it. Also, the variable has no exponent higher than 1.  Examples: x, a, b, y, 2a+b, mx+b

Strategies for adding, subtracting, multiplying, and dividing integers and linear expressions

• Using the number line; Start at zero. A positive number will make you move forward, and a negative number will make you move backwards. Your ending location is the answer! Ex: -4 + 7 = 3

• When adding ONE POSITIVE AND ONE NEGATIVE, ignore the signs and subtract the numbers. The sign of the number with the larger absolute value is the sign of the answer. Ex: -35 + 29 = -6

Strategies for adding, subtracting, multiplying, and dividing integers and linear expressions

• When adding TWO NEGATIVE NUMBERS, ignore the signs and add the numbers. The answer should still be negative. Ex: -19 + -30 =-49
  

• Subtraction Means Add The Opposite…So, change the subtraction sign to an addition sign, then change the second number to its opposite. Now, follow the rules for adding integers. 

• Sometimes, parenthesis are used to simply “hold” a negative number...you can proceed as if he wasn’t even there! Ex: -5 -(-13) = 8 

Strategies for adding, subtracting, multiplying, and dividing linear expressions

• Operations with integers can be applied when adding, subtracting, multiplying, and dividing, linear/mathematical expression as well.

• Combine like terms (adding/subtracting)

• Apply Distributive property

• PEMDAS: Parenthesis, Exponent, Multiplication, Division, addition, subtraction; the order of operations.

Guided Task

Let's practice

Check for understanding

Do work with purpose to understand

Operations With

Linear Expressions

Multiple Choice

Simplify: 6 + -7 =

• 13

• -1

• 1

• -13

Multiple Choice

Simplify: -47 + 20 =

• -27

• 27

• 67

• 37

Multiple Select

How many different ways can 37 be written?

• 67+ (-30)

• -17 + (-20)

• -20 + 57

• -36 - 1

Multiple Choice

multiply

 $\left(2\right)\times\left(-\frac{4}{3}\right)=$  

•  $\frac{2}{3}$  

•  $-\frac{8}{3}$  

Open Ended

Divide:

 $3\div\left(-24\right)=$  

Open Ended

Simplify the following expression by combining like terms:

 $2w+5w-6+4w$  

Open Ended

Simplify:

 $4\left(5m+3\right)+2m$  

Multiple Choice

Which expression is equivalent to:

 $\left(7x-5\right)-\left(3x-2\right)$  

•  $10x-7$  

•  $10x-3$  

•  $4x-7$  

•  $4x-3$  

Thank you

Tap yourself in the back. You did great