Expressions & Equations MGSE.7.EE.1

​Standard

MGSE7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Math | 7th Grade

Learning targets for MGSE.7.EE.1​

​Learning Targets for 7.EE.1

​Create equivalent expressions by applying the distributive property.

Create equivalent expressions by combining like terms.

Create equivalent expressions by factoring.

Identify equivalent expressions without evaluating them.

Expand or simplify linear expressions with rational coefficients.

Explain how quantities in an expression are related to the context of the problem situation.

Represent real-world scenarios with expressions.

Math| 7th Grade

Learning targets for MGSE.7.EE.1​

​Vocabulary

Math| 7th Grade

Learning targets for MGSE.7.EE.1​

Algebraic Expression: A mathematical expression that contains one or more variables.

Coefficient: A number or constant multiplied by a variable in an algebraic expression.

Distributive Property: When a single-term expression is being multiplied by a sum or difference, the single-term expression can be multiplied by each term before finding the sum or difference.

Equation: A mathematical sentence or statement relating two equal expressions. Must ALWAYS contain an equal sign.

Equivalent Expression: Two or more mathematical expressions that have the same value.

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​Vocabulary

Math| 7th Grade

Vocabulary for MGSE.7.EE.1

​Expression: A mathematical phrase without an equals sign.

Inequality: A mathematical sentence that compares two quantities.

Inverse Operation: Operations that undo each other: addition and subtraction or multiplication and division

Numerical Expression: A mathematical expression that does not contain a variable.

Variable: A letter or symbol that represents a missing or unknown value.

Constant: A number that stands on its own.

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​Vocabulary

Math| 7th Grade

Vocabulary for MGSE.7.EE.1

​Addition Property of Equality: Adding the same number to both sides of an equation produces (makes) an equivalent equation. a=b , a+c=b+c

Subtraction Property of Equality: Subtracting the same number to both sides of an equation produces (makes) an equivalent equation. a=b , a-c=b-c

Simplify: To use the rules of arithmetic and algebra to rewrite an expression as simply as possible.

Like Terms: Terms that contain the same variables raised to the same exponent.

Unlike Terms: Terms with different variables and/or exponents.

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​Vocabulary

Math| 7th Grade

Vocabulary for MGSE.7.EE.1

​"Don't Carry Any Snakes Down Mountains"

Distribute, Combine Like Terms, Addition, Subtraction, Division, and Multiplication.

Simplest Form: An algebraic expression that has no like terms and no parentheses.

Hidden Coefficients

For the expression -y the coefficient is a -1

For the expression p the coefficient is a 1

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​Vocabulary

Math| 7th Grade

Vocabulary for MGSE.7.EE.1

​​Multiplication Property of Equality: Multiplying the same number to both sides of an equation produces (makes) an equivalent equation.

a=b , a x c=b x c

Division Property of Equality: Dividing the same number to both sides of an equation produces (makes) an equivalent equation.

a=b , a/c=b/c

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​Essential Question

Math| 7th Grade

Vocabulary for MGSE.7.EE.1

​​How can I apply the order of operations and the fundamentals of algebra to solve problems?

Numerical Expressions

Numerical expressions are number "sentences" that represent word phrases that include one or more mathematical operations like +, -, x, or division.

Here are some examples:

• 4 subtracted from the sum of 5 and 6

• ( 5 + 6 ) - 4

the product of 7 and 8 subtracted from 60

60 - ( 7 x 8 )

Multiple Choice

A mathematical phrase that contains numbers and operation signs

• Evaluate

• Order of operations

• Simplify

• Numerical Expression

Fill in the Blank

An EXPRESSION DOESN'T HAVE AN __________.

Numerical Expressions

​An Expression that contains numbers and operations.

• ​4 + 6 = 10

• ​250 - 150 = 100

• ​12 x 12 = 144

• 99 / 11 = 9

Basic math operations include four basic operations:

● Addition (+)

● Subtraction (-)

● Multiplication (* or x)

● Division ( : or /)

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Expression

• The sum of terms that are either rational numbers or the product of a rational number and a variable.

• Expressions do not have equal signs.

• An Equation has an equal sign.

Multiple Choice

expression or equation?

• equation

• expression

Terms

• a constant number, a variable, or a variable with a coefficient

• Terms of an expression are separated by + or -

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Multiple Choice

How many terms does this expression have?

4x + 8 + 3x + 7

• 2

• 3

• 4

• 5

Multiple Choice

How many terms does this expression have?

3x² + 7x - 8

• 1

• 2

• 3

• 4

Coefficient

• A number multiplied by a variable in an expression

• The coefficient is "attached" to the variable

Variable

• A symbol for a value we don't know yet. It is usually a letter like x or y.

• Example: in x + 2 = 6, x is the variable

Constant

• A constant does NOT have a variable "attached" to it.

• A numerical value that does not vary (change)

Multiple Choice

In the expression:

5y + 9

The coefficient is __________.

• 5

• y

• 9

• +

Multiple Choice

In the expression:

5y + 9

The variable is __________.

• 5

• y

• 9

• +

Multiple Choice

In the expression:

5y + 9

The costant is __________.

• 5

• y

• 9

• +

Become familiar with the parts of an expression.

Multiple Choice

In the algebraic expression,

4 + 3x - 10 + 5x

How many terms are there?

• 6

• 5

• 4

• 3

Multiple Choice

In the algebraic expression,

4 + 3x - 10 + 5x

What is/are the coefficient(s)?

• 4 , -10

• 3, 5

• 4, -10, 3, 5

• +, -

Multiple Choice

In the algebraic expression,

4 + 3x - 10 + 5x

What is/are the constant(s)?

• 3, 5

• x

• 4, -10

• -10

Multiple Choice

In the algebraic expression,

4 + 3x - 10 + 5x

What is/are the variable(s)?

• +

• +, -

• 4, 3, 5 ,-10

• x