Algebra

For example, the expression
(3 + 5)² means you are
adding 3 and 5 together to get 8².
8² means 8 times 8 so,
(3 + 5)² = 64.

In 6th grade, we begin to explore the world of algebra through numerical expressions. A numerical expression is a combination of numbers and operations (like addition, subtraction, multiplication, and division) that represents a value.

​We can evaluate numerical expressions using the PEMDAS rule.

A mathematical phrase that includes numbers and operations, but no variables. For example, 4+34+3 is a numerical expression.

Numerical Expression:

NC.6.EE.2 Write, read, and evaluate algebraic expressions. 

● Write expressions that record operations with numbers and with letters standing for numbers. 

● Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

● Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems.

Identifying Parts of an Expression

Every algebraic expression has different parts. These parts include terms, coefficients, variables, and constants.

• Terms are the parts of an expression that are added or subtracted. For example, in the expression (3x + 4), there are two terms: (3x) and (4).

• Coefficients are the numbers that multiply the variables. In (3x), the coefficient is (3).

• Variables are the letters that represent unknown values. In (x), (x) is the variable.

• Constants are the numbers that stand alone. In (3x + 4), the constant is (4).

Evaluating Expressions

Evaluating an expression means finding the value of the expression when we substitute the variables with specific numbers. For example, let's evaluate the expression (2x + 3) when (x = 5):

= 2(5) + 3 Substitute (5) for (x)

= 10 + 3 Calculate the multiplication

= 13 Add the numbers together

So, when (x = 5), the value of the expression (2x + 3) is 13.
Evaluating expressions is useful in real-world problems, such as calculating expenses or scores.

Using the Distributive Property

For the expression 2(3+x), we can apply the Distributive Property:

• Original: 2(3+x)

• Equivalent: 2(3)+2(x)

• =6+2x

Distributive Property: This property allows us to distribute a multiplication over addition or subtraction. For example:
a(b+c) = ab + ac

Properties of Operations

Understanding One-Variable Equations

When we see an equation, we want to find out what value of (x) makes both sides of the equation equal.

For example, in the equation (x + 5 = 12), we want to find out what (x) is. To do this, we can use the process of inverse operations. In this case, we need to get (x) by itself on one side of the equation.