Algebra

Expressions and Equations

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.

NC.6.EE.1 Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents.

​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:

Important Vocabulary

Match

Match the following expressions:

• 6 + 3²

• (6 + 3)²

• (5 - 1)³

• 5 - 1³

15

81

64

4

• 15

• 81

• 64

• 4

Multiple Choice

7²– 24 ÷ 3 + 26 =

• 67

• 32

• 15

• 34

Multiple Choice

0.2³

• 0.008

• 0.6

• 0.8

• 0.08

Multiple Choice

2(1 + (5 − 4)³) =

• 4

• 8

• 2

• 6

Apply and extend previous understandings of arithmetic to algebraic expressions. 

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.

Algebraic expressions are a key part of mathematics that help us understand how numbers work together. They consist of numbers, letters (which represent unknown values), and operations such as addition, subtraction, multiplication, and division.

Match

Match the following verbal phrase with the algebraic expression:

• 7 less than 3 times a number

• 3 times the sum of a number and 5

• Twice the cube of 𝑧

• The quotient of the sum of x plus 4 and 2

3n - 7

3(n + 5)

• 3n - 7

• 3(n + 5)

• 
  $$2z^3$$

• $$\frac{x+4}{2}$$

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).

Match

Match the parts of the algebraic expression: 8m + 9

• coefficient

• variable

• constant

• number of terms

• exponent

8

m

9

2

1

• 8

• m

• 9

• 2

• 1

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.

Multiple Choice

What is the value of the expression (4b + 7) when b = 1?

• 11

• 48

• 32

• 47

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

Multiple Choice

Which of the following expression is equivalent to 6(2c + 3)?

• 12c + 18

• 12c + 3

• 30c

• 6c + 18

Multiple Choice

Which of the following expression is equivalent to 3(h - 7)?

• 3h - 21

• 3h - 7

• h - 21

• 3h + 21

Reason about and solve one-variable equations.

NC.6.EE.5 Use substitution to determine whether a given number in a specified set makes an equation true

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.

Poll

Solve: x + 5 = 12

• x = 5

• x = 12

• x = 7

• x = 17

Multiple Choice

Which of the following makes the equation x+3=7 true when substituted for x?

• 5

• 4

• 3

• 1

Multiple Select

If x=3, which of the following equations is true?

• x − 1 = 1

• x + 5 = 9

• 2x=6

• x ÷ 3 = 1

Multiple Choice

In the equation 3x=12, what value of x makes the equation true?

• 2

• 3

• 4

• 6

Poll

Ina wants to serve salad at her party. She will need one head of lettuce for every 6 guests who attend. Write an expression she could use for deciding how much lettuce she needs

• 6∕g

• g ÷ 6

• 6g

• g + 6