Beginning Algebra: Concepts and Problems

Nowadays, children begin learning algebraic concepts in kindergarten through addition and subtraction equations. A summary of beginning algebra concepts is presented here, with example problems and solutions.

Find available tutors

Beginning Algebraic Concepts and Problems

Addition and Subtraction Equations

In kindergarten, children are exposed to linear equations for addition and subtraction. They also learn to add and subtract for numbers 0-5. In first grade, they begin doing more complex problems, using numbers up to 100. To familiarize students with equations, ask questions such as:

Which of these is not correct?: 5 = 5, 8 = 9 -1, 6 + 2 = 4 + 3, 4 + 3 = 3 + 4; Answer: 6 + 2 = 4 + 3

At first, the numbers in equations are all constants. For a challenge, an unknown answer may be represented with a question mark, a box or a similar symbol.

Examples:
5 + 4 = ? --> 5 + 4 = 9
7 - 6 = ? --> 7 - 6 = 1

Examples of more complex problems that are presented later are:

x + 4 = 12 --> x = 8
r - 3 = 6 - 2 --> r = 6 - 2 + 3 --> r = 7

Multiplication and Division Equations

Third graders learn two more operations: multiplication and division. Students may use visuals, such as models or drawings, to solve for unknown quantities. Problems common for third grade include:

25 ÷ y = 5 --> 5y = 25 --> 5 = 5. The problem may also be written as 25/y = 5.
8 x a = 16 (may also be written as 8a = 16) --> a = 16/2 --> a = 8

More complex problems include combinations of the four operations: addition, subtraction, multiplication and division.

Examples:
2x + 5 = 9 --> 2x = 9 - 5 --> x = 4/2 --> x = 2
8a - 2 = 50 --> 8a - 50 - 2 --> a = 48/8 --> a = 6
7r/4 = 7/2 --> 7r = 7/2 x 4 --> 7r = 28/2 --> 7r = 14 --> r = 2

Order of Operations

At first, students learn to do problems where the answer will be the same no matter in what order the operations are performed. In sixth grade, students generate equivalent expressions by using the properties of operations. This sometimes requires the use of parentheses in an equation.

Examples:
4(3 + x) is the same as 12 + 4x
15x + 30y may also be expressed as 5(3x + 6y)
a + a + a + a is the same as 4a

The actual order of operations is presented later. This order is:

  1. Do operations that appear in parentheses. If there is a set of parentheses inside another set of parentheses, do the innermost one first.
  2. Do all multiplication and division problems, starting at the left and moving to right.
  3. Do all addition and subtraction problems, again starting at the left and going to the right.
Examples:
x = 20 ÷ (4 - (10 - 8)) --> x = 20 ÷ (4 - (2)) --> x = 20 ÷ 2 --> x = 10
y = (6 - 4) * 49 ÷ 7 --> y = 2 x 49 ÷ 7 --> y = 98 ÷ 7 --> y = 14
b = 45/{8(5 - 4) - 3} --> b = 45/{8(1) - 3} --> b = 45/5 --> b = 9
Did you find this useful? If so, please let others know!

Other Articles You May Be Interested In

  • More Blog Articles
    Algebra for the IPad Generation

    For many students, algebra inspires apprehension and dread. Today, students are increasingly dependent on tools, such as iPads and even their phones, that can do the work of algebra for them. This makes the job of a teacher trying to convey algebra's importance difficult. Yet there are still ways to make algebra relevant,...

  • More Blog Articles
    Not Your Father's Algebra As 45 States Look to Math Reform

    One plus one will always equal two...but just how students are taught math is going to change. Nearly every state in the country has adopted the Common Core Standards; for math, this means new and more in-depth approaches to teaching the subject. Have we seen the last of traditional algebra and geometry classes?

We Found 7 Tutors You Might Be Interested In

Huntington Learning

  • What Huntington Learning offers:
  • Online and in-center tutoring
  • One on one tutoring
  • Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online

K12

  • What K12 offers:
  • Online tutoring
  • Has a strong and effective partnership with public and private schools
  • AdvancED-accredited corporation meeting the highest standards of educational management
Online Only

Kaplan Kids

  • What Kaplan Kids offers:
  • Online tutoring
  • Customized learning plans
  • Real-Time Progress Reports track your child's progress
Online Only

Kumon

  • What Kumon offers:
  • In-center tutoring
  • Individualized programs for your child
  • Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online

Sylvan Learning

  • What Sylvan Learning offers:
  • Online and in-center tutoring
  • Sylvan tutors are certified teachers who provide personalized instruction
  • Regular assessment and progress reports
In-Home, In-Center and Online

Tutor Doctor

  • What Tutor Doctor offers:
  • In-Home tutoring
  • One on one attention by the tutor
  • Develops personlized programs by working with your child's existing homework
In-Home Only

TutorVista

  • What TutorVista offers:
  • Online tutoring
  • Student works one-on-one with a professional tutor
  • Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only

Help Your Child Succeed

Our Commitment to You

  • Free Help from Teachers

  • Free Learning Materials

  • Helping Disadvantaged Youth