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.
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 05. 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:
 Do operations that appear in parentheses. If there is a set of parentheses inside another set of parentheses, do the innermost one first.
 Do all multiplication and division problems, starting at the left and moving to right.
 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
Other Articles You May Be Interested In

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,...

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 indepth 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 incenter tutoring
 One on one tutoring
 Every Huntington tutor is certified and trained extensively on the most effective teaching methods
K12
 What K12 offers:
 Online tutoring
 Has a strong and effective partnership with public and private schools
 AdvancEDaccredited corporation meeting the highest standards of educational management
Kaplan Kids
 What Kaplan Kids offers:
 Online tutoring
 Customized learning plans
 RealTime Progress Reports track your child's progress
Kumon
 What Kumon offers:
 Incenter tutoring
 Individualized programs for your child
 Helps your child develop the skills and study habits needed to improve their academic performance
Sylvan Learning
 What Sylvan Learning offers:
 Online and incenter tutoring
 Sylvan tutors are certified teachers who provide personalized instruction
 Regular assessment and progress reports
Tutor Doctor
 What Tutor Doctor offers:
 InHome tutoring
 One on one attention by the tutor
 Develops personlized programs by working with your child's existing homework
TutorVista
 What TutorVista offers:
 Online tutoring
 Student works oneonone with a professional tutor
 Using the virtual whiteboard workspace to share problems, solutions and explanations