Posted by: degarcia | April 2, 2009

Big Ideas: Equations and Inequalities

Why This is a Big Idea:

3rd Grade Standards:

Represent numerical relationships as expressions, equations, and inequalities.

Order and compare whole numbers on a number line and use the inequality symbols <, >, ≠, and = when comparing whole numbers.

Represent numerical relationships as expressions, equations, and inequalities.

4th Grade Standards: 
Objective 2
Use algebraic expressions, symbols, and properties of the operations to represent, simplify, and solve mathematical equations and inequalities.

5th Grade:

Use algebraic expressions, inequalities, or equations to represent and solve simple real-world problems.

6th Grade:

Describe simple relationships by creating and analyzing tables, equations, and expressions.

Write, interpret, and use mathematical expressions, equations, and formulas to represent and solve problems that correspond to given situations.

Properties of Equality

Properties of Equality

• If the same real number is added or subtracted to both sides of an equation, equality is maintained.

• If both sides of an equation are multiplied or divided by the same real number (not dividing by 0), equality is maintained.

• Two quantities equal to the same third quantity are equal to each other.

EQUATIONS & INEQUALITIES: Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.

Examples of Mathematical Understandings:

• A solution to an equation is a value of the unknown or unknowns that makes the equation true.

• Properties of equality and reversible operations can be used to generate equivalent equations and find solutions.

• Techniques for solving equations start by transforming the equation into an equivalent one.

• A solution or solutions to a linear or quadratic equation can be found in the table of ordered pairs or from the graph of the related function.

• Techniques for solving equations can be applied to solving inequalities, but the direction of the inequality sign needs to be considered when negative numbers are involved.

More Information:

An equation is simply an assertion that two expressions are related by equality.

In mathematics, an inequality is a statement about the relative size or order of two objects, or about whether they are the same or not.

An understanding of equalities and inequalities is so important. Students at a young age should be exposed to the importance of equality and the true meaning of an equal sign. Children can also be exposed to inequalities at a young age. It’s important for students to develop their own understanding of equalities and inequalities so they can apply future mathematics principles to these big ideas. A lot of mathematics rely on using equations and that is why it is such a big idea that needs to be used inside the classroom. 


An equation is a sentence involving numbers, or symbols representing numbers where the verb is equals (=). There are various types of equations:

3+4=7 True Equation

3+4=9 False Equation

2x+5x=7x Identity Equation

x+4= 9 Conditional Equation

Equations are used to state the equality of two expressions. 

Inequalities are demonstrated through the following signs:

  • The notation a < b means that a is less than b.
  • The notation a > b means that a is greater than b.
  • The notation a ≠ b means that a is not equal to b, but does not say that one is bigger than the other or even that they can be compared in size.

In all these cases, a is not equal to b, hence, “inequality”.

These relations are known as strict inequality

  • The notation a ≤ b means that a is less than or equal tob (or, equivalently, not greater than b);
  • The notation a ≥ b means that a is greater than or equal to b (or, equivalently, not smaller than b);

Lesson Plans:  Commutative Cookie activity for 3rd graders where students create a commutative equation.   Lesson plan for kindergartners or 1st graders on understanding what the equal sign means. Lesson Plan for 4th graders on understanding what is an equation and what is not an equation. Lesson plan addressing different strategies to solve equations for 4th graders. Lesson plan for 4th graders on symbols in inequalities. Lesson plan for 4th graders on relationships between equations. Helps students understand equal values.

A list of 5th grade lesson plans on equations. 

Games: Matching equations with answers. For upper Level elementary grades. Another equation game finding answers to equations for upper level grades. Speed math inequality game for 5-6 graders. 



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