Understanding Not Equal In Mathematics
The “≠” symbol, read as “not equal,” represents a relationship where two numbers or expressions do not have the same value. For example, in the statement 5 ≠ 7, the symbol shows that the number 5 does not have the same value as the number 7. Similarly, 6 + 3 ≠ 12 indicates that the sum of 6 and 3 is not equal to 12.
Introducing the “not equal” symbol helps students expand their understanding of mathematical relationships. While the equal sign (=) is often associated with balance and equivalence, the “not equal” sign emphasizes inequality and comparison, helping students develop a more nuanced understanding of how numbers relate to one another.
Teaching Strategies For Not Equal
Addressing Common Misunderstandings Of Not Equal
Students may initially struggle to understand symbols like ≠ because the equal sign (=) is often misinterpreted as simply meaning “find the answer.” This misconception can make it difficult for them to fully grasp the relational nature of the not equal sign. Teachers should proactively introduce ≠ alongside = to highlight its role in describing inequality versus equivalence.
Connecting Models, Words, and Symbols Of Not Equal
Pairing physical models, verbal explanations, written symbols, and drawings supports students in moving between representations and deepening their understanding of mathematical relationships such as not equal.
- Use a balance scale to show unequal quantities. When the two sides aren’t balanced, the scale tips, visually reinforcing that one side has a different value.
- Draw a representation of two groups. For example, draw five circles on one side and seven on the other to illustrate that they are not equal.
- Verbally describe the relationship: “These two groups are not equal because one has five and the other has seven. The group with seven has two more.”
- Write the inequality using the not equal (≠) symbol: “5 ≠ 7.”
Reinforcing Conceptual Understanding Of Not Equal
To build a deep understanding of “not equal,” give students opportunities to compare quantities and explain their reasoning using models, words, and symbols.
Hands-on comparison with manipulatives is one effective strategy. Using tools like Unifix cubes, have students build two towers—one with 5 cubes and the other with 7. Ask them to compare the towers and determine if they are equal.
Guide the discussion with prompts like, “How do you know these towers are not equal?” Encourage responses such as, “This tower has 5 cubes, and this one has 7. Seven is two more than five, so they are not equal.”
Afterward, help students represent their thinking symbolically by writing the inequality: 5 ≠ 7. This activity reinforces the connection between physical models, verbal explanation, and mathematical notation.
Comparing values through equations and expressions is another way to highlight the meaning of “not equal”. Present a statement such as 8 + 2 ≠ 15 and ask students to determine whether it is true.
Begin by having them simplify the expression on the left side (8 + 2 = 10) and then compare that value to 15. Support their thinking with guiding questions: “What is the value of 8 + 2?” and “How does that compare to 15?”
Use number lines or counters to make this comparison visible. For example, show 8 + 2 as 10 on a number line, then illustrate the distance to 15. This helps students see not just that the quantities are different, but by how much, strengthening their conceptual grasp of inequality.
Building Mathematical Communication Using Not Equal
Encourage students to articulate their thinking when working with not equal using precise language. For example, by saying things like, “Five is not equal to seven because five is less than seven.” and “The two sides of the scale are not balanced, so they are not equal.”
Using clear explanations alongside the not equal symbol is a way for students to build confidence in their reasoning and strengthen their mathematical vocabulary.
Framing Not Equal with Equal, Greater Than, and Less Than
Relational symbols work together to help students describe how numbers compare:
| Symbol | Meaning | Example |
|---|---|---|
| Equal To (=) | Shows that two numbers or quantities have the same value | 5 = 2 + 3 |
| Greater Than (>) | Indicates one number is larger in value than another | 10 > 6 |
| Less Than (<) | Indicates one number is smaller in value than another | 4 < 9 |
When students learn not equal alongside equal, greater than, and less than, they develop a complete understanding of numerical relationships. Teaching these concepts together reinforces comparison skills and encourages flexible thinking about numbers.
