Posted by Angie Seltzer on 8/26/2023 to
K-5 Algebraic Thinking
Introduction
Do your students understand the equals sign and equations? Many students struggle with understanding the concept of equality. However, equality is a foundation for algebra. In this article, we'll explore tips and tricks to help your students conquer the equals sign, avoid common misconceptions, and take equations to the next level.
1. Emphasize the Meaning of "="
In the early grades, simple addition and subtraction exercises are often shown with an equals sign before and answer blank, such as "4 + 3 = __." Students may get the mistaken idea that an answer always comes after an equals sign, and that "=" means "put the answer here." This notion, unfortunately, is not correct.
The equals sign is used to represent mathematical equivalence, indicating that two expressions or values are equal to each other. In a TRUE equation, the numbers or expressions left or right of the equals sign have the same value. If the left and write sides of the equation do not have the same value, the equation is FALSE. If there is no equals sign, it is NOT an equation.
You may want to explain that sometimes we add, subtract, multiply, or divide with the numbers under each other. This is a way to make computation easier by aligning place-value positions. It is not a form of an equation.
2. Mix Equations into Computation Practice
To SOLVE an equation means to find values for the variable or missing number(s) to make a true equation. That is, find the missing number(s) so the left and right sides have equal value.
Surprisingly, some students can write all basic facts but still cannot fill in missing numbers when the format is different. For example, when shown a simple equation such as 4 + __ = 9, a student may write 13 as the missing number. They see the plus sign and assume that addition is required, rather than thinking about what number is needed for equality, or to make a true equation.
Help your students in Grades 1-5 get a head start on algebra thinking by including simple equations with computation practice. There are many ways to do this. Remember that subtraction is used to find a missing addend, and division is used to find a missing factor. So, subtraction and division can be used to solve an equation with a missing addend or factor as shown below.
3. illustrate Equations with Visual Models
To avoid this common misconception that the symbol signifies where to put an answer, teachers can use visual models. The important concept equivalence. For early addition and subtraction, a bar model can help show combining or comparing parts. You can also encourage students to use small objects or draw pictures to represent parts of an equation. This can help solidify the concept of equivalence.
When you use visual models, avoid mixing operation symbols with the picture.
Emphasize that the numbers are a way to show a real situation with math. The apples can be shown but the plus sign or equals sign should not be mixed in. Show the entire equation, or an equation with empty boxes or blanks, below the apples.
4. Relate Equations to Real-World Problems
Working with word problems or real-world scenarios is an excellent way to apply the concept of equals sign in a practical context. It is also helpful to have students write situations to match equations. Or, have students translate real-world situations into mathematical expressions, using the equals sign to show that two expressions have the same value. As students write and solve more complex equations, make sure they do not write run-on equations. Consider the following example:
Because 4 x 6 is not equal to 24 + 3, the equation is not true. If several expressions are connected in a row with equals signs, all of the expressions must be equal.
For the problem above, another option is to write TWO equations:
4 x 6 = 24
24 + 3 = 27
To discourage students from improperly connecting expressions, help them make the corrections. You can coach a student by asking, "Are the left and right expressions equal?" For older students, you may want to deduct points when you see run-on equations within student's work.
Conclusion
In conclusion, while the use of an equals sign may seem obvious, it's important to encourage good habits and to address any misconceptions that may arise. By emphasizing the meaning of the equals sign, mixing a variety of equations into computation practice, illustrating equations with models, and relating equations to real-world problems, you can help students develop a stronger understanding of the concept of equality.
I hope your students have more success with equations!
Angie
