After many years of teaching middle school math, I finally realized that my students had no idea about the true meaning of the equal sign. Most students were trying to memorize steps to solve for "x" instead of thinking about the equation logically. It took me a while to finally figure out that they were completely lost without understanding the role of the equal sign.
So one day, I stopped used the word "equal" and starting saying "the same as."
x + 15 "is the same as" 20
Every time I read an equation, I replaced the equal sign with this phrase. Soon, my students started using similar language and began looking at equations in different ways. They were starting to make sense of the problem instead of just solving for the variable. All of a sudden my students became flexible with lots of different equations and were able to determine if their answer was reasonable. It opened so many doors for them, and I saw a huge increase in their understanding.
Fast forward years later, where I was a math coach working with students in grades K-8. I started to realize this wasn't just a middle school problem but one that starts as early as first grade! I remember very specifically the day I was visiting a third grade classroom. I wrote several equations on the board and students had to identify if the equations were true or false.
Most of the students got the "usual" equations correct:
2 + 3 = 5 is TRUE.
But with any equation that looked "different," many of the students got wrong:
5 = 2 + 3 most students labeled as FALSE.
Then I wrote on the board 5 = 5 and asked for each student to identify if it was true or false. Every student said false! I was amazed and the teacher was stunned! 5 does not equal 5? I couldn't believe it! After that, every classroom I walked into I started doing activities revolving around the equal sign.
A great visual to use to help children understand the equal sign is a balance scale. Here are some printable scales to use to help your children solve and/or look at equations with understanding.
Another way to create flexible thinking in children is to expose them to equations that look "different" at an early age. Here are some examples:
10 = 3 + 7
6 = 12 – 6
4 + 6 = 5 + 5
17 – 8 = 4 + 5
Use the balance scales to help your kids understand that these equations are true. Then have them solve for the ? using the scales:
? = 8 + 4
15 = ? + 11
7 = ? – 7
9 + ? = 6 + 8
Any equations using addition, subtraction, multiplication, and/or division are great practice for all children!