Absolutely convinced. How can you give an answer if there are numbers and letters and who-knows-what-else on both sides of the equal sign? How can you add, subtract, multiply or divide if there is no empty space in which to plop your sum/product/quotient/difference?
You know how long it took me to get what the equal sign really means? I was 33. Really. 33. I had to take remedial algebra to get into the college of education. Finally I got it, after having an instructor who really understood the demise of mathematics for so many. She explained that the equal sign meant "both sides are equal." Like, how simple. Really? It's just like a pan balance or a scale? Both sides have to "weigh" the same or they aren't equal. Bingo.
I'm making it my mission as a teacher to make sure my students understand this deeply before they leave me in the spring. = doesn't mean "I want an answer". = means "how can you make each side weigh the same?"
It's brilliant. It's one of the Big Ideas that topple the house of cards when it isn't understood.
I created a couple of activities that nail this concept. It's just a few smallish practice activities, but they are Valentine themed just in time for February 14th. Check 'em out.
My primary and intermediate hearts were arguing whether to make these for little ones or big ones. I appeased them both and created addition and multiplication sets. Each are $2, a wee price for an activity that can easily fit into a 30 minute block of time.