Have you ever asked students to solve 12.6 x 10, and they respond that the answer is 12.60? I have, many times. Students who do this apply a pattern that works when they multiply whole numbers by 10—they tack on a zero to the end of the number they’re multiplying. But then they apply the same pattern when working with decimals. What can we do?
I thought I was on the right teaching track using real-world contexts to talk about fractions with a class of fourth and fifth graders. Then a surprise occurred! I’m still mulling over what I could have done. I’d love your thoughts. 
When teaching students to add decimals, I wind up reminding students to “line up the decimal points.” This makes sense to some students while others follow the rule without understanding. How can we teach adding decimals to develop understanding and skill? Here’s a possible suggestion: Give the correct answer up front. 
I believe strongly that mistakes are learning opportunities. At least that’s what I regularly tell students. But it sometimes feels different when the mistakes are mine . . . and especially when they are pedagogical mistakes that I make while teaching. That happened to me recently when teaching a lesson to fourth graders. 
I love Twitter. On November 3, 2017, I saw this image in a Tweet posted by @MarkChubb3. The image stuck with me for several days. After talking about it over dinner with a teacher friend, and then again over lunch with another, I became curious to find out what students might think. I made arrangements to “borrow” three fifth-grade classes and made plans to teach the same lesson in each class.