Common core State Standards

  • Math:  Math
  • MP:  Mathematical Practice Standards
  • 6:  Attend to precision.

Download Common Core State Standards (PDF 1.2 MB)

My Favorite No: Learning From Mistakes

Lesson Objective: Use mistakes to quickly clarify concepts
Grades 6-8 / Math / Warm-Up


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Thought starters

  1. How does this strategy allow for immediate re-teaching?
  2. What criteria does Ms. Alcala use to pick her favorite no?
  3. How does Ms. Alcala use assessment data to inform her teaching?
I was sent here from Stack Exchange / Mathematics Educators where RUFERD gave me (this answer)[]
Recommended (0)
Hello Leah, Thank you so much for sharing this! Can you provide suggestions on how to use this strategy in a foreign language class? Thank you!
Recommended (0)
This is a great idea. I thought it was great that you rewrote the math problem so no students would be embarrassed by having their card shown. It would be great to have a student that got it correct go up and work through the problem with the class. This is a great formative assessment done everyday.
Recommended (2)
I loved how you improvised with using notecards to replace clickers. This is a great way to gather data on what percentage of students understood the problem. It's also a great warmup activity to share that everyone makes mistakes.
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It is great. I have seen such a warm up in the movie, "Stand and Deliver", in which the teacher would start every class with a little quiz like this. I believe it is a great way to focus on the problem right away and most importantly, without frustrating the ones who have made mistakes, you give the students the message "Don't be afraid of mistakes" so they don'y feel under pressure and can use their potential. I will make a routine of this and start classes with a little warm up question or problem related to the topic. Thanks. Awesome
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  • Great Lesson Ideas: My Favorite No with Leah Alcala

    Leah: Hi. My name is Leah Alcala. I teach eighth grade

    Great Lesson Ideas: My Favorite No with Leah Alcala

    Leah: Hi. My name is Leah Alcala. I teach eighth grade math, and this is my warm-up routine that I do with my students almost everyday. I call it "My Favorite No."

    "OK. Good morning, you guys. Your warm-up is on the board. I'm gonna hand out your index cards."

    I put a warm-up problem on the board, hand out index cards to all the kids, have them write their answer. I collect it, and then I sort it, and I say "Yes, no, yes, no", and I look for my favorite wrong answer, or my favorite "no." And, we analyze that.

    "Four minutes to work on it."

    Everyone makes mistakes. We're gonna see your mistakes. You're gonna see my mistakes, but a mistake is your opportunity to share with me how much you understand. And if I don't know that you don't know something, I need to teach you before the test. The test is too late. And, this is a great spot for me to teach you.

    "Make sure your name is on your card. Put your pencil in your pencil slot, and pass your cards to the center."

    I started my warm-up routine to replace clickers that a lot of classes are buying. So, that was a clicker for each student; you ask a question, they lock in an answer. And then you look at your computer screen, and you know what percentage of your students understand the problem. Well, we didn't have the money for that. So, instead,

    "Here we go!"

    I thought, well, what if I gave everyone index cards, collected them real quick with their answers already written on it, and then I can just sort them as quick as possible, and find out what percentage of my kids know the answer.

    "No, yes"

    Costs 40 cents instead of 15 thousand dollars.

    "Yes, so we have quite a few yes's and some very interesting no's. 1,2,3,4.."

    I then took that a step further, something I couldn't do with clickers - look at the ones who are getting it wrong, how far are they from getting it right, and showing that work to the other kids.

    "OK, my favorite "no" - someone wrote this."

    I say it's my favorite "no" because I want the kids to first of all recognize what they're about to see is wrong. And, I want them to recognize that there's something good in the problem, like there's a mistake, but it's my favorite "no" because it showed some good math.

    "So, that's the wrong answer, but they did some things that I love. What, in that problem, am I happy to see?"

    We always talk about what's right first. So that if it's any students' work, they are like, "Oh, I did do that right."

    There's a mistake, but the mistake didn't ruin the whole thing.

    "What do I like about this problem. Yep."

    Student: "Well, um, they distributed both, um, with the 4x and the negative 2."

    Leah: "Very nice. And, what..."

    Today's lesson was on factoring. So, I needed to make sure they understood how to distribute.

    "They distributed, and what, what lets you know that they distributed? David?"

    David: "Uh, how they're no more parentheses."

    Leah: "There are no more parentheses, and they didn't just drop the parentheses..."

    So they're asked to distribute a term with a variable. They're asked to distribute twice. They're asked to distribute a term with a negative sign, which is often a very common mistake that kids make. And, my students do not. Like, I have three years of CST data now to show that one mistake my students do not make is distributing a negative, which is amazing, 'cause they used to all the time.

    "Distributing negative two to negative six is positive 12. And, that was one mistake I was absolutely looking for, and I did not see, which made me very happy."

    Not until the very end is we've gone over different sections of the problem that are right, that I will then ask, "OK, now what is incorrect?"

    "What does this person not understand? Where is the mistake?"

    If I get a third of my class raising their hand, ready to tell me the mistake, that, it's pretty high engagement at that point.


    Mia: "Um, like 4x times 2x equals 8x squared."

    Leah: "Very nice. This 4x times 2x multiplies to 8x squared. Can someone convince me of that? How do we know that 4x times 2x is 8x squared?"

    My low-level students are very engaged. They feel like they're not getting penalized for being wrong. They're not being made fun of. I'm not looking at them; there's no peer pressure at this point. But, they're like "Wow, that's my mistake, and now I understand."

    It's very comforting. I mean, I feel very with my kids at all times. I'm not surprised by what they don't know. They're not surprised by what they don't know. It's how it should be. It creates more of a dialogue with me and them.

School Details

Martin Luther King Middle School
1781 Rose Street
Berkeley CA 94703
Population: 1027

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Leah Alcala
Math / 7 8 / Teacher