Picture a number talk in your classroom. All of your students are gathered and listening attentively.
You ask a question and students indicate that they have an answer by putting their thumb on their hearts. Excellent! Some kids will put two or more fingers up showing that they have the answer, but they also know multiple strategies. Even better! You also have kids that make the signal for “me too” to indicate that they have the same answer as one of their fellow students or perhaps that they have thought of the same strategy as another student. At first you are excited – they get it! But you start to wonder…how do you know what those students actually know?
Sometimes, when you’re doing number talks and even trying to incorporate the Math Mights strategies, there is a fear that many students will just jump on the bandwagon and say “me too,” when in fact they don’t. In every class you have what I call “first responders,” kids that immediately shoot their hands up saying they know the answer. Typically, we call on those students and they do have the answer! Often, we anchor around those kids to help produce the conversation we’re looking for in our math talk that will help build the math culture we’re looking for. For our average students, we know that having models of A) good vocabulary, B) good conversation, and C) the types of strategies available, is very beneficial. However, when the same kids are always responding, even though they can model for other students how the strategies work, the other students don’t have the opportunity to take ownership of the strategies themselves.
In order to determine what your students actually know, you have to engage them. There are several ways to do this.
This works very well when you have a group of first responders that you can count on to share how they would go about solving that problem. I make sure the rest of the students know that they are not off the hook! At any point in time I can point a student and say “repeat” and that student has to repeat that strategy the same way the student that talked before them did. Let’s say that somebody was using the Value Pak as a strategy and talking through how they decomposed 23 into 20 and 3 and then decomposed 52 into 50 and 2. Then, they went through the scenario of how they added the 10s together and then the 1s to arrive at their answer. The child who is charged to “repeat” will have to say that strategy the same way, so they have to make sure they are paying attention! If the repeating student wasn’t listening or doesn’t fully understand the strategy, the student that’s giving the strategy can help coach or explain further.
Strategy: Prove It
This strategy helps engage all students in hands-on activity while you’re doing the number talk. Ask the students to “prove it” using a manipulative, like an abacus or, in the example above with partial sums, the place value strips.
At the end of the day, however, while these strategies help students demonstrate knowledge of a particular strategy, they don’t necessarily tell me if the child has the necessary skills to solve problems multiple ways. That child might perform well during the number talk, but go back to their problem set or their independent sheet in their math journal and just continue to solve the traditional way. So, how do you know if that child has the flexibility and skills to be able to solve problems multiple ways?
We have been so excited to introduce our Math Mights characters for addition over the past few weeks during Math Mights Mania! (Subtraction has a some different characters, so stay tuned to meet them soon!) The Math Mights Addition Strategies poster is the visual anchor for your students as they learn these addition strategies. It demonstrates each character and their strategy, giving several example problems to allow students to see the strategy in action. The students see the poster over and over again as you refer to it during your number talks, and it is designed with build in review because the new characters always join the familiar characters as students learn new strategies.
But, how do we take these addition strategies and know that kids have actually learned them? It’s one thing to have the Math Mights conversations, to get kids to understand the characters, and to get kids to solve the problems. But in my opinion, we really need an exit ticket from our number talks to see if kids are flexible in their thinking, to see if they really have the understanding of what the different strategies are called and how they how they are used.
Our new Math Mights Addition Download Companion will take your Math Mights Strategy poster to the next level, and provide you with that exit ticket! The Companion Download gives an in-depth description of each character (D.C., Abracus, the Value Pak, and T-Pops) with character traits and examples to help the kids get to know them better. Then, for each character/strategy, we’ve taken problems in our beginning and advanced strategies to help kids (and teachers!) be able to prove that they can solve the problem different ways.
In a classroom setting, I might do one or two weeks of number talks on learning the character of D.C. using the one-page character sheet, helping kids see how to decompose using the Math Mights Addition Strategies Poster, using other tools if necessary, and then, at the end, I would give an exit ticket from the companion download.
The exit tickets give kids four problems to solve using D.C. You can choose problems in a beginning strategy, or maybe an advanced strategy. Additionally, at the end of every character’s section, there is a “create your own” exit ticket page where you can type your problem on to the PDF.
My goal is to collect that exit ticket and use the information to guide my number talks. Am I ready to move on to another strategy? If kids aren’t ready and they don’t have a lot of strategies, we want to be able to be able to give them the tools to access those strategies before we continue on.
The beauty of D.C. and any of the different strategies is that you could decompose one number or the other number, or you can decompose more than once, so kids can use the strategy in multiple ways at once if they wanted to.
The next part of the Math Mights Addition Download Companion will show Abracus, and that will be the topic of my next series of number talks. I have the character description, and then a series of exit tickets using beginning strategies that the kids could try out using four problems, and then advanced strategies. I also have the “create your own” exit ticket.
As you go throughout the download, there are two characters introduced and then we’ll do a review, to see “can kids answer math problems using both of the meetings we just got done with. We’ll do some review to see if kids can answer the problems using both of the strategies – Abracus and D.C. So let’s say you’re working with 1st grade and you really want to keep those problems friendly, like 8 + 5 and 9 + 6 and you want to keep that “make a 10” strategy very specific, but you want D.C. on the paper to help remind the kids what D.C. does.
Value Pak is up next. Once again, you’ll have the character page, then beginning problems, advanced problems, and blank spaces where you can add your own problems. At the end, here’s a review if kids can answer a math problem using three characters.
The last section of the download brings in T-Pops, with beginning and advanced level and “create your own.” Here, I’ll want students to spend time with the place value discs as well, making sure kids understand in a non-proportional way how to add numbers, especially 2nd-5th grade.
The last four pages in the download companion will support all four strategies (remember, it’s “three ways plus the traditional!”!) because we want kids to solve problems multiple ways.
At the end of the day, students are going to choose the strategy that works for them. But they only do so after they have really great communicative thinking and understanding and flexibility around all of the addition strategies. I hear a lot of teachers say things like, “just pick whatever strategy works for you.” That’s fine, but too often when that child picks a strategy and I question them about it or ask them to look at it differently, they don’t understand the strategy as deep as we think.
So, how do we know if students have mastered a strategy? We check! Use the exit tickets from the Math Mights Addition Download Companion to help you see where to guide your instruction and maybe even as an independent station.
How do I Get One?
If you already have the Math Mights Addition Strategies poster, as a loyal reader of this blog, we’re would like to offer you 10% off of the Download Companion! Use this code: mmdl10
If you don’t have your poster yet, you can purchase the Math Mights Addition Strategies poster and add the Addition Download Companion for only $8!
Also, get excited for Math Mights Video Resources coming Fall 2018!