math

8 Mathematical Language Routines

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I have been on a journey to educate myself on the 8 Mathematical Language Routines (MLRs). While they were designed with Multilanguage Learners in mind, I find that they are just good teaching. So what are they?

  • Stronger & clearer each time
  • Collect & display
  • Clarify, critique, and correct
  • Information Gap
  • Co-craft questions
  • 3 Reads
  • Compare & Connect
  • Discussion Supports

So what does each one entail? Well, rather than sit and explain, I’d rather give you a resource that does a far better job breaking it down. It’s also one of my favorite resources.

Consortium on Reaching Excellence in Education

Part of my deep dive allowed me to align Math EduProtocols and these MLR’s. Doing this has my mind working on how to incorporate more MLR’s within Math EduProtocols.

With all this in mind, I have begun to curate some resources for teachers. I break down each MLR and give links to activities. It’s not a comprehensive list, so I will continue to add to it as I find more. If you have something that should be added to the document, let me know!

Nacho Problem

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What’s a problem that’s not yours? Nacho Problem!

It’s that time of year, Test Prep time. Which makes me think about using EduProtocols for Test Prep. One great one that really promotes deeper thinking and understanding is Nacho Problem. This was created by Ligia Ayala-Rodriguez. It’s a fun way to do error analysis with your students. I have done this with students as young as 7.

One of the advantages is that you begin by telling the students the answer is wrong. This seemingly takes the pressure off. I like to have the students talk it out the first few times. I guide them along the way to help set the expectations. Just like in an ‘Analyze the Error’ on the test, students are expected to express their thoughts in writing. This can present an additional challenge if they haven’t exercised this skill. I’m not saying we should do this solely to prepare for the state test; the benefits of students being able to do this go far beyond that idea.

How to Get Started

As a class, they are presented with a Nacho Problem. We read and analyzed the problem together; starting with “What do you notice?” and “What do you wonder?” I explicitly tell them the answer is wrong and that we must find where I went wrong. I have found that looking at the question and working out the problem allows us to focus on the process (that the problem is asking us to solve) rather than the arduous task of finding a mistake. Once we work it out together, and later independently, students can then go back and compare their process with the original (wrong) process. It makes it more obvious where the original problem solver went wrong.

The written explanation can be the most difficult part. When I started doing problems like this, students would explain, in an addition problem, “I started in the ones and added 8+7. I left the 5 in the one’s place and regrouped the 1.” While technically that is true and we as teachers understand, that’s not showing an understanding. That is why practicing the structure of Claim, Evidence, and Reasoning (CER) is so important.

Claim: Ms. N. did not draw a quadrilateral.
Evidence: The student example with explanation.
Reasoning: Definition of a polygon and Ms. N’s error.

Finding Problems

One of the easiest ways to collect incorrect problems is from your class. Whether you use exit tickets or collect information from the day’s lesson, you have a plethora of options. When using student errors, it’s advisable to use a common mistake by many students. Done early, this can correct any misconceptions before they become habits. Ligia suggests using mathmistakes.org

Results

Teachers and students alike enjoy this math EduProtocol. Students find it ‘fun’ to find the mistakes. Teachers report that it takes little time to begin implementing in their classes. Doing this a few times a week can really improve understanding. Let’s face it, students LOVE to point out teachers’ mistakes.

If you use this, I would love to hear how it went. What changes did you make? How have your students improved with error analysis?

Free Bingo Cards

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Recently I had a teacher ask me about some review games. Bingo is always a hit so I went on the search for a 3rd-grade Geometry Bingo game. Sadly, I couldn’t find what I wanted. Which then led to a search for Bingo card creators. I was not about to sit and recreate 25 Bingo cards. I like to use my time a bit more efficiently. And that’s when I found it! My Free Bingo Cards

This awesome sight creates simple Bingo Cards. They have several ready-to-go, broken down by categories. There is also the option to create your own. I opted to create my own. The process was simple. I plugged in all the words the students were to review. I then pressed one button for the program to create 30 unique Bingo cards. I did play around with it to see if I could insert images via copy/paste. No such luck. That was okay; I had a backup plan. The program also created a sheet for me to track which words were used and calling cards. I opted NOT to use the calling cards.

What did I use instead of the calling cards?

Instead of the calling cards I created a wheel on Wheel of Names. This was part of my backup plan: I used images. I could have also opted for the definitions, but I felt the images were more engaging and less repeating. This game was a big hit!

If you’re a 3rd-grade teacher and would like to play this here are the cards and here is the wheel.

If you’ve never used Wheel of Names before, you’re going to love it! There’s no need to guess where the spinner landed. The program tells you which one. Then you have the option to remove the selected item from the wheel to avoid mishaps.

Summer Presentations

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This summer, I will be presenting at two academies for EduProtocols. My sessions will have a math emphasis; shocking, I know. So this past week when I was asked to come up with titles and descriptions, I struggled. I wasn’t feeling it. Luckily, a friend called before I could toil for too long. I relayed to her my lack of motivation at the time, and she came up with some catchy titles.

  • 🍸The Mixology of MathReps – MathReps
  • Wheel Of Word Problems – Word Problems with Random Emoji
  • Playing with Parts – 8 p*ARTS meets word problems
  • 🌶️🌶️ Spicey Solutions to a Bland Curriculum – Nacho Problem
  • 👩🏽‍🍳Chef’s Kiss – Sous Chef
  • Frayas for Ya Playas – Frayer and, honestly, my favorite title
  • 🦹🏻‍♂️Math is a Villain: Comic Strip Math

Then it was time to get started on the descriptions. This is where I got inspired. I doubled down on the titles and all descriptions fit that theme. I mean, check out this description for Comic Strip Math:

In a world full of villains, the fine citizens of Mathemagicalville are up against the most evil, vile, sinister one around. Master of Dark is relentless in the pursuit of conquering the city. It is up to you, the superhero, to prove Master of Dark wrong and find the errors that were made. You create the comic, find errors, explain processes, and become the hero the city needs.

Yes, Mathemagicalville is a mouthful, but the names I wanted were all taken, and so I had to become creative. When I was creating this description, I felt that I had to be very careful with my wording. The character ‘Master of Dark’ was created by my 5th-grade class at the time, around 2019. The character was created to be gender-neutral. However, in today’s political climate, with hundreds of anti-trans laws being introduced throughout the country, I want to be sensitive to this. In 2019, the intent was to NOT represent one group as ‘evil’ or ‘bad’ but to keep the focus on math while empowering ALL the students in my classroom. The empowerment came from not having the gender stereotypes that boys are better at math than girls, and by taking the gender out of character seemed like a good solution at the time. However, as I began writing the description, I tried avoiding any pronouns. I don’t want to put a negative focus on any group.

I may be overthinking all this, and I may not be. However, in cases like this, I would rather err on the side of caution. So what do you think? Am I overthinking this? Does this character need to be revisited? Do I simply avoid using any pronouns as it’s not critical to the purpose of thinking critically about math? I would love to hear from everyone, especially those in marginalized communities.

Okay, that took a serious turn. NOW if you’d like to join me in Laguna Beach or Notre Dame this summer, here’s more information. I can’t guarantee that all seven sessions will be presented at both, but I can say that MathReps and Comic Strip Math will be presented at both – if I have a say.

92%, Say What?

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92%So what’s the big deal with 92%? A lot when it comes to having 3 weeks off and the likelihood that none of my students practiced their multiplication facts.

Monday was our first day back after winter break. As we do every day, we practiced our math facts using the Fast & Curious Eduprotocol. I had an anticipated drop from our usual 96% – 98%. I predicted, to myself,  it would drop to around 89%.  I wasn’t too concerned as I knew that they could easily get it back up to our normal within a week.

Well, to my surprise, my class scored 92%. Seriously, I was happily surprised that they really didn’t lose as much as I had feared. YES! The continuous rep practice has worked. The facts are sticking.

I was so giddy, I needed to write this quick post to celebrate the success my class is finding. I was sold before, but now I’m a believer for life!

Tic Tac Toe Math

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I have been on a creative streak lately. I LOVE #EduProtocols by Marlena Hebern and Jon Corippo. I LOVE #MathReps which were inspired by Jon Corippo’s 8 p*ARTS of Speech (read the full story). As a result, I have been working on Math EduProtocols. My latest one, that is ready to share with the world and receive feedback, is Tic Tac Toe Math.

Tic Tac Toe Math (1) This is a sample I created for my class. My intent was to review some basic math concepts while having fun. The rules are simple:

Each player writes their name and chooses either X or O.

  1. Player 1 chooses a square to complete. BOTH Player 1 and Player 2 independently work out the problem in the chosen square.  If Player 1 is correct, Player 1 gets the square and circles their symbol (X or O)
  2. IF Player 1 is incorrect, Player 2 has a chance to ‘steal’ the square. Player 2 MUST complete the problem correctly AND explain where Player 1 was incorrect.
  3. Player 2 chooses a square, even if they stole Player 1’s square. BOTH players must work independently to solve the problem. If Player 2 is correct, Player 2 gets the square. If Player 2 is incorrect, Player 1 has a chance to ‘steal’ the square. Player 1 MUST complete the problem correctly AND explain where Player 2 was incorrect.
  4. This continues until someone wins or all squares have been completed.

I tested it out on my students. They liked it and had some good feedback. Some wanted ALL algorithms. Some wanted harder problems. This was a fair statement as I purposefully chose easier problems. I wanted to hook them before going all in. Two students worked on the middle square together and decided that they both claimed it; that worked for me. Overall, it was something that they all enjoyed.

The set up of the problems was purposeful. The four corners are meant to be easier problems (DOK 1). This allows all students success. Those that are between the four corners are meant to be a bit harder. Finally, the center square is to be the hardest. A challenge problem. A player can still win without choosing the challenge problem. I did like the modification my students came up with for that middle square. It takes the pressure off one particular player and allows for collaboration, problem-solving, and communication between players in a friendly manner.

I have created a template with directions and the above sample. Feel free to copy and create your own. I would love to hear how you are using it and how your students feel about it. What modifications have you made? Please share!

#MathReps Work!

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Several years ago I created #MathReps (EduProtocols for math) for my classroom. The original idea was based on Jon Corippo‘s 8 p*ARTS of Speech. When I first designed it I was excited and blogged about it. Since then, the idea, and resources have grown. And being who I am, I constantly doubt myself and my creations. I constantly question whether I’m doing good or harm.

MathReps Logo

Yesterday, some of my doubts were cast aside and my creation was validated. Recently, I was talking to another 5th-grade teacher at my site. We were talking about some tasks that we have students do. She follows the curriculum to a T; I, however, do not. This is in NO way a slight towards her (she’s new and is doing as she is instructed). She shared that she pulled out a concept the students hadn’t seen in a few months (our curriculum doesn’t spiral. I have much more to say about it, but won’t do it here.). It was adding/subtracting with decimals. I thought THAT was a great idea, so I did the same. She reported her students having difficulty remembering to line up the decimals doing the task. As I gave my students a similar task, I observed that they instinctively lined up the decimals. I found this not only interesting but satisfying. My students had been exposed daily to almost 5 months of this concept on various #MathReps. Needless to say, I was elated and felt somewhat justified in doing what I do.

After completing the task I had a frank discussion with my class. I asked, even though I already knew the answer if they had any trouble adding the decimals. I asked about lining up the decimals. They all looked at me like I was crazy. Of course, they knew to line up the decimals….duh! I then shared WHY! I also shared that a class that doesn’t use #MathReps had trouble remembering that important piece of information. And that it was because we practiced these concepts DAILY that they had no trouble with that part. (They had trouble with the task but weren’t confused about how to perform the actual skill of adding decimals.) Because of the culture of our class, they focused on the fact that #MathReps actually do help them and not on the class that had trouble. It was so awesome to bring to light to them, and me, that this protocol really works. One student even remarked that while they may not like doing them it does help them to learn.

Just like with anything, if we don’t use newly acquired knowledge we lose it. In addition, John Hattie puts repetition at a 0.73 on the Hattie Check Scale. I would caution that there are different types of repetition and we need to make sure that our reps are meaningful.

I did share this with the other teacher. I assured her it was no slight on her, and she understood, rather it was a slight on the adopted curriculum.

Cootie Catcher Math

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Playing with the Cootie Catcher

I am so over our math program! It’s soooooo boring! And if I’m bored, the kids are too. So today we did ‘Cootie Catcher Math’ aka ‘Fortune Teller Math’. This was not completely my idea. The original paper came from Scholastic. I liked it, copied it, and added to it. So simple, so fun, so NOT boring!

I copied the Cootie Catcher from a book by Scholastic. This was interesting because my students aren’t really into them at the moment so neither of us knew how to fold them properly. After a brief refresher, we were on our way! This was a very simplistic one. We needed to practice subtracting fractions. This one had like denominators so it was perfect for the first go-around.

The students worked in pairs. They had 2 tasks to complete for each round. Round one had them answering a subtraction problem while round two had them answering a more difficult word problem. But, because I know how 5th-graders work, there had to be some accountability attached otherwise it would be a free for all.

Students were tasked with solving all problems on their whiteboards. Then they were to take a photo and insert it into a slideshow that I shared with them via Google Classroom. Essentially, the students had a 2 slides presentation to complete. Problem 1 and challenge went on one slide show while problem 2 and the attached challenge went on slide two.

It was a success! All students completed the task successfully. I plan to do it again! I’m feeling better and better about math as I stretch what can be done outside a textbook. Last week we did an Iron Chef, Math Style.

Math Video Practice

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I hate monotony. I hate doing boring work. I hate workbooks. However, sometimes the simple fact is that kids need to do some of that boring work to get the process down. We have been working on multiplying decimals for a week now. They are getting it, but need more practice. If I suggested doing more work from their math books, I might have had a mutiny on my hands.  So I tricked them!

I made copies of some of their math book pages. They were given partners and one problem to solve. In the end, they were to record their process. This was a great exercise for everyone. A few groups used physical manipulatives to show their thoughts while others chose to use the algorithm. I think my favorite was this group who tried to subtract before multiplying. During their group work, I was able to sit with them and help guide them after listening to their reasoning

Manipulate This!

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img_2277I don’t use manipulatives enough in math. Over the past few years, I have used fewer manipulatives than ever before. I take partial responsibility for this. I should have incorporated more into my lessons. However, other factors contributed to this: my district not providing any manipulatives, adopting a half curriculum (half because the state doesn’t recognize it) that makes no mention of using any, and the pressure to keep moving along the curriculum/pacing guide. Well, this year I am making a conscious effort to do better.

No more excuses. Last week my class explored decimals and multiples of ten. I didn’t think they were really understanding that they moved the numbers a column (base-10 number chart) because we have a base-10 number system. They could do it, but were they understanding the why? The answer was, no. So, I broke out the base-10 manipulatives (rods, flats, etc.) to illustrate this. THEY worked as a group  (table groups) to prove that 0.26 x 10 = 2.6. Yeah, that lesson was a total failure! Each group created 10 groups of 0.26, but when they combined them they grabbed everything; including the unused manipulatives.

I did not want to give up the opportunity for them to make a connection. I regrouped after the failed lesson and reflected on what went wrong – management on my part. The next day we tried it again with greater success. Once they had their 10 groups of 0.14 I had them clean up the extra pieces (duh). They still weren’t completely making the connection, therefore, several conversations were had. Several finally saw the connection.

I’m not saying that this lesson hit it out of the park, obviously, it didn’t. I do need to make sure the students are getting more and more exposure to the manipulatives. With practice, we will all get better.

For as much as I write about my successes, I need to also write about my failures. This is a lesson that I am still thinking about nearly a week later. How can I make it better next time? Where did I go wrong? Any and all suggestions welcome.