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Alligators Are for Swamps, Not Comparing Numbers

There, I said it. And while I’m at it, PacMan is soooooooo 70s! It’s time to move past using alligators for comparing numbers.

There are really two steps involved in comparing numbers. First, students need to understand quantity and determine which number is larger. That’s an exercise in place value and is best handled through lots, LOTS, LOTS! (sorry, didn’t mean to yell…) of concrete practice building and comparing numbers. The second is understanding the symbols: < and >. That’s often more difficult because they are abstract symbols and totally meaningless to children. They understand that one of the symbols means less than and the other means greater than, but they have trouble remembering which is which. Enter the alligator. Yes, yes, the alligator eats the bigger number, and it helps kiddos remember the difference. But there are different, more “mathy” ways for kids to show their thinking in writing. A way that I’ve found works great with students is to put small dots on the symbols. Two dots always face the bigger number and one dot always faces the smaller number, because two dots is bigger than one dot. It’s basically a more dignified version of the alligator method for comparing numbers and takes much less time than drawing teeth.

 
Alligators are for swamps, not comparing numbers

I heard another great idea today from a fellow math coach. Look closely at the ends of a number line and what do you see? Exactly! The less than and greater than symbols. The 27 is closer to the > symbol and the 18 is closer to the < symbol. She said that she had been working with a second-grade class and they totally saw the connection and were able to use it.

Alligators are for swamps, not comparing numbers

This post generates tons of comments on social media about using alligators for comparing numbers. It’s always great to hear different perspectives, and I appreciate the discussion.

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124 Comments

  1. Sorry! I know that I could give them a more math-like example to get them to understand, but “why fix what ain’t broke?” The alligator eats the greater number is fun and my students “get it” when we use him for greater than and less than. I think they pay more attention to the alligator than dots. I love your blog and I use many strategies you recommend, but I’m sticking with the alligator. Thanks for the ideas and keep them coming! 🙂

    1. The “why fix” issue is that eventually kids will need to get away from the alligator as they get into higher grades. Upper grade teachers don’t do the alligator thing and the kids have to relearn how to define the symbols. I have seen a great graphic that show the word “greater” in large letters and “than” in small letters with the appropriate symbol between them. Same with “less than”. Sort of like (forgive the capitals, please): GREATER>than and less<THAN. I do love the number line idea, though. That’s brilliant. It fits in with the idea of using the number line to encourage kids to think of the whole number instead of just its parts.

      1. I had to address this exact issue in my 7th grade math class today!! I have taught them the dot method to replace the alligator, but old habits die hard, I guess. And in response to the “why fix what ain’t broke?”… it IS broken! The whole “alligator eats the bigger number” works up until maybe 5th grade, and then you have to fix the students understanding… it hurts our students… we need to fix it!!

        Do the upper levels a favor and stop with the alligator!!

        1. I agree. My sixth graders understood which one the alligator wants to eat, but could with any accuracy identify the name of the sign. With the alligator idea I don’t think many of them felt the need to know because the knew the desired direction. So in their mind is was a waste of time.

          1. We teach this so that students can understand the concept of which number is greater or less than another not so they can identify the symbol. Master of the concept is the objective and it should be taught many different ways

            1. Actually, in most cases, I think teachers are using it to identify the symbol. Understanding which number is greater or less depends on counting and/or place value understandings. Many students, for example, could tell you that 18 is less than 20 from their experiences using counters on a ten-frame or seeing numbers on a number line. The alligator comes into play when they must use the inequality signs.

        2. I know this is an old post but I’m so curious as to why US teachers in higher grades don’t use the crocodile! I’m a maths teacher in the UK working with kids up to 18 (just pre-college) and I use the crocodile all the way up, it’s one of the most effective mnemonics we have. I honestly don’t see how the dots or number line method is any more mathematical – they’re all just visual tricks to help it stick in kids’ minds. And I think a greedy alligator does help them to remember what the sign is saying about the value of the numbers or expressions, whereas once you’re dealing with say algebraic inequalities, the number line arrow version loses effectiveness in my mind.

          1. I think it comes down to being able to “read” the comparative symbols. In other words, knowing that < is read less than. The alligator method is all about knowing which quantity is bigger and then appropriately placing the alligator. If you think about the inequality 7x < 28, you have to be able to read the symbol to solve the inequality. If all you know how to do is look for the bigger quantify and place the alligator, you'd have difficulty solving this, because you don't know which quantity is greater.

      1. Ms. Boucher, I also taught my students that the symbols come from the number line, and that when you’re comparing numbers, it’s all RELATIONAL. It might not seem important, but oh, it really is!

        When comparing numbers, we’re really looking at where they are in relation to one another (and to zero) on the number line, so the symbols are important. Even kindergarteners and 1st graders came to understand.

      2. Hi Donna, I’m a loyal fan and I love your posts but I do disagree on this one for several reasons. Students do need to know the greater number in order to place the alligator mouth correctly. And if they know the greater number, then logically, they know the lesser number. Their conceptual understanding of inequality is taught with an abundance of place value practice – base ten materials!!! The alligator mouth is simply a mnemonic to help students know how to place the abstract symbols. But the dot method is also a mnemonic! As teachers, we don’t stop there. We don’t teach a mnemonic in isolation or in the absence of the concept. I continue on, explaining to students that the way we read an inequality is from left to right, as we read words or sentences. And because they already recognize which quantity is greater and which is less (shown by the fact that they were able to place the “alligator mouth” correctly), with practice students are able to read and write inequalities accurately. I learned the alligator method decades ago in elementary school and it still stuck with me. It made total sense. And I just finished covering inequalities with my first graders and also see their success. For me, it’s more than a cutesie mnemonic. I am definitely team alligator!!

        1. Molly, it’s sounds like you do a wonderful job teaching the alligator! I think the problem comes later when they can’t tell which quantity is greater, for example in an expression like x + 3 > 2. You have to be able to read the sign to read and solve the expression. Yes, the dot method is similar to the alligator in many ways, but it focuses on reading the symbol as well. That’s not typically part of using the alligator, but it very well could be.

      1. As a high school teacher, please stop with the alligator and the butterfly and the cowboy on the horse and all the other cutesy tricks. All of these tricks expire in the upper grades and teachers have to start from scratch reteaching those concepts. Students struggle unnecessarily due to misconceptions that are ingrained from an early age. Taking the easy road now puts the students on a rocky road later on. Do what’s best in the long run instead of focusing on a quick fix now.

        1. I totally agree. I also teach HS students, and while I also love the utility of mnemonics, my experience has been that the alligator one often expires. I am confident that when there is mathematical reasoning to connect to what we wish students to recall, it is best to connect it to understanding. (Example: PEMDAS should be accompanied with how exponents come before multiplication because they are repeated multiplication, higher order, etc.). The students performing in the bottom quartile often recall there was an alligator, but they mess up inequality and all the mnemonic at that point has (falsely) taught them is that math is a bunch of memorization that neither makes sense to them nor can be remembered by them. I’m 100% convinced the alligator is not the way to go for most students. I like the dots as they relate to quantity. I often use this…. “Let’s pretend we are inventing the symbols that compare numbers and expressions. As we look at an equal sign it seems very logical that the distance between the endpoints of the line segments on their left is equal to the distance between the endpoints on the right. (This is all accompanied by visuals and examples and students manipulating the line segments.). Now let’s consider this number on the left side being bigger now, so we won’t want an equal sign, right? Let’s make the distance on this left side bigger. Note that as we push it apart on the left, the endpoints on the right get closer together. Why does this make sense? Okay, so ‘as we create these new symbols’ for when the sides are not equal, let’s just push the two endpoints on the side with the lesser value all the way together.” Now the concept is bound to the symbols with mathematical sense-making rather than a potentially easy-to-forget or mutate mnemonic. Ditto for “butterfly method” (AKA cross-multiplication) which students often apply to wrong contexts since they’ve (poorly) memorized without understanding.

    2. I have used the One Dot-Two Dot method for several years now and I think it helps students draw the symbols more easily. I often found that they had trouble orienting those alligators or still drawing them the wrong way. When you place two dots next to the bigger number and one dot next to the smaller and then connect, they have no problems making the sign correctly.

      1. I agree completely! I have students that came to second from first grade and said their teacher taught them the alligator, “but now they forget”. I also have students that have come back from Middle School to share that ‘my’ trick of one dot is less thn 2 dots are one of the things they will never forget that i taught them. It just makes sense! I live in Florida….get rid of the alligator! LOL

    3. I agree, I have taught the alligator in the past, but I noticed my kids could never read the alligator if it was greater than or less than. They just memorized the “procedure” but not did not truly understand the concept. I have started really spending more time on the concrete to make sure they get the math behind it… Then moving to the representation then on to the abstract.

      1. As a 5th Grade teacher that “alligator” eats the bigger number drives me crazy. Students will turn a problem around to make the alligator eat the bigger number because they have no understanding of what the symbols mean. Thank you so much for this post. I wish everyone would stop teaching alligators.

    4. The difficulty becomes clearer as students get older. In junior high students need to read statements with greater than and less than statements with letters involved, and they need to conceptually understand which side of the inequality is bigger/smaller. It isn’t just about placing the symbol correctly, it is about reading the math statement correctly.

      1. Thank you Kara! You are absolutely correct. In middle and high school, students must read statements such as x + 9 < y. As secondary teachers we need them to understand that < is less than. The alligator cannot help them with x + 9 < y. The alligator actually confuses them at this point.

    5. As a former middle school teacher who now teaches first grade, I have seen first hand what a disaster it is for a child that can’t just look at the (> and and ,,

      if x = 2 – then you would fill in the blank with =

      if x = 1 – then you would fill in the blank with stand for greater than.

      When I first introduce the inequality symbols, I have been having the kids write out the words greater than, and less than, equal to. And then one day, I say I forgot to tell you there is a quicker way to write it. And I show them, how it takes less then one second to write and they love it. For a while I write the words with the symbols below, hang it on the wall as a reference, and so on. I let them pick which way they want to write their comparisons and of course most of them choose the symbol. Then one day I take it off the wall but I still tell them they can write the words instead of the symbols. Well, let me tell you, none of them want to write the words so it seems that with the games and activities that I have them do, they do just fine. I have never give them a trick, they just remember it the same way they learned to remember b, d, p, q. Exposure and practice. The symbols are just a skill to remember like a sight word, not a concept that you have to develop for them over a longer period of time. Teach the concepts of comparing numbers, let them remember the symbols through frequent practice, exposure, and application.

      Here is an activity I have the kids practice to get more comfortable with the symbols.
      Kind of like a “math” dictation test

      One student reads aloud without showing the card to his partner: “Twelve is greater than 6”

      On a dry erase board, the partner must write: “12 > 6”

      Put the question and the answer on index cards so the kids can self check.

      Then do the same activity but reverse it

      One partner writes on the dry erase board: 10 < 15

      The other partner has to say "Ten is less than 15"

      Then they can make up their own comparisons too.

    6. That’s true until you have middle school students still needing to use the ‘hungry alligator’ language because they never learned the true meaning…

    7. Actually, why teach it incorrectly when you can teach it correctly. I’m sorry, I’m really not trying to be rude; I’m pointing out that conceptualizing and deep understanding are important for a firm base in mathematics. Your kindergarteners will be able to understand this, too. Mine did.

    8. I am mother not a teacher, but I graduated college, and took trigonometry in Collegend and past with an A. The left hand makes the less than sign, and always eats the bigger number…. yes, forget about drawing teeth..I used my hand like an alligator and my 2nd grader got it…. Do what works, besides in real life your never going to make less than, greater than, equal, or aligator signs… Keep the aligator going strong says the mom of a 6th grader, 2nd grader, prepaid schooler, and baby….

      1. I actually (as an adult) have ran across several scenarios that were referring to age and cost. You had to understand what meant to know what the cost was. I have also seen it used to denote various costs for purchasing different quantities of items. Is it used every day? No probably not, but it is a usable skill.

    9. I teach 8th grade. I had a student actually draw the alligator head (teeth, eyes, and snout). The problem is, she had the alligator eating the wrong number. Any time that we use little tricks instead of having our students truly understand the math concept the students are losing out in something. And many times another math teacher has to fix the misunderstanding.

    10. Please, as a HS math teacher stop with the alligator! How will students ever understand expressions like y > x? They don’t know what to do or even how to read this expression because there are no number clues.

      1. I do the same thing Gina. Though I admit to using the “alligator” with my littles in intro lessons in the past, I use the dots and we practice READING the expressions. It’s the most difficult part for the kids. They have become more comfortable with it. I see the kids holding up both hands to make the symbols and then say “left is less”. Some of the little children who keep confusing their left with their right do well with reading it by remembering that the arrow points to the smaller number. It takes them longer to read it though. I see them say, “It’s pointing to the 18, so 18 is less than 25”. Both of these give them a better understanding of how to read it and will be more helpful than that old alligator in the the future!

    11. As others have said, it is seriously broken. The symbols are arrows pointing to the left and right and meant to ultimately express values that an unknown can be. When students are given x < 5 and then represent this value with a circle above the five on a number line and then an arrow moving to the right of five because that is the way the alligator eats, they demonstrate zero understanding of inequalities. This snowballs into major issues with domain and range of functions, which truly has a negative impact on students acquiring a solid understanding of Algebra and, ultimately, the Calculus. As a high school mathematics teacher who spends ridiculous amounts of time trying to fix this deeply-ingrained, pedagogical and mathematical error, I implore you to teach it correctly and not perpetuate a conceptual misunderstanding that is truly a detriment to students.

      Simply draw a number line with two tick marks and ask where you would write the first number, on the left of the other number. It will take a little more time than the alligator, but it will not create an incorrect understanding of inequalities. Instead, students will begin a journey down the correct path towards a deep understanding of functions.

  2. I teach 2nd grade and have used the “dots” trick for several years. It works great for kids who understand the symbols but have small-motor issues or visual perception issues . . . They know which way the want the arrows to face, but they just can’t make it happen. The “dot to dot” method works great for those types of kids . . . LOVE IT!

  3. Thanks for posting this! I’ve been saying this to fellow teachers for what seems like forever. I get that it’s a cutesy way to teach greater than/less than, but it’s an injustice when kids never understand what the symbols mean. This was illustrated for me very clearly last school year when I presented a 4th grader with a “<” in isolation and asked her what it was called. She replied, “I don’t know, there aren’t any numbers there.”

    1. The alligator method is very engaging, and I have no problem with it being used to introduce the concept of the symbols. I’ve heard of teachers who have alligator puppets and they act out eating the larger number. Definitely memorable! It’s more the drawing of the alligator teeth that I think I prefer options for. And you’re absolutely right–kids need to understand that the symbols stand for the words “is greater than” or “is less than”, just like the = sign is read “equal’. Thanks for commenting!

  4. I love the dots trick. While the alligator is cute, I think you are absolutely right..kids need to think in more “mathy ways”.:)

    1. They can always THINK alligator and draw dots. Again, as long as they know what words the symbols stand for. 🙂

  5. I always start with the alligator analogy, but I, too, get so annoyed at how long it takes them to draw the little teeth.

    From there, I have them use their hands to make the “alligator mouth” in the air, which helps them start to transition to drawing without the teeth.

    I always make a point of having them read the sentences with the symbols, too! Then I slowly take away one number, and then the other. I encourage them to “imagine” numbers to think about if it’s ‘less than’ or ‘greater than’.

    Like you said, the alligator is one way to start it, and it’s not evil- but it’s not enough to stop there!

    Jenny
    Luckeyfrog’s Lilypad

    1. Yes! Having them read the sentences is so important. I love the idea of taking away the numbers and having them provide numbers that would fit. Thanks for sharing that!

    2. I have always used the alligator as one way of remembering which is which, much like using visualizing the word bed as a bed for my second graders who struggle with the difference between b and d. I don’t allow the drawing of teeth and eyes.

      My biggest suggestion is to teach all three symbols at once. I teach the kids to read the symbols as “is less than , is greater than, and is equal to”. This has made a huge difference in comparing each side of a number sentence in the past ten years I’ve used it in both 2nd and 3rd grade.

  6. I have teaching my kindergarterners, greater than and less than symbols with the alligator, but I would like to use the dots one, as exposure and more appropriate to introduce them as math symbols that students will see them more often higher grades.

  7. I taught this very lesson Friday in my 3rd grade classroom. Everyone knew about the alligator, but when I shared the dots, many of my scholars got “the look” and exclaimed – “That makes so much sense! Can we use the dots instead of the alligator?” Love it when a strategy makes meaning instead of memorizing. I also use sentence stems: ___ is greater than ___. and include the > sign above the words “greater than”. This is a great strategy for my ELL learners. They refer back to the sentence stems to help with their work.

  8. I am “new” to teaching 4th and 5th grade math, after not having taught any math for about 8 years! You could say I am rusty at best. Just today I was guilty of using the alligator analogy. I rediscovered your blog and am SO thankful I did!! I love your ideas for teaching a conceptual understanding of math. It just makes sense for kids. I’ll definitely be back again and again!

    Hokie Teach

  9. Brilliant! Love the connection to the number line. It is more concrete than an expression by placing the numbers in context. Again, brilliant!

    This website has been a wonderful resource for me over the past year. The research-based lessons, tips and activities are tangible and can easily be reimagined for different concepts or grade levels (as I’ve done for my 6th grade classes). I am looking forward to sharing both the website and ideas with my colleagues as I begin my first official year as a math coach. Any words of advice or resources that you might have for a rookie?

  10. I learned the alligator way when I was a kid and it didn’t really help me as I got older. I heard about the dots from another teacher and have used it for years!

    My answer to someone who prefers the alligator method is “That is a great trick, but we have to teach understanding. The dots push them to understand.”

    I noticed the number line connection when I was teaching it this year (after not having taught number lines for years because it wasn’t a state standard! Boo!). I just hadn’t sat down to really look at it. Thanks for bringing it up here.

    I just LOVE LOVE LOVE your blog. I repost your entries on a Facebook page I belong to for teachers in our district who are struggling with CC Math. Thank you!

    1. Hey, Ruth!! Thanks for sharing your experiences with the alligator and number line. I think it’s an important conversation to have! Honored that you feel my posts are worth sharing. 🙂

  11. I love using the dots method to teach. I remember thinking, “What a crock…an alligator is going to eat whatever is closer, not whatever is bigger, but OK.” when I was taught the alligator method in class. I teach first graders, and it is so easy to to use the dots to teach more and less! The kids really get this method…I have seen much confusion with the alligator. Thanks!

    1. Ha ha, love it! “Alligators are going to eat whatever is closer”. I totally agree that the dot method is very easy for first graders to learn and understand. 🙂

  12. The alligator method is fun, but it has no meaning to students when they see the symbol in isolation. My first graders love the dot method and understand and know what the symbol means in isolation. I love the number line connection. I love your blog!

  13. I was taught many years ago that you should understand what the symbol means, not using a trick. So I always teach my students that it is an arrow. The less than arrow points in the direction that numbers get smaller on a number line and the more than arrow is pointing in the direction the numbers get larger on the number line. Number lines are vital to understanding quantity. Thanks for the blog on this.

  14. I have used the alligator (I say “crocodile,” but potato, poTAHto, right?) for years, but I also teach how to READ the sentences using the symbols. We discuss which direction we READ (left to right), and so therefore, we have to “read” the part of the symbol we come to first. For example in a less than sentence, we come to the “skinny” side of the symbol first (<), so we say “less than.” In a greater than sentence, we see the “big” side first (>), so we say “greater than.” We practice reading sentences by stopping to discuss which side of the symbol we come to first and remind ourselves we have to “read” that side first since we read left to right. It helps SO MUCH. The light bulbs turn on before my eyes, lol.
    However–I LOVE the idea of the dots. Thanks for the tip!

    -Gayla
    Teach On.

  15. Thank you for this post! I am teaching 2nd grade Math for the first time (after 20 years in 4th). I learned comparing numbers using the alligator when I was in school. I have to admit I still think about it when I am teaching it to my students, because the symbols are confusing. Now, I have two new strategies. Hopefully the next generation will be better prepared.

    1. We’ve all learned or used the alligator at one point or another! I think the dots are very straightforward and a great alternative. Good luck with that switch from 4th to 2nd!

  16. I’m coming late to the conversation, but let me give you another reason to ditch the gator – fractions! When kids spend all of k, 1, and 2 learning that alligators eat the bigger number, their minds are blown when they get to fractions. Here they are, trying to grasp that 1/6 is greater than 1/8 (difficult and abstract!), and they see that damned alligator and are SURE he wants to eat the 8. Because that’s what he’s always done. Just one more hurdle to jump with fractions, and God knows we don’t need any more of those.

  17. Confessions of a former alligator-lover… I promise I’ve stopped using it now! I have used the two-dot/one-dot method and that has helped kids.
    I love the idea of looking at the ends of a number line to remember which symbol is called “less than” and which symbol is called “greater than.” I’ve always told my kids that to me, the < looks sort of like a crooked L, which is how I remember that it’s the “Less than” symbol, but I’m going to add the number line discussion to my teaching this year! Thanks!

  18. I like this! I will try it this year. Last year I did the alligator way. I didn’t feel like they struggled with understanding quantity and being able to tell which one was bigger. They struggled more with remembering what the sign stood for (less or greater). The way I taught them to remember was if you saw 5 < 9, that would read 5 is LESS than 9 (the < is like a smushed L for ‘L’ess), Then they would compare the numbers to make sure it was true. I really like your way better as it is more concrete. 2 dots are greater than 1. I will def. use it, thanks for sharing.

  19. I didn’t bring out my alligator once last year…and my students were still a little foggy (for the most part) on the concept. That tells me we need to practice even more than our textbook covers. The number line arrows are eye-opening! LOVE this!
    SweetSchoolMoments

  20. Another approach: <, Less than, points to Left and >, greateR than, points to right.

    Could you also discuss PEMDAS with its problems eg. PEDMAS, PEMDSA, and PEDMSA?

  21. You learn something new every day. I honestly, until today, did not know the signs had to stay a specific direction. I always just thought you looked at the numbers and opened the “mouth” to the biggest one, in whatever order the numbers were facing. I do like the Left/Right thing as well as the “arrows” on a number line tip, but those to me, seem just as much a “trick” as remembering the “mouth wants to eat the most cookies” or an alligator….

    1. Students definitely need a device to remember what the abstract symbol means. The reason that the number line arrows seem like less of a trick to me is that they are grounded in math. Students are familiar with the number line and know that the arrow on the left side “points” toward smaller numbers and the one on the right “points” toward larger numbers. It gives them a reference for the < and > symbols.

  22. I work in math intervention. I teach my students to read number sentences left-to-right like they would word sentences. If they get to the small part of the symbol first they say, “less than.” If they get to the big part of the symbol first they say, “greateer than.” Laurie in Wisconsin

  23. In the instructional implications of the new teks (via led forward’s field guides), the idea is to help students understand conceptually rather than using tricks to memorize math foundational concepts.

    1. Exactly, Kimmie, which is why I’m not a fan of the alligator. Students do need to know the symbols, and the dots are an easy way to help them remember.

  24. Thanks for repost of this will include this on my anchor chart. I have been looking for a way to get away from alligator!

  25. Kim Sutton introduced this strategy many moons ago. I completely agree in regards to the alligator strategy. It doesn’t help the students understand the concept- just a trick. Thanks for continuing to share this strategy. It is always my go to when comparing!

  26. I used your method with my kids this year and had soooo much better success. We worked really hard on which number was bigger and how we knew that. The next step, putting the two dots next to the bigger number came so much more easily. Thanks!

  27. I went to a Math training session with a man from India who talked about this concept in a way I had never thought of…..the symbol points to the smaller number whether it appears on the left OR the right. So, rather than this symbol “<" meaning "less than" it can be read as less than or greater than depending on whether you are reading left to right or right to left. He mentioned that in the west we read left to right but in other cultures they read right to left. So, he suggests we read 4 < 6 as "4 is less than 6" and also "6 is greater than 4".
    Ann Elise

  28. Hello! In middle school we have to fix that “trick” that they learned in elementary about the ends of the number line looking like the less than and greater than symbols. I would stray away from using that technique because students see inequalities written backwards so that technique does not work. We have to un-teach it.

  29. I teach sixth grade math and the alligator trick definitely does NOT help kids understand what the symbols mean. I teach them to read the symbols like you read words…from left to right.

  30. I am a 7th grade math teacher and taught my students how to solve and graph inequalities this year. I can’t tell you how many times my students got hung up on this “alligator” method.

    I may as well been drawing alligators on the board because they just couldn’t get past comparing one side to the other and the “alligator eating the bigger one” for the longest time. It made it difficult to scaffold their previous understanding of solving equations and understanding/verbalizing inequality symbols to understanding the more complex one of solving and graphing inequalities.

    Relating it back to a number line and continuously emphasizing it during their math education will help prepare students when they get to solving and graphing inequalities. The dots method would be a great way to check their work (i.e. if the two dots are next to the bigger number, it is correct) but it may not be enough to solidify their understanding if taught without emphasizing the use of a number line.

    Thank you for the tip. I will definitely be trying it out this next school year. Thanks!

  31. I am a middle school math teacher and I understand that the alligator method makes it fun to teach but the “alligator eats the bigger number” is all they remember! Year after year! This puts all of their focus on the bigger number, always. That’s why it’s hard for them to remember what each sign means when there are no numbers to compare, or if they are solving an inequality.

    Math is a language and it should be read left to right. It is so important to have kids read the comparisons left to right so they can get used to using the correct symbols in context.

    One trick I have the kids use to identify the signs is “less than, left hand”. You can make the less than symbol with your thumb and pointer finger on your left hand.

  32. If you Google “Nix the Tricks” there are two PDFs of “math tricks” and reasons not to use them. Remember that math content knowledge builds over time and each lesson at each level should be connected to a building block vat a higher level. Doing things like the alligator builds individual buildings and eventually can lead to misconceptions and incomplete understandings.

  33. Love this! I’m afraid I was never very good at explaining the alligator thing. The dots are actually more concrete, and the number line idea is just so obvious, once someone points it out!

  34. I like to also make the connection about the “opening.” The Bigger opening goes with the number that is “bigger” or greater. The little point points to the “littler” number! We just talked about that this week!! 🙂

  35. I teach 2nd grade and we teach the students that when comparing numbers they have to determinebif the number is to the right or to the left of the other number resulting in arrows that turn into greater than/less than symbols.

  36. While the alligator seems to be a good idea, please keep in mind students have to eventually replace those numbers with a variable. They must understand how to read an inequality. They have to graph inequalities and all these little tricks (like shade the direction the symbol is pointing) are causing major misconceptions. What if the variable is on the right? How do you read the statement? Where do you shade? Please elem and middle school teachers, teach them how to read inequalities, not just tricks. Use the number line all the time. The conceptual understandings will be so much greater.

  37. I have taught middle school math for 30 years. I don’t recall ever hearing any alligator or Pac-Man references until I started teaching. I learned the small side of the symbol is closest to the smaller (lesser) number, and the larger side is closest to the larger (greater) number. I use this same description when teaching comparisons. Every year, I have students who act as if the lightbulb just went on for them as this is so intuitive that they finally have clarity for interpreting these symbols.

  38. I have never used the alligator analogy. However, I introduce the concept by first asking if they ever want the biggest piece of cake at a party. We all agree that’s what we want! The biggest one! Then I ask them to think about a mommy bird bringing a worm back for her babies, and how the baby birds all want the biggest piece, so the bird with its mouth open is going to get the biggest worm because the open mouth can eat more that the little mouth. I use this analogy only for the first few lessons, mixing in “greater than” and “less than” more and more until we read all equations using this terminology. Interestingly, I never wanted to use alligators! Second graders find enough other ways to waste time, I don’t need teeth added to the list!

  39. I never remembered which way the sign was supposed to go; until I heard about the alligator sometime after college, would’ve made things so much simpler for me in the eighties! I think the alligator or any other teaching trick needs to be pulled out when kids aren’t getting it one way. If you have a teacher that’s just using the number line and some kid isn’t getting it, maybe what they need is the alligator. If you have kids that aren’t getting the alligator, then give them a piece of cake or some dots! (Drawing teeth is stupid though, it’s the picture you want to paint in their mind – not what you want them to draw.)

  40. A long time issue for me. The alligator doesn’t teach them the meaning of the symbol. Kids throughout elementary and middle school will read the inequality from right to left in order to read the alligator correctly. Example: 5 < 7 will be read "seven is greater than five.". True…but wrong symbol. So…I have liked strategies that focus on helping understand the symbol itself. The number line mentioned above is a good one. Another mnemonic that seems to hold is that the less than sign looks more like an L tipped over. L is for less.

  41. “I heard another great idea today from a fellow math coach. Look closely at the ends of a number line and what do you see? Exactly! The less than and greater than symbols.”

    I just discovered your blog this week and I LOVE IT! (yes, I did mean to yell) 🙂 Can I please address this latest “trick” with the number line? DO NOT USE THIS method PLEASE. Here’s why: When students begin using variables, they will need to be able to read the equation from the variable. 4 < 5 reads as 4 is less than 5, however, 4 < n will be read as n is greater than 4 but students get it wrong because the sign is pointing toward the left and they learned that this means "less than" — they were not taught that this trick only works when you read the inequality from left to right, which is not the way it is always read.

    1. So glad you like the blog, Dawn. My students routinely read inequalities either way, so they could read 64 < 88 as 64 is less than 88, from left to right, or 88 is greater than 64, from right to left. We specifically practice that. When they are looking from right to left, they see the "larger" side of the symbol, so they read 88 is greater than 64. When they are looking from left to right, the see the "smaller" side of the symbol, so they read 64 is less than 88.

      1. I couldn’t agree more! I took a class once from a professor from India…he reminded us that not everyone in the world reads left to right. Never forgotten that!

      2. I would think that unless they had a true and mathematical grasp of the inequality symbols that when they get an incorrectly written problem they will struggle. It’s not that they can’t read true statements with numbers they know it’s when they don’t know the number understanding and the inequality symbol is incorrect that they struggle. Curious as to why it has to be said n greater than 4 ? why can’t it be read ‘4 less than a number’? I teach it both ways so just wondering how I am leading them wrong on this.

  42. It’s the first day of college here and … the SIQ (student in question) *loved* the big vertical number line from @mathequalslove but her first “piece of pie” lesson to do on ALEKS was stating whether assorted integers were or = … and I could tell by her look that… were just the same thing, thank you. Is a chair not a chair if it’s upside down?
    (ALEKS is the computer software that thankfully our teachers use for practice, NOT instruction… their “math course” has 348 or something like that “pieces of pie” that are math procedures broken down into teeny tiny slices — but it is all procedure, procedure, procedure, so the “explanations” that are sometimes called “instruction” …can be the antithesis of what we’d call teaching for understanding.)

    I used the one-dot two-dot to explain, with some visual/kinesthetic “expanding to the bigger one” and yes, she read them all from greater to lesser (and asked me please, to write “-3 is greater than -5” under the example so she could study it — but study to understand, not learn a trick to pass the test. Math angels were hovering and smiling…)

    THanks 🙂 🙂

  43. Hate the alligators. When my fourth graders had to tell me what those symbols meant, they were lost and actually called it the alligator. They can understand and remember the correct words. Use math language.

  44. Don’t know if anyone has mentioned as a sort of retraining tool for early middle schoolers that come to you with the alligator method…I demonstrate and have the students replicate holding their hands in front of them with the thumbs out and the fingers to the sky. They see the L shape of their left hand vs their right hand and then we hold it up to the symbols and they see that the less than symbol also points to their left hand. L for left and L for less than. Then we practice, practice, practice reading those inequalities properly.

  45. I am so glad you addressed this topic. I teach 6th graders and they have been taught the alligator method. I just draw their attention to the number line and the arrows directions. We discuss numbers greater than and less than zero. Which will help them understand the symbols as well. Thank you!

  46. I have been using this method for years. It was shared with me by a resource teacher that I team taught math with. It ALWAYS works and there is no confusion in drawing the symbol or correctly reading the number sentence.

  47. I’m a thirty-year veteran K-1 teacher who is guilty of the alligator in math. I have changed my ways, but I still feel that depending on where your curriculum comes from and how well your students have developed their number sense plays a part in how “cute” we make math. It also goes into how we’re teaching math at the primary level. Is it find and circle the number that the “greater gator” is after, or are teachers looking at each number such as 4 < 8 and building each number and truly building number sense and comparing numbers? Many of us in primary, not everyone, need to slow down and look at why we're teaching this standard/concept now and where it needs to take a student later. Once we know, more we can and should do better with our teaching practices. I know I am trying my best.

  48. There is nothing wrong with introducing the concept using the alligator or even Pac-Man. (Btw, retro is back in style.)

    1. Point taken! I think there’s a big difference between using the concept of the alligator to introduce the symbol and having kids draw the teeth and never move on from that.

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