Tuesday, February 12, 2013


Kal-El working the subtraction snake game with an incredibly long snake

I wrote this post maybe two months ago when Kal-El was just finishing the addition memorization sequence and Me Too was just beginning it.  It was never posted and got lost in the shuffle because I was unable to use the video I intended to for one of the demonstrations of the snake game.  I finally drummed up the courage to MAKE a video to go with that section.  So, I can finally post this information but the timing of the post would have made more sense two months ago.  Here it goes:

(From two months ago) You may have noticed recently that we reached an interesting moment in time between the two boys in which Me Too is at the very beginning of the memorization of addition sequence and Kal-El was at  the very end of the memorization of addition sequence.  What may have seemed odd is that Me Too began the sequence with the addition snake game and Kal-El ended the sequence with the addition snake game.  Kal-El has now begun the memorization of subtraction sequence with the subtraction snake game and in our home that sequence will also conclude with the subtraction snake game.  How is it that the snake game came to be at both the beginning and the end?

If you have access to multiple albums as I do, you will find the snake game in different places.  I have found that there is a distinct difference in the style of use when it is used at the beginning rather than the end.  If you only were familiar with one style of use it would be very difficult to imagine using the game at the opposite end of the sequence.  In other words, the way you use it has an awful lot to do with with where it should go.  The primary album I use for math is Meg's Montessori by Hand album (an AMI album).  She places the snake games at the beginning of the addition and subtractions sequences.  I LOVE her eloquent explanation of how it fits into the sequence:

Memorization is introduced at a time when the child is incredibly comfortable with the four operations and numbers.  We have not brought attention to memorization before--it is introduced gently now.  There is a pattern to the way the child will memorize the facts.  First there is a Sensorial experience--The Addition Snake Game--without any recording.  The purpose of the Sensorial experience is to be able to explore a bit and to initially encounter the facts.  Secondly, the child works with an orderly experience fo the facts (tables) while using Sensorial materials--The Addition Strip Board--to find the answer, yet now she records.  Finally, the child works with charts--The Addition Charts--; she encounters facts in a random way and writes the whole equation, the problem and the answer.  There is no material representing quantity here...When the child reaches the third step, she has basically memorized the facts already through working with the first two steps.  The material for Subtraction is very similar to that of addition, there is a Subtraction Snake Game, a Subtraction Strip Board with a pre-printed orderly way to record facts, and one Practice chart (one blank, and one for the control). 

                                    -Meg Montessori by Hand Math album

I love the idea of using the snake games at the beginning of the addition and subtraction memorization sequences to provide a Sensorial experience without any recording. When a snake game is used at the beginning of the memorization sequence the child counts each individual bead using a notched tag that they leave in place each time they reach 10.  The beads tend to stay in-line with the snake until they are collected for safekeeping.  So if presented with 7 and 9 as the first two bead bars in his snake, this child will count 1...2...3...4...5...6...7...8...9..10 and leave his notched tab in place between the third and fourth beads of nine bar.  They will place a golden bead bar above the beads they just counted.  Then, they will count the previously uncounted beads on the opposite side of the notched tab 1...2..3...4...5...6 and place a bar from the black/white bead stair above those beads.  Here is a video example of this style of snake game from Oak Haven Montessori School (you can see the portion of the game in question around 2:17):

When a snake game is used at the end of the memorization sequence the child will not be counting individual beads as described above.  Rather, they will look at the each bead bar as a number (having the number memorized according to color really helps at this point) and will use the addition facts they have just memorized through the sequence of addition boards to complete the game.  I love the idea of using the snake game at the end of the addition and subtraction memorization sequences so that the child can USE the facts they just memorized to play the game.  In this style the child will often start at the beginning of the snake and pull a pair of bead bars forward to isolate the addition equation at hand.  So, if presented with 7 and 9 as the first two bead bars in his snake the child might pull those two bead bars and say silently or aloud "7 plus 9 equals 16."  They will then get a golden ten bar and think of how to make the sum of 16 with 10 as one of the addends.  Then they will grab the six bar from the black/white bead stair. I am bummed :(  I thought that the addition snake game was one of the free samples Montessori Live had up on YouTube and that I could link to it to show you the other style.  Unfortunately, that video is by subscription only.  If you have math albums from either Karen Tyler (AMS) or Montessori R&D (AMS) the addition snake presentation given at the end of the memorization sequence presents the snake game in this way.  For those of you who get all turned around when trying to turn the steps in the albums into a real-life presentation I MADE A VIDEO.  My heart rate jumped up to dangerous levels while making this video.  I was super nervous.  It's not perfect, but it is a quick look at the addition snake game at the end of the addition memorization sequence.

Like I said, I like both ideas.  Both the Karen Tyler and Montessori R&D albums like both ideas as well.  The first version of the snake game is included, not in the memorization section, but in the linear counting section of these albums.  The second version is included at the end of the memorization sequence.  What I think can get lost here is that the "linear counting" version is an important part of the start of the memorization sequence.  It is likely that an experienced Montessori guide knows this and if you could lay out all of the different sequences of the math album across one another so you could see "periods" as in the Gettman book you would find that the child reaches the "snake game search for 10" in linear counting just before beginning the memorization sequence so that it IS the beginning of the memorization sequence.  I really like how strongly the AMI albums position the early snake game in the sequence.  They don't, however, seem to have it again at the end. Not only do I like that Kal-El was able to play the game using his newly acquired addition facts, but frankly before we could BEGIN the subtraction sequence with the subtraction snake game we needed to revisit snake game procedures anyway and it was easiest to do so with the addition snake game.  So, perhaps this happens naturally.  He had to be taught NOT to count the beads of the snake individually.  With all of the work he is still doing with the long bead chains, t was neat to see him appreciate how much less cumbersome it was to just"know" the answer rather than count every individual bead.  Also, as he nears completion with the long and short bead chains he is much more familiar with which color equals which number with the bead bars.  I know they supposedly pick this up when they use the teen bead bars with the sequin boards.  My kids didn't.  They most definitely worked out which color was which number through working with the long bead chains.  There is a REASON the colors of these things stay consistent across all of the Montessori materials.

Montessori Monday


  1. I guess you could say I am new to trying the Montessori approach - new as in, I have no albums, and am still learning the approach to teaching. So far the extent of my 'Montessori' teaching has just come from what I've seen others do on their blogs, but so many have a focus on the younger ages, which i do have three 5 and under, but I also have a 7 and 8 year old. So far anything I have tried with them, apart from a few fun game-type works, is really below where they already are, and they usually just want to 'do the math in their head' or do it as we have always done it, which is very traditional. With your boys being older, am I starting in the wrong place with them, or is there somewhere you would suggest I look for ideas to use with my older ones? I might add, as of this point, I have almost nothing authentic Montessori as far as materials - those are still in the works, as much of what I do have that I have put in with their materials is DIY and leans more to the younger three... And I LOVE the demonstration and am very curious about the game itself and why the different bead bars - is there a purpose more than just what I see for having the black/white bars?
    Sincerely -
    the Newbie!

  2. Amy - welcome to Montessori :)

    You might like to visit Montessori Nuggets as these are some of the questions I try to answer over there. I'll check to see if I post up about the black/white bead bars and add one if I don't.

    The black/white is there to show that these are a partial answer. The goal with the snake games is to turn a multi-colored snake all gold except the very last bit. So the black/white bar is a place-holder while counting and exchanging.

    Then there are various stages of verifying the answers that allow the gold bars to be re-matched with the colored bars - thus, if all the colored bars have been replaced, and you don't have an even multiple of 10 (you usually don't), that black/white bar is still different from and can be compared with the colored bars.

    Too many words! Need photo! Will find a blog post! ;)

  3. Haha! Finally got the video to load (I was on an old computer at first) - LOVELY!!!!

    And it does explain the black bead bars well - place holder and used for the verifications.

    And yes, my primary albums focus on it at the beginning but the children keep working with it in a classroom (or at least have the option), so it ends up being at both ends and in the middle for some children :) My son still loves playing it now though he doesn't need it - gold snakes with red tongues is his goal ;)

  4. That was an awesome video! You did not sound nervous at all and your voice was very pleasant!

    I've seen the usual way of counting before the memorization and an automatic switch to do it the easier way after at our place. But I can see how you can point out that kids can use their newly memorized facts if they don't discover it on their own. Thanks for taking the effort to make the video, I am sure it would help a ton of people! Great job!

  5. Thank you so much Jessica! I will enjoy looking around and reading your posts! I can definitely use all the help and good ideas that I can get!

  6. Amy,

    My boys are 5 and barely 7 and have been doing Montessori since they were toddlers. They are also the only kids I've ever done this with, so I don't really feel like I have specific advice for you with your two having been traditionally schooled and are likely both older than my oldest. I would direct you to Jessica and her Keys of the Universe course. For a very reasonable price you will then have albums, a helpful forum, and most importantly EXPERIENCED COUNSEL :) I know that figuring out where to plug older kids into the sequences and which materials to do and which to skip are Jessica's specialty and she helps you with that as part of the course.

  7. I love all the research you put into this ... and your video is very helpful for anyone wanting to present the snake game! I always found the differences among various training programs fascinating, it's great that you decide which presentation is best for your family. I'm so glad you link up with Montessori Monday. I featured your post at the Living Montessori Now Facebook page: http://www.facebook.com/LivingMontessoriNow

  8. This may be off topic since (I think) I'm talking about a different version of the snake game. But, I searched your blog for "snake game" and couldn't find anywhere you mention the Snake Game: Search for Ten that is in the Montessori R&D manual. I know you said you used the MBH manual and supplemented with the R&D one. (I'm considering getting the R&D manual because it seems like the MBH one is missing a few things.) Anyways, did you do this snake game? And did you present in the order of the R&D TOC? So that would be Short Bead Stair, Snake Game: Search for Ten, Teen Board Quantity then Symbol. MBH doesn't break things up this much, so it seems like I'm skipping steps.

    1. Ok, now I almost want to delete my comment and read some more. You mentioned above that "in the Gettman book you would find that the child reaches the "snake game search for 10" in linear counting just before beginning the memorization sequence so that it IS the beginning of the memorization sequence. " But Montessori R&D has it at the beginning of linear counting. So, I'm definitely missing something (I probably just need to buy that album or leave it alone!)

    2. Something to note when looking at the table of contents of albums such as the MBH albums and others - the table of contents doesn't always include/note "everything" - so many times, there are follow-ups and extensions including within an album page rather than being separately listed out in the TOC. I suppose more album providers could note these things as sub-headings in the table of contents, but 1) the tables of contents would get LONG, FAST and 2) more people would use the tables of contents to put their own program together and entirely miss out on the nuances of when/how/why/even-IF to do those extensions/follow-ups - to cover those sorts of needs, it would become a scope and sequence and should be called thus ;)
      Also, just because something is listed in a particular place doesn't mean it "stops" being worked on before moving on to the next thing - so many times we move on to the next thing and the previous thing still has 1-3 years of extensions on it to return back to it while still moving forward.

      Thus only the album pages themselves are of the most help :)

      I *think* (it's been a long time since I looked) that MBH includes everything *necessary* (or pretty close) -- while R&D includes a lot of extras (not all things they include are necessary but they're not always clear on what...)

    3. Mel,

      On top of the page on the R&D album that has "the search for ten" at the beginning of linear counting I have written really big and in all caps "WHY IS THIS HERE?" because I couldn't for the life of me think of a good reason why it was there. So, I wouldn't go buying another album for it. Something Jessica wrote elsewhere gives me a suspicion as to why it is there. She wrote something lately in a forum comment about Montessori classrooms doing "similar" work on "many" materials jus because of the many students/one of each material ratio. So, a child who needs to practice finding ten would normally do this with the golden beads, but can't necessarily use the golden beads all day. Doing it with the snake maybe is just an extra way to practice it when things are crowded.

      I feel like the only thing that is truly missing from the MBH albums for math is work with equation formats...one parenthesis, multiple parenthesis, binomials, 6=2+4 vs. 2+4=6 vs. (1+1)+4=6 and so on.

      However, I noticed as I work further with the AMI elementary math album that the whole section on the communitative and distributive properties can or do cover this.

      I like having the R&D albums but for odd reasons. One is that it helps me "self-train." Reading two different approaches to the same material helps me "own it' more. Two is that I am strongly in favor of the AMI approach except I don't always like the "let the child make up his own equations and make sure he covers any variants while he's at it." R&D lists the variants and lists the types of equations they should be doing so that I can make them and let them draw them out of a drawer or basket so I know everything gets covered without having to be terribly observant. OCCASIONALLY, such as in the case of the snake games, I find something novel and valuable in the AMS approach that I didn't pick up on in the AMI approach so I ADD it to my mostly AMI approach. So, it is important to know that I'm not using both albums because I feel the AMI albums are inadequate in any way.

      Getting used to having both sets of albums at your disposal is inexpensive in primary but EXPENSIVE in elementary as AMS has six or seven albums you have to buy for $20-$40 each.

    4. Thank you both for your great responses! I feel a lot better, I thought I was missing something or just not understanding! I plan on sticking with MBH and Gettman from now on :) I do like the idea of having some extra activities, just because Link gets to where he doesn't like to repeat things. However, those extra activities tend to overwhelm me if I feel like I have to do them.

  9. Thanks so much for making this great video! That is super helpful. My oldest son will be thrilled :)