Montessori Elementary Homeschool Blog - with documentation of our infant Montessori, toddler Montessori, and primary Montessori experiences; as well as preparation for the upcoming adolescent Montessori homeschool years.

Saturday, March 1, 2014

REVIEW POST: Primary Grade Challenge Math - Zaccaro

(UPDATE 10/28/14: We have added Upper Elementary Challenge Math to our repertoire and couldn't be happier :) See the associated Montessori Trail post.)

Legoboy has another New Love:

Challenge Math by Zaccaro

We are starting with this one - covering grades 1-4 for "gifted children".

I ended up purchasing the entire of books in this series for several reasons:
  1. looking for a good set of word problems to review earlier concepts
  2. Montessori math and geometry do not align with any other available curriculum (I group the Montessori-inspired curricula options somewhere in the middle)
  3. Something just didn't sit right with me concerning the other options. They are useful; I will not say don't use them (especially if they are working great for you! Keep going with what works!) - but there was a mis-match for our family, my principles and my understanding of Montessori. 
  4. This set of books (there are several in the series) are designed for gifted children - children of younger ages who have particular gifts that correspond with typically older children. 
  5. I wanted to review them for the sake of other families looking for a resource to fill a similar need. 
  6. This series also includes some of those allegedly missing concepts, perfectly tying them into the included album pages (associating money with decimal fractions, converting into percents, etc. (NOTE: Please do not flame me in comments regarding missing concepts - I've covered this topic before, I am not saying Montessori is wrong, and I'm not saying the concepts aren't there - I am fully trained, I know where the concepts are and where they fit in. Comments of a flaming nature will be removed. I'm done with flaming when I speak peacefully. Thank you for speaking respectfully.)

Word Problems: 
     A few people have shared a few solutions to the dearth of word problems - and the lack of time to create their own (and my lack of time to create my own!) for each and every concept. Especially in a sporadic co-op/tutoring, mostly homeschooled by himself situation, there just aren't classmates around to pull up the caliber - and I am one person unable to cover everything (stop laughing!). ;) 

Montessori Mathematics and Geometry Studies: 
     Montessori math and geometry use hands-on materials to bring the children to the point of abstraction. In some areas, it seems that the children hold on to the materials longer than their public school counterparts, but once they release the materials, they are almost always ahead in conceptual understanding. Where we have children not able to apply the concepts, we have a situation where the adult likely didn't assure the child was working with appropriately challenging work and likely didn't ensure there were appropriate real life word problems and experiences available. 

Not sitting right: 
     What is about the other options that didn't sit right? I think because they are geared towards public school curriculum, several of the options have already been re-written to correspond to Common Core (the dumbing down of our country's children), and I just don't want to participate. 

     In addition, I really wanted something that more closely resembled Montessori. Life of Fred is a great complement to Montessori elementary mathematics but there are few word problems. 
     I think this is my main thing - I don't want to dig into 4th grade books to find word problems to give to a 1st grader, just to find math skills that fit.  

Young Age - Older Work: 
     Isn't that the mis-match of Montessori to other expectations again? 

Perhaps my reason are the same thing over and over - with different words: I wanted something that better corresponds what we are doing as compared to constantly tweaking, reading, adjusting, pulling "7th grade" materials for a 2nd grader who isn't "special" in that way, but simply has been given the tools to go deep with his understanding.... I was (and am!) tired of tweaking already!!!!

What we are using: 
     Legoboy is 1st year upper elementary, or 4th year elementary - and I would NOT say he is gifted in this way. However, he has received the keys provided through Montessori throughout his life. As a "4th grader", we started with the primary level book to review past concepts - kind of catch up in the word problem category. We did great for 1st-3rd grade, but I'm done tweaking (have I said that yet!?) and I have to be done looking too. 

Legoboy loves it! He is actually working out the math in his head or on paper as needed, then he challenges me with it. Even with Life of Fred, I have to "encourage" him to record any work, or answer out loud. He just wants to read the story (although he can do the math in the books). 

How it is set up: 

Each chapter contains some background/how-to-solve information on a particular topic - most is review for Legoboy, some is new or said in a new way. Then there are 4 pages of problems - 1-2 page(s) for each "level". The chapters can be done in any order, but easier concepts are towards the beginning. Chapters can cover a variety of topics but are generally somewhat grouped together.

The four core books we will be using are the following: 
  1. Primary Challenge Math - grades 1-4: Includes chapters on Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. This book includes topics that Montessori has in upper elementary. Guess what? That tells me it is likely to trust a child's abilities and correspond well. I am NOT disappointed. 
  2. Upper Elementary Challenge Math - grades 3-5 (this is available for pre-order, shipping in April)
  3. Challenge Math - grades 4-9: Includes chapters on Astronomy, Algebra, Problem Solving, Percents, Fractions, Decimals, Ratio & Proportions, Physics, Statistics, Probability, Metric System, Perimeters, Area, Volumes, Trigonometry, Calculus
  4. Real World Algebra - grades 4-9: Includes chapters on Language of Algebra, Geometry and Algebra, Proportions and Algebra, Physics, Levers, Pythagorean Theorem, Percents and Algebra, Simultaneous Equations, Algebra and Money
We also have the following that at first skim have been great: 
  • Becoming a Problem Solving Genius: A Handbook of Math Strategies
  • 10 Things All Future Mathematicians and Scientists Must Know (but are rarely taught)
  • 25 Real Life Math Investigations That Will Astound Teachers and Students
  • Scammed by Statistics: How we are lied to, cheated and manipulated by statistics and why you should care

I am working on something of a correlation between the AMI mathematics album and these books - slowly creating a correlation. I will share this on the Keys of the Universe Discussion Community in Excel format and will likely post it on this blog at some point in pdf format (this will happen faster if those who are interested, let me know - I'll prioritize it ;) ). 

Sample - Chapter 4 - On Money



  1. Thank you so much for this review.

    I think that this is something that T would be very interested in too. I know that your guy is older than T and a bit further along in the movement toward abstraction. T is still working on this, and I know that some of the pages you posted (thank you for those, they are so very helpful) he could do with ease and others he'd need some practice with. Do you think that we could use these as just that, practice to really achieve abstraction? Or should we wait a little bit until he has done more abstract problems after manipulatives first?

    Also, I can totally see me re-writing some of these problems if he needed more "practice." (I haven't done all the tweaking you've done.) We also have a testing requirement here, so I think that this work could really improve his confidence in that area.

    Reading your message boards and blog posts is fast becoming a not-so-inexpensive hobby! :)

  2. What I am about to write isn't entirely "true" but for the sake of using familiar terms - this is how I personally decided to organize this Primary Challenge Math in my own head:
    Level 1 is 1st grade
    Level 2 is 2nd grade
    Level 3 is 3rd grade
    Einstein is 4th grade

    Not a perfect correlation - still follow the child - at least allows me to focus in on where Legoboy might be in the progression. And I've not fine-tune correlated the topics with the Montessori album either, so there's another caveat. (the in-progress document is posted on KotU message boards for those who are interested).

    So if I were start this book with Legoboy when he was 6, we would go through the pertinent to our Montessori studies chapters and only "expect" level 1 word problems to be worked on. The next year, we'd go through those chapters again doing level 2 (or if he was totally ready the year before he could move ahead), and add in any new chapters based on our Montessori studies, start with level 1 and proceed forward until stuck.

    Since he is starting this book in his 4th year of elementary, we're just going through chapter by chapter and going as far as he can handle; then moving to the next chapter. We'll cycle back through before going to the next book.

    So $25 for 4 years of word problems - most of which are easily re-writable to keep the same format and different numbers - and you have other children behind T - not just TOO bad ;)

    Definitely helps with testing! I think T could probably do level 1 of most of these chapters and probably some level 2 as well. Just guessing based on what you've shared on your blog of course :)

  3. I can't figure out why your posts don't show up on bloglovin for me, grrrrr! Glad I remember to check back every now and then. We have this book and my older one who is now 7 (would be in 1st grade PS) enjoys this book very much. At present, she can easily go through the Level 1 problems. Level 2 is a hit or miss depending on the topic and whether we have already covered the concepts in Montessori or elsewhere.

    Have you taken a look at Beast Academy? That is another love here. Though the books start right now only from 3rd grade, my daughter is able to work through them and enjoy it. This could probably because of the advanced geometry in Montessori.

    1. Thank you for sharing your experience with the Zaccaro books - I hope that more people will share so that we can all have a better idea what to expect with children using Montessori :)

      I have not yet looked at Beast Academy, though I'd like to. Between Life of Fred, Zaccaro, Montessori math and geometry, Key To Mathematics and geometry workbooks, and living math books (my son LOVES to read), I'm not sure where we'll have time --- perhaps a lull from other schoolwork ;) I just recently shared a file correlating all of the above on the Keys of the Universe discussion community as well.

  4. How did you organize this material for your son? Did you just give him the book? Or did you photo copy/laminate/file/mount on poster board each problem? Wondering how to "present" these to T. (Finally got the set...though am sad that the Upper El book doesn't come in the set.) He is already flipping through to see all the illustrations... Thanks. We are almost unpacked and ready to start.

    1. Abbie,

      Did you already order the Upper El book? If NOT, contact Ed via the contact form on the website and tell him you would like to order that book with the set - or that you have the set and would like to add that book. He MIGHT give you a discount. I got an after-the-fact discount because I ordered the set before the Upper El book was ready. And he does recommend going through the Upper El book before starting on the middle school level.

      Legoboy just went through them - we read through a chapter intro together, then do the level 1 problems together, on our own paper. Move forward until we get stuck. Then move to the next chapter. The idea being to loop back around in later years with the challenging levels. He did finish the first book relatively quickly with few bumps. He is now ready for the Upper El book, which we will start soon.

      For future children or in a class or if I have more of my own children - I would consider copying the problems onto cardstock and trimming them (saving time cutting, mounting, etc) - and unbinding the book to have the intro sections for each chapter in a binder, with a pouch/folder behind each intro with the problems. Pull each one out as we are working with it.

    2. Thanks so much for the advice, I think at this point, that I am going to keep the book intact and not do all that photocopying. I am going to try to "highlight" the pages T should do (like the example and level One problem pages) with a "removable highlighter" tape, and then use a bookmark so that he can keep his place in the book. It will probably be another half a year or so until S gets to this, so then I'll change the highlighter color for her and use another bookmark to keep her place in the book. Then for little D, well, no one else will be using the book when he needs it. :)

      I will try that to get the Upper El book. Thanks for the tip that this one is useful before the Middle school book. So far, I really like the layout and the problems. A worth-it-purchase for sure. Thanks.

      Oh and I think (though I can't for sure remember) that the Scammed by Statistics book that comes with the set, well my grad-school stats prof. assigned us that book!! Certainly a humorous read if you like that kind of thing.

  5. Update to this post: We now have Upper Elementary Challenge Math - see this post for more details:

    Short answer: LOVE IT.