Tuesday, June 16, 2015

The Right Math Workbook for the COGAT

So far we covered the sentence completion question from the Verbal Section, quantitative matrices and number puzzles from the Math Section, and figure matrices from the Non Verbal section.    That leaves 5 question types.

The COGAT was designed to predict academic performance, and it does this by measuring academic skills or study skills.   Test Prep is quite involved because there are a lot of skills to master.

Many of these skills can be found in real math, and therefore I use math as a shortcut.  I find many of the remaining skills in the Vocabulary Workshop series.

Last Saturday, I went to my favorite bookstore in Lincolnwood to review every math workbook ever written to see if any of these would be suitable for use with cognitive skills test preparation like the COGAT, OLSAT, or even Weschler.  I was very disappointed.  Almost all of these math workbooks have almost no thinking involved.

On bright spot was FlashKids for 4th grade.   There weren't a lot of word problems in this workbook, but the ones that were in their were suitably convoluted and multi-step.

I was really disappointed with the 5th and 6th grade versions of all books, including Brain Quest and FlashKids, both which let me down.

Singapore Math has a series called Challenging Word Problems and Intensive Practice.  I haven't tried either.  I have high hopes.

I have high expectations for the new Eureka series, and will bum a copy off of a teaching friend once school starts.  It's not available yet.

There is a text book/workbook combination called "Hard Math" by Glenn Elison.  The elementary version is not hard, but the Middle School version for IMLEM competition looks promising, but only for 5th grade and up.  The IMLEM questions, on the other hand, are fantastic.   Now all I need is a math competition for 2nd and 3rd graders that publishes its questions and we're set.  Maybe I can dumb down the questions from the IMLEM for my own use.

Here's my Test Prep Math Work Book Honor Roll.  You may be on a different schedule, meaning that you might need 6 months to get your child caught up.  This list is for a child that is already caught up.  Note that I work ahead to force thinking, learning, and going slow.

PreK:  Sylvan Kindergarten Math, to be completed by preschool using my vocab list I put in the figure matrix question review.
Kindergarten:   Spectrum 1st grade math.  This isn't going to help with test prep but there's a lot of time to fill between age 3 and age 6.  At this point, we did very little math and mostly Building Thinking skills workbooks.  We also did the 2 Every Day math work books for second grade somewhere in here, which I used for our "6 months of catching up".
1st Grade:  Spectrum Math Word Problems for 3rd grade.  "Dad, how do I divide?"   With lots of thought my friend.  With lots of thought.
2nd Grade:  I'm going to use Flash Kids 4th grade math
3rd Grade:  No clue yet. I'm leaning toward experimenting with the Singapore math books.
4th Grade:  I can't find anything suitable for a general audience.  We're using the High School SAT test prep book.  How pathetic is that?  We also do about 1 page of the Mathletes book every week, which is hard even for me.   If anyone is brave enough to try Mathletes, feel free to ask questions of how to get your child through a problem without peaking at the solutions.  Parents need training too. My son now official prefers brain teasers to math workbooks.  (Note:  tonight there was a problem in the SAT book that neither of us good get correct after numerous attempts so we gave up.  I think that experience was worth 2 years of math in school.   Nonetheless, I'm going to print the IMLEM released tests like this one  and do those for a while.)

As I walk through the good material, I'm seeing patterns in the questions which make up the trickiness of the COGAT. 
  1. Problems that have 2 different answers, with preceding problems leading the child to the obvious answer that is not in the answer set.
  2. Little tidbits thrown in the question which are easy to miss but required for the solution.
  3. Some overly complicated problem that requires 2 steps to solve or starting with an easier problem and working the way up in complexity.
  4. Answers that require a subset of an equation to solve, not the whole equation.
  5. Questions where the only way to solve the problem is to check every answer.
  6. Problems that are intentionally misleading, letting sloppy or quick students to jump to an incorrect answer.
  7. Solutions with order of magnitude issues that require taking a step back with common sense to ensure the correct answer.
  8. Problems that say something that is the opposite of what is really meant.  These are hard to create but I see them.  More common are problems with dual meanings.
  9. Problems that you are guaranteed to get a wrong answer to, followed by a problem that seems hard but isn't in order to test grit.
  10. Problems where you don't know the answer, but with a little thought you can rule out all of the other ones.   I was given an example from the OLSAT by a 4 year old.
  11. Problems guaranteed to make you assume the wrong thing, and problems that assume something you have to figure out for yourself.
Does anyone have a contact at a publisher?  I'll start writing my own math book.


  1. I think you need to save up all your posts and put them in the form of a book, someday, when you have time on hand (or are reaping the success of your efforts!!).

    Just wondering and could do with your inputs. Do you rely entirely on Vocab Connections or make your material too. Is vocabulary actually that extensive an effort for COGAT or am I just overdoing it. With boys it is hard to get enriched vocabulary in everyday conversation, so I am having to effectively put it together in the form of tests (sentence completion, analogies and find the odd one out). However I am just so spent. Besides, it is not just plain vocabulary, but has grammar, sentence structure, homophone, homonym etc. tricks too. Just wondering.

  2. To clarify, I keep a wall chart with lots and lots of books on it that I get at the library for them to read or for me to read to them. See my next post.

  3. Norwood, just to clarify, we are using Vocabulary Workshop and not Vocabulary Connections. I just read your most recent post and would like to clarify that we are doing Vocab Workshop - Purple and Orange. I hope it was not my post here that may have triggered your plans to pick up Vocab Connections 2nd grade for this summer. The reason we do both Purple and Orange is because we already had covered a lot of the vocabulary separately though home-made program which I have addressed above).

  4. I think you will like the Singapore Math Challenging Word Problems book. I'm a Chinese mom after-schooling my 1st grader in 3rd grade math, using Singapore Math Level 2. The word problems book has 1 unit with 2 sections of questions each, that correlate to each Singapore Math unit. Each section has 10 questions. The first section in each unit is standard run of the mill word problems. The second section in each unit is the one you want. It has questions meant to trick you, with 2 or more steps required, extra unneeded info in the question, or really requires drawing a picture or visualizing the problem in order to get an answer. Followed by an easy question that looks hard. Then at the end of the book there's a few more sections of extra hard word problems. You will probably want to do just the challenging sections and the end sections.

    As far as I can tell, Intensive practice is just more of what they have in the regular Singapore Workbook. Same material, more hours. I did not get it. It's not what you are looking for.

    I wanted to ask if you've ever used Dreambox on the computer for math. I don't know what it's like past the end of second grade, but up to that point, it is very good at instilling a solid number sense, and making you manipulate numbers in your head in a complex way. As long as you are working 2 grade levels up, of course.

    1. I can't find anything called 'Singapore Math Challenging Word Problems'. We tried 'Singapore Math Must Know Word Problems' for grade 3 (for a first grader) and it was 1/5th the level of complexity that I desired. Do you have an ISBN number?

      We never use computers for math. The computer is a bad habit in this house. I spent many months training my kids to just do their work with old fashioned pen and paper without complaining and spent 4 years looking for suitable material..

  5. The "Must Know Word Problems" is an American knock-off workbook. The correct books are actually called "Primary Mathematics Challenging Word Problems". Here is a link to the Level 3 book on Amazon: http://www.amazon.com/Challenging-Word-Problems-Primary-Mathematics/dp/B00E4UNSBU/ref=sr_1_2?ie=UTF8&qid=1442513293&sr=8-2&keywords=singapore+math+challenging+word+problems

    You can also get them straight from the Singapore Math website http://www.singaporemath.com/Challenging_Word_Problems_s/284.htm

    ISBN: 9789810189730

    Singapore Math is generally one grade level ahead of US Math, so SM Level 2 will correlate loosely with US Grade 3. But in order to make sure you are getting the right level, go to the following page and look at the placement tests, and figure out which level your son needs before getting the workbook.


    I just read some more reviews, and apparently the Intensive Practice workbook also has some challenging and novel problems at the end of each unit. So maybe I shouldn't completely write it off. If you end up getting them both I'd love to read your opinion on it.

    Love your blog, by the way. Most of the posts make me want to stand up and cheer.

    1. I just ordered it. It would be great if someone out there bought and tried every workbook, but since I can't find this person, it's me.