Thursday, October 1, 2015

Test Prep Math Level 3

August 2017 Update - This article is now a bit dated, but I am reluctant to delete it. Test Prep Math Level 2 and Test Prep Math Level 3 are big hits. Both are now in their 3rd edition, and both have the addition of a quantitative section and a visual spatial section that followed the same successful formula as the word problems.  I had all of this material but thought then and now that the word problems would pay off the most down the road, so this is where I started.

Test Prep Math Level 3  is making it's debut.



I created this book because after buying and trying dozens of workbooks from 1st through 5th grade, I've been really disappointed.  There are 3 primary groups of math workbooks: one group is too easy, one group overdoes computation and calculations with no learning or thinking involved, and the third group goes into advanced math.  My kids don't care about number theory at a young age.  The GAT practice test books are great for their role - to review the format and find out before the test if your child is going to get confused and blow it - but these books aren't good at teaching skills and are really easy in my opinion.   By age five, my second child completed all of the GAT test prep books through 6th grade and I don't think we learned anything.  I didn't even use them with my first child and just stuck with more difficult material that I created.

I spent 5 years researching GAT tests, 2 of it trying to reverse engineer them.  You'll see in my articles that I slowly built a list of skills and abilities that these tests were trying to measure, and then focused on teach them.   The problems in Test Prep Math are designed to teach these skills.

I'm getting questions about whether or not younger kids could use Level 3.  Since the "View Inside" isn't available yet for the book, I'm going to show you sample problems and describe how they unfold, and then comment about Level 2.

I expect the child to do the arithmetic in their brain, even though that might take a few tries to get it correct. There is a 5 page coaching guide about how to get through this book, and in the solutions I include commentary on harder or unusual questions.

Here is the first problem.  I tried to make it as easy as possible simply to introduce the thinking that is going to be required and encourage the child to do the problem mentally.  This seems easy enough, but I'm surprised how many bright kids get to the end of the question and forget what was asked.

Dragonflies and damselflies were sitting on a boat.  There were 5 dragonflies and 4 damselflies.  4 more dragonflies landed on the boat.   8 more damselflies landed on the boat.   How many more damselflies are on this boat than dragonflies?

Bonus Question:  A flock of birds comes by and ate half of the damselflies.  How does this change your answer?

Notice that the child has to solve 3 equations.  The pattern of matrices problems is 1 and 1/2 equations (solve one equation and apply the delta to another number), so I doubled it to be on the safe side. There is a new word in the problem that you'll have to google.  Then for this question, there is a bonus question that requires tapping the working memory once again.

Question 2 has the wrong answer!  Arrgh.  I'll have another edition out to fix it in 2 weeks.  I undermined myself with a last minute edit to the question.  Fortunately, all of the solutions show the equations so mistakes are easy to spot.    Ironically, since I've been making my own material, my kids and I have had lots of questions and/or solutions that didn't work   They have a whole different approach to math, but I wouldn't intentionally put this in a book.

During the next 40 or so questions, the characters are introduced and the plot slowly unfolds (as much of a plot as I could muster given that I'm working with as much space as a haiku).  At about the middle of the book, the questions look like this:

In the center of Metroville, there is a super villain named Destructovil breaking into the Metroville bank.   Rubberband girl got a distress call on her cell phone, but she is on the south end of the city in a train station. There is a train leaving at 3:00 pm that will take her to the Metroville bank.  The train takes 12 minutes to go from the train station to the bank.  She has to wait 4 minutes for the train.  Speedy Man is in the next town over, but he can get to the bank in 8 minutes because he is Speedy Man.  First, he needs to finish his cup of lemonade because he's too thirsty to be speedy.  That will take 7 minutes.  It is a very large cup of lemonade.  Destructovil's getaway car is coming to pick him up at exactly 3:14 pm.  Who will save the bank?

Bonus Question:  Who is Rubberband girl?

My 10 year old told me "your problems aren't lame."  I think that was a compliment.

If you had been doing all of the problems, you would be able to figure out who Rubberband girl is.  If not, you have to refer back to a previous problem (officially an academic skill which I call for repeatedly) to figure out.  Note that this is not a question a child can read once or twice and then solve.  I also use time a lot because it requires an extra degree of thinking to do the arithmetic.

By the end of the book the questions fill the page and become even more convoluted and goofy (all with proper grammar except when the pirate character talks.)  At this point, we're basically in math-reading-comprehension space, which I invented.  I'll write a whole article on reading comprehension because I'm becoming more and more convinced that it is a pillar of success on a GAT test, and by way of the GAT objectives, to a strong academic career.  As the book progresses, I start to move on to more advanced skills and because of that, some of the questions look like brain teasers, but they aren't, because everything can be derived logically after a few days of debate.

I'm working on Level 2 for younger kids which removes the need to read questions over and over again to understand what the problem is.  I'm using a math abstraction that I invented to make things really taxing on the brain.  I think some kids will find Level 2 harder than Level 3 and vica versa, but in both cases I'm seeing results and am pleased.  Level 2 will take a few months to finish.  By next year, I'm going to introduce Level 1 which I can only describe as diabolical.  Level 1 was in the works since the beginning, but 3rd grade is the biggest gap for people right now so I started there.  Then if I'm not completely exhausted, I'm going to work on Level 4 which teaches the Most Powerful Math Skill ever, which I can't find anywhere in any elementary aged book, but which we routinely use to solve anything.

So if this sounds like something that fills a need in your At Home Schooling or test prep, give it a try and let me know how it goes.  Provided I don't sell more than 12 copies (which is going to be the case unless I find the time to do any marketing), I'll respond quickly.

21 comments:

  1. Ok got the Level 3 book in the mail today. Here is my first report back. My just-started first grade son tried the first problem. After looking up pictures of damselflies he was able to get the first problem right in 1 try after about 15 minutes. He hasn't gotten the bonus question right yet. He did figure out what half of twelve was but just thought that was the answer. My just-entered-fourth grader got the first problem and bonus questions both right after about 7 minutes. She got the second question wrong 4 times. But...is your solution in the back wrong for question 2? I am not sure why you only added 6 men to the second float. It should be 6+10 for the second float, right? Then 16-10=6.

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    1. Arggg! Undone by a last minute change. I forgot why I changed the question 2, but the solution didn't change. Fortunately, my publisher has a 3 day turn around time on new editions, and I decided to write out all of the equations in the solution so it should be easy to spot if I did that again, despite doing the whole book 10 times.

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  2. My just-entered-4th grader did the third problem tonight. I told her it was wrong and she tried again and got it right on the second try.

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    1. The skill set in this book is really age-agnostic. 2nd graders who are advanced readers will learn the skills, and 4th graders may have forgotten this skills set over the last few years of school. You should email me at norwood.chicago. The "at" is the most popular email site and search engine. Hopefully you can get past this brain teaser. Then I can provide more feedback specific to your kids.

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  3. Wondering if I can get your recommendations on cognitive skill workbooks. Finishing building skills (not verbal sections because those are too hard for my kids), and running out of materials. Any other workbooks we can try? We have a year to their tests and stocking up workbooks is challenging. Thanks!!

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    1. The only material I'm aware of are puzzles, drawing classes, and reading comprehension books. The only other book that sets out to teach cognitive skills is Level 3. That's why I made it. If your kid was a really strong reader, like hours a day, he/she would pick up these skills as well. Frequent adult level conversations also work.

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  4. Is there another edition of Level 3 book that is coming out with any changes then? Or if I order your book through Amazon, I will get the newest edition?

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    1. It is my understanding that the new edition will take 3 days to be made available once I submit it. So I expect it to be there in about 17 days. The changes are minor. I will list them here as well. Then l will open a marketing channel.

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  6. Small update / fix. We were doing a few of the problems last night and one (question 8 maybe) asked which person had "less" of something. Proper grammar would be fewer. When you can count discrete objects the right word is fewer. With it is not discrete, like a glass of milk, it is less ("which glass of milk has less milk in it?"). The grocery store checkout lanes that say "10 or less" are incorrect and drives me nuts.

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  7. Today we did two problems from your book (my fourth grader). They were in the teens (maybe 13 and 14?). One of them had trees with pink and white flowers. She was able to get that correct on the second try by herself. She was sloppy and mixed up the starting numbers in her first try. The second one had boys that brought cards to school. It caused a full blown cry. I can't tell exactly how many times she had to read it to get it correct because in the end I had to coax a lot. She didn't have a first answer she had a big question mark drawn on the page.

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    1. I once knew a little 1st grade girl who was excellent at math. So I assigned her a word problem book, and she was so mad at me. Finally, after about 4 months, her dad brought the book back to me complete. "What's this?" I asked. She asked him to show me that she did every problem because she was so proud that she met the challenge I gave her.

      Only do one page per day because the kids get emotionally engaged in the problem and 2 doesn't work. Plus, what they learn solidifies when they sleep, and the second problem undoes the first. Also, there's a rhythm that they will pick up that needs time because a new brain lobe is forming.

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    2. It's so much worse in this house. We just chug along and eventually the crying stops, then the yelling, then the arguing, and finally we go through 5 tries and no one cares.

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  8. In question number 15 you have 4 motorcycles. In the solution you used 3.

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    1. That's what i get for using a 7 year old editor. I'm taking off next week to work on the 2nd grade book. I came up with a question type that while doable will make the GAT test look like a coloring book.

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  9. Can't way for your second grade book! I need more material for my just-entered-first graders. I have two Guinea pigs that can give you feedback.

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  10. Wondering how you would compare your book to singapore challening word problems. I am getting both books soon and do they have similar types of word problems?

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    1. It depends on which grade you are working with and which publisher. The real Singapore for 3rd grade covers math concepts comprehensively. I cover thinking skills with much easier math but much harder questions to answer. Since my child already has a math class, if he does extra work, then I want it to be something not being taught in school. Otherwise, he'll just end up bored with math and that's a much harder problem that I don't want to deal with again. The result so far is that school math has become much easier and I don't have to explain or teach anything. That is my objective.

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  11. As I have been reading the blog I have noticed references to other projects you have been working on (a level 1 math book!!!) are these projects still in the works or have you moved on to bigger and better things?

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    1. Thanks for asking. I've been finishing The Gifted And Talented Phonics book for parents who don't have gifted and talented 3 or 4 year old kids and have to catch up. When this is complete, I'm going to solve the violence and poverty problem among the African American community in Chicago. I'm on the fence with the 1st grade math book, but will eventually complete it. Also, I'm constantly distracted by the Prime Number theorem and solving the Riemann conjecture. Plus, I have to work and raise 2 kids.

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    2. Oh is that all?! Lol - I can't seem to get my hair washed on a good day. Well I will keep a look out for the phonics book and the math book for my littles -- I'm not great at math, but let me know if there is anything I can do to help :)

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