Math Skills and Logical Thinking

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Coming from Europe and having heard from my students (I taught high school) who spent a year in an American school how easy the math here is, I was terrified that if my kids ever go back to the Czech Republic, they would be awfully behind in this subject. It may or may not be true; in my opinion, the school systems and approaches are just different.

Fortunately, our district adopted the Singapore math approach which is supposed to be one of the best so I calmed down a little when my kids started school. However, my husband and I find that even though our kids make occasional silly mistakes, they do fine in school and they could tackle more challenging problems. We agree with the statement that “Mathematics is the core of every academic discipline and in essence the art of thought.”

Our daughter is now in 3rd grade and I know that her knowledge is limited. When faced with a more challenging problem she has difficulties figuring it out on her own. If she takes after me, she is not going to be a mathematician but she should be challenged with more complicated and tricky problems. She has occasionally brought some home from school as homework but we felt that she would be better off in the long run if she teased her brain on a regular basis. Although our son is only in 1st grade and still learning the basics, we would like to do extra stuff with him too very soon.

To make a long story short, I went online, did a research, read reviews, bought some books and here is the result (Note that I ordered some of these books last year but some only a few weeks ago so I haven’t done all of them with my kids). Read the reviews and make your own choices. This information is gleaned from different websites and recommendations.

Let’s start with books that can be used with all ages, not just school children. Each problem has a question for 3 levels (wee ones, little kids, big kids). These problems are fun, they are not a boring worksheet. Read the article about this series here (a new title will be released next year!).

bedtime mathBedtime Math: A Fun Excuse to Stay Up Late
My son hates to do math at home. If he hears the word “math activity”, he almost throws a fit. However, it was he who was asking me to keep reading another and another problem the other night because they were fun he said. Not only did he have to think a bit but he also learned some interesting facts, such as what makes vegetables heavier (water). The pictures and choice of words are very appealing to kids, which makes them want to do more. What a clever idea!
bedtime math this time its personalBedtime Math: This Time It’s Personal
You can also find a lot of ingenious ideas on their website.
math dice jrWhile we are on the subject of math fun, let me throw a game in here. Math Dice Jr. is a fun way to practice math facts and it is definitely worth having at home. When your kids outgrow it, buy the original set Math Dice.

Building Thinking Skills

I have looked for the best books to develop critical thinking skills and the following series is probably the best out there. It has great reviews everywhere. If there is only one book you could buy, this would be it.

We have Level 1 and Level 2 at home. I have not seen Level 3 but it is supposed to be for higher grades. My friend also bought the pre-K Level with the manipulative blocks (that are needed for this level) and is happy with the set. On the company’s website  you can look inside each book, or you can read reviews of the books on Amazon. You can also get a discount on bundles and 10% off if you sign up for their newsletter I think.

building thinking skills 1Building Thinking Skills® Level 1
My daughter did some pages from #1 last spring (2nd grade) and I did about 56 pages with my son (now in 1st grade). The first 35 pages were easy for him  but I didn’t want to skip them because the practice is needed for more difficult tasks later. I will give you an update when we progress more.
building thinking skills 2Building Thinking Skills® Level 2
We haven’t done anything from #2 yet; I think we will have more time in winter. I’ll come back and give you an update.
visual discriminationVisual Discrimination
This one was pretty easy for my daughter although it became more difficult toward the end (last 7 pages, she is in 3rd grade, 8 ½ years old if this helps you). It was a good practice for my son (he is 6 ½), who makes frequent mistakes because he does not pay close attention and picks the answer that looks right to him without thinking about it. When we ask him to think carefully, he usually chooses the correct answer but the end of the book was definitely hard for him. If it was a test in school, he would make a lot of mistakes because he would not have the feedback from us (he knows that his answer is not correct if I don’t move on to the next task immediately). I think he is at the right age for this book. I would definitely recommend it to my friends, especially if they had a 1st or 2nd grader at home.
challenging word problems 1Challenging Word Problems for Primary Mathematics, Level 1
I ordered this level for my son because I love level 3 for my daughter. Some of the problems are just normal difficulty (similar problems that are done in school) but some are challenging for him but at the right level. I like the book a lot.
challenging word problems 2Challenging Word Problems for Primary Mathematics (2)
We only used some parts of this book (the end) for my daughter (now at the beginning of 3rd grade). I ordered it mainly for my son who is in 1st grade when he gets to this level (probably in 2nd grade).
challenging word problems 3Challenging Word Problems for Primary Mathematics 3
My daughter is in 3rd grade and I couldn’t find this title on Amazon (I was able to find the first two but not #3) so I ordered it from a different website. So far I am very happy with this book because the problems pose a challenge for her but are not overwhelmingly difficult–i.e. she can solve the problems but needs help. I am glad I ordered it and I would highly recommend it to anyone looking for more challenging word problems. Update: as we don’t always have time to sit down with our daughter to guide her through the word problems (because she gets stuck), I found some parts in #2 of this series (above) that are a good challenge she can work out on her own.
singapore math challenge 3+Singapore Math Challenge, Grades 3 – 5
It is definitely worth a buy. My daughter could not figure out the number patterns immediately, they were not easy for her. She was able to find the patterns eventually. It is good practice for her and I think she will get better as she learns different ways how to look for the patterns The book does not contain only patterns but we have not moved on to the other parts yet.
Primary grade challenge mathPrimary Grade Challenge Math
We didn’t have a chance to do anything from this book yet. It has excellent reviews and I only flipped through it. Based on what I have read online it is excellent.
Mind bendersMind Benders Book 3: Deductive Thinking Skills
There are several books in this series. I chose this one for my daughter (now in 3rd grade). So far she did only a few puzzles, some of which were easy and the other ones in the middle according to her. She had trouble figuring out a puzzle because she did not know what “show business and valet” were for example; she needed my help explaining it to her (The task was to match the names with their occupations actor, valet, and comedian. The clue said e.g. Marta is not in show business). I’ll give it a few more tries and then get the higher level if she is not challenged enough. I did two puzzles with my son who did okay but I guided him through the process. I will buy level 2 for him to work out the problems on his own. Update: The puzzles are not too easy but my daughter doesn’t seem to have any problems with most of them. I ordered Level 5, which is perfect for her. Sometimes she gets stuck because she doesn’t see the clue but can still figure it out on her own or with a tiny hint from me.Mind Benders Book 2  I have recently bought this level for my son in 1st grade. It is great for him. We have done a few puzzles and all were easy so far.
perplexorsMindWare Perplexors: Level A
This book is somewhat similar to Mind Benders but instead of minuses and pluses you cross out and circle. My daughter (8) has done only three so far and they were not hard. A nice exercise, I didn’t feel like we were wasting her time but not very challenging. The problems might get harder as we progress though so I will give you an update later. Update: The puzzles were not difficult for her so after reading reviews of the next levels I decided to buy Level C. She says they are more difficult than Level A but they are not difficult for her. She has not asked me once for help. She prefers Perplexors to Mind Benders for some reason–she just likes them better. Mind Benders Level 5 might be a bit more challenging for her I think.Mindware Perplexors Basic Level  I just ordered this level for my son in 1st grade. I will let you know how it goes.
think analogiesThink Analogies A1
There are many books on analogies out there. I don’t even know if my daughter has encountered analogies in school but I decided we would try this book that was recommended on a website. So far I am very happy with it. I don’t think it could be done better.
mental math grade 3Mental Math, Grade 3: Strategies and Process Skills to Develop Mental Calculation (Singapore Math)
This is just a regular math practice, extra practice for mental math. I just felt my daughter would benefit from it because she writes everything down on a piece of paper and I would like her to do the calculation in her head. It is a good supplemental book.
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