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  1. There is not a good review that I have found of this books, so my new hobby this season is sharing my reviews of books and curriculum that I am finding out about and am trying to be "fair" in my assessment. I want to share my bland judgement, but not my prejudice so hopefully this can go well for everyone. Please know that I am ESL, so my English is not perfect and sometimes I say wrong things because I don't have good command of English tone for communicating things. Without body lanugage sometimes it sounds "snobby" but that is not my intent. Okay, lets go. ****** Hard Math for Elementary School Background: My son has been exposed to many topics in basic maths. He understands the concepts for almost all of arithmetic skills, but he could not always solve any arithmetic problem. He would know how to do something on Monday and forget by Thursday so he is a forgetful child and he is emotional about it--he is frustrated and discouraged by not being able to remember how to do it, because he knows what he is supposed to do, but can't always make it work. To help him master the doing part of arithmetic, we got him started in a maths book called Saxon Math. He likes maths and we want him to have success. My son did 2 math contests and really liked them--one he succeed in, the other he was not happy about :(. So he wanted a new book to use and we are trying out Hard Math for Elementary School. This book is my early impressions because *I* have not finished the whole book, but have gone over the first ten chapters and done the material with my son that we have not already discussed or studied from the book. If the topic looks like this my son and I have gone over the material. If the topic looks like this then I *think* that we will use that chapter also but have not read that far yet. The Book: This book has 21 chapters and these are the topics of them 01 - Addition with Carrying 02 - Base 8 03 - Mental Math 04 - Tiling Floors 05 - Addition Puzzles 06 - Multiplication Table 07 - Prime Numbers 08 - Subtraction 09 - The Distributive Property 10 - Finding Areas 11 - Modular Arithmetic 12 - Long Multiplication 13 - Combinatorics 14 - Squaring Numbers in Your Head 15 - Regular Polyhedra 16 - Unmultiplying and the Prime Factorization Number System 17 - Fractions 18 - Probability 19 - Division 20 - Fractions Part 2 21 - Decimals Material: As you see, I have only read the first 10 chapters of the book. I plan to read the rest and share more material with my son but probably not all of it. Hard Math for Elementary School is "enrichment textbook" and also there is a workbook with sheets in it that go along to each chapter and another book which is answer key but we do NOT have workbook and answer key. We only have the textbook. We have been working from the textbook only and I have been working the material ahead of my son. We are up to chapter 10 now. This is a nice enough book, but not very good. I have highlighted the chapters I feel are most beneficial for a child who knows basic arithmetic already, but I will read it all in case there is something nice in the book that I can't see about from the topic. Presentation: You can look into the book on amazon, but it does not give you a look at the lessons you can see only the preface or instructions to parents on Amazon. In my opinion the student material is not easy to read for a student. Admittedly my son is ESL and a weakling reader so I have to read his school books and share with him the explanations, but these books are not easy for an elementary student to read at all, I think. The formatting is very close together with the instructions and explanations as lots and lots of paragraphs, just like on this web-board so it isn't easy to see step 1, step 2, step 3. A student would have to be a fluent and careful reader who is good at going back and forth in the lesson to read through the explanations of an example. So, even if my son was a good reader I do not think that he could study from this book, which is not graceful writing. The book is "boring" to study from . There are no colors and few pictures or diagrams, but in my home we do not care about that because mama is the one who reads the book, then explains the lessons to the son. Some moms may want color or better diagrams, or if your student can read the book maybe they want diagrams and pictures, but I do not care about that and because he does not study the book independent my son does not care either. My Thoughts on Teaching and Topics: Bad News: I was a little disappointed as I feel that for a child who has made it to 3rd or 4th grade, most of this is not new material and the title had promised Hard Maths lessons, but most of these lessons are not hard, but is okay. It is actually giving my son lots of confidence to think that he can do hard maths. I think that this book could be used to extend lessons to many 3rd and 4th graders and being specially bright in maths is not the prerequisite skill needed. For the chapters 1, 2, and 8. I just gave him the problems and he could do them, no wordy explanation needed. I do not like the way that US books teach number awareness. This way that I see often in US maths books makes poor sense and is often illogical to me, so I do not teach my son to do math facts like they recommend in US Maths books. To me, numbers make sense, and I teach my son the way that shows the sense of numbers. I was not liking chapters 6 and 7. In chapter 6 they talk about the multiplication table, but do not teach commutative property. They talk like 1 x 7 and 7 x 1 are different facts when they are not. Whoa no way! I do not let my kids think that 1 x 7 and 7 x 1 are seperate, I teach him so that he knows that they are the same, no comment. I feel that a book calling itself Hard Maths and meant to be used by kids who are interested in maths should be including insights and clarity that is not in the elementary texts, not allowing the same medium level explanations and certainly not teaching in a sloppy way. Chapter 7 is about prime numbers but they did not teach in a logical way and I was very sad to see their teaching of this. To teach prime number the books teach kids to count how many times a number is in the multiplication table--if a number is in the table twice (as a x b and b x a since they do not teach commutative property), then it is "prime"!!! :confused: Oh no! That is incorrect and unreliable and crazy. A number is prime if the only factors are 1 and the number itself. That is easier to teach, more logical, reliable and actually correct every time. If the book explained what a prime number was first, then it is easy and logical to see that a prime number appears once in a multiplication table. But a number is not prime because it is only on the multiplication once. And if you want to consider a bigger number, say 153, then are kids supposed to do a 14 x 14 times table??? :huh: This is silly, so I didn't teach that part of the book. My son was familiar with prime and composite numbers from our discussions and even though it is not in Math 54, when we did Math 54 and covered the multiplication table I included some talk of prime numbers again and again with him. Saxon will teach prime numbers in Math 65 also so he will have Prime numbers again. There are some parts in Chapter 7 that are okay: 7.4, 7.5 and 7.6 are useful to teach, but I would preview 7.1, 7.2, and 7.3 and teach this differently if you are not comfortable with careless teaching styles. This type of teaching is one reason why I am very glad that I am reading the material ahead of my son because I would not want him to have wrong teachings in his mind about maths--or anything, but certainly not maths. You try and make maths fit with what you learned from your textbook and so if your textbook is bad it is going to grow into bigger and bigger problems later. No thanks! A big annoyance for me in this book is made up terms for maths. Saxon does this also and it makes me a little crazy, but I see that this is an American English thing to do, and so I do not get angry as it is clearly cultural. Personally, I do not like the word "borrowing" and "carrying" in arithmetic. The translation to me is so weird to think because you are not borrowing anything, you will never give it back. You are restructuring the number--that is all. The quantity does not change, but its form does. You change the form to something simpler so that you can perform the additions and that is all. I think the term would be better as "stealing" but I do not know Americans do not just say "regroup" "rebuild" or even "rearrange". Oh well. Chapter 9 is on Distributive Property and again it had weird and ungraceful explanations. The property is the property, there is no "single sided" or "double sided" version. The property can be extended, but the general idea holds no matter how many parts you are distributing over. It was still good to walk through the property again, but we did not teach difference of squares formula. It is not important to know it before you really understand it. Good news: even though I am not very happy with the teaching of the material, the topics are okay and most important, my son is enjoying the material in this book. He likes that it is called Hard Maths and he gets confidence from doing the lessons--even if they aren't usually hard. This book has good topics that my son would not get to yet other wise. When we do extra lessons with him, it is concepts or problem solving for him, but rarely exotic topics like base-n number systems. Honestly, my son loved Base 5 in Saxon Math 54 and since Math 65 does not teach new Base 5 material, we was happy to see Base 8 lessons from this book. We have done the first 10 chapters and will start the 11th chapter soon. My sons favorite sections so far was Chapter 2 (Base 8) and section 8.6 ("Borrowing" with Base 8). My problem with Chapter 2 on Base 8 is that it uses The Simpsons as an example throughout the whole chapter. I looked up The Simpsons and this is not good TV show for a kid and I do not understand why he picked it. There are many, many, many cartoons who have 4 fingers and I feel that the the author was thoughtless of his audience to include The Simpsons. My son will never be allowed to watch The Simpsons in my house, but he can watch Mickey Mouse and Pocoyo or something else that is innocent enough for kids. There are many cartoons he can watch that have 4 fingers (even though he does not like cartoons.) When we did Base 8, we did not use Simpson examples. We used Pocoyo. UPDATE: I forgot to mention that one thing that I did not approve of in the section on Subtracting in Base 8 (page 78) is that when working in base 8, Mr. Ellison uses the digit "9" which, does not exist in base 8. In base 8 you should only access digits 0, 1, 2, 3, 4, 5, 6, and 7. Once you go higher than 7 you regroup into the the next power of 8. So from units to 8s, and from 8s to 64s and from 64s to 512s and so on. I feel that this lack of consistency is not fair to students who are learning from this book. My son was not deceived because he has done a lot of work in base-10 and base-5. We talked for a long time about why quantity xxxxx xxxxx x was "11" and not something else like say..."A" or some other symbol and all of this was made even more clear by working in base-5 End of Update Then he liked Chapter 4 which is on Tiling patterns (tessellations and geometry)--something that he likes. Chapter 9 was distributive property and even though my son he has met the distributive property many times-- papa and I teaches this before we teaches the algorithm for multiplication by 2+ digits so kids know why multiplying 8 x 36 works, and Saxon Math 54 also teaches the distributive property, and Saxon Math 65 teach it by name and now this book too. My son enjoyed doing some of the problems though so it was not a waste and we extended the distributive property to many, many places until we had: (a + b + c+ d + e + f+ g+ h + i + j + k + l + m) x (n + o+ p +q+r+s+t+u+z+w+x+y+z). My kids had a lot of fun distributing and adding up the numbers and so I do not regret doing Distributive property again. Now they should never forget it. Ever. Chapter 10 is on Areas and this is also something that my son enjoyed--it wasn't all new to him, because Saxon Math 54 taught it in a project that we did, but he likes geometry and is always ready for more shapes and numbers. This chapter was actually a little better written than some of the other chapters on basics like addition, subtraction and multiplication. The explanations are not so wordy that you can't follow, formulas are found by discussion first and then summarized so that you understand why the formula is what it is. My husband and I, we do not like too many formulas for area and perimeter. It is my opinion but I feel that my son should be reasoning it and figuring it out each time during the elementary stage and once he understands it fully for a year or two, then he can memorize it--because this boy needs to memorize and drill or he will forget everything. Even his name. My poor child will have it hard in life his memory is so bad. :lol: The Ending: We have 11 more chapters and even though there are things wrong with the book, we are planning to finish it. I also plan to buy and give my son the workbook to review materials we've covered already and when he does the chapters on material that the text didn't teach well, he will just use the mama and baba way that he knows and it will not be a big loss. I will update my review to share my oponion and experience when I am done with the whole book. To be clear:So far, this book is not bad--it just isn't very good. I wouldn't want to hand this book to any child to learn from, because I do not like the clumsy and half-correct explanations. I would use this book as a guide with any child who has finished or is doing well in a 3rd or 4th grade maths program. I think that any kid who does well with Math 54 would enjoy this book for its extra topics. I wouldn't teach new material from this book that would be covered in maths class--such as division or subtraction, and I wouldn't rely on this book for mental math strategies. But this book has neat topics for kids and interesting problems that are not that hard, but are novel and if they get them right, they feel like they are cool and if they get one wrong its okay because it was "hard" and they want to try again. It isn't exactly what I wanted for my son, but my son is liking and enjoying the book and more than anything, his enjoying maths is important to me. I think that if we had the workbook it would be better as we are going fast through the book. When we finish the textbook, I will probably order my son the workbook so that he can review and solve more problems--he likes the problems and there aren't enough of them in the textbook for his liking. Hopefully, this review will help others who are considering this book.
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