# "Hard Math for Elementary" -- Full Review **Part 2 in #16**

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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.

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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

02 - Base 8

03 - Mental Math

04 - Tiling Floors

06 - Multiplication Table

07 - Prime Numbers

08 - Subtraction

09 - The Distributive Property

10 - Finding Areas

11 - Modular Arithmetic

12 - Long Multiplication

13 - Combinatorics

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.

Thank you!

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Wow, thanks very much for the detailed explanation. I agree with you 100% about the "explanation" of primes and frankly I'm horrified to see that considered appropriate for any student, let alone mathematically talented ones.

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Wow, thanks very much for the detailed explanation. I agree with you 100% about the "explanation" of primes and frankly I'm horrified to see that considered appropriate for any student, let alone mathematically talented ones.

Yes, very strange. I am grateful that Mr. G. Ellison took the time to write this book, but I would rather he have written less topics and done them correctly than include vague or sloppy teaching of even basic topics. I am not prepared to write a "better book" right now, so I will not be complaining :lol:!

ETA I just feel that I should say that I disagree with the idea that mathematically talented students are some how more deserving of "accurate" explanations than those students who are not mathematically talented. I believe that all students deserve clear and coherent instruction no matter what the discipline is. Mathematically talented students may deserve stronger problem sets so that they can develop their talents and hone their skills, but everyone should get the same reliable and accurate explanations, in my opinion.

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Wow, thanks very much for the detailed explanation. I agree with you 100% about the "explanation" of primes and frankly I'm horrified to see that considered appropriate for any student, let alone mathematically talented ones.

I haven't actually seen Glenn Ellison's book, but the way the OP describes this sounds like the way Miquon develops the Sieve of Eratosthenes. Schwartz(an endowed chair of math at Brown) does the same thing in "Counting on Monsters" before moving on to Euclid's proof of the infinitude of primes.

Could you elaborate on why this is a "problem"? For an older kid, moving straight to factors might be faster but for a 1-3rd grader it seems that a sieve approach is fine... it might be even better to use geometrical examples, impossible rectangles and all that..

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I haven't actually seen Glenn Ellison's book, but the way the OP describes this sounds like the way Miquon develops the Sieve of Eratosthenes. Schwartz(an endowed chair of math at Brown) does the same thing in "Counting on Monsters" before moving on to Euclid's proof of the infinitude of primes.

Could you elaborate on why this is a "problem"? For an older kid, moving straight to factors might be faster but for a 1-3rd grader it seems that a sieve approach is fine... it might be even better to use geometrical examples, impossible rectangles and all that..

The idea is not developed as the Sieve of Eratosthenes or as anything else. The idea is not developed at all It is just stated exactly like this.

*** I'm including EXACTLY what the book says***

Chapter 7

Prime Numbers

As you were working on your multiplication table you may have noticed that some numbers like 24 come up as the answer to multiple multiplication problems while others like 7 are only the answer to two very trivial problems, in this case "Whats 1 x 7?" and "Whats 7 x 1?". If so, you were on your way to discovering a concept that has fascinated mathematicians since the time of the ancient Greeks: prime numbers.

7.1 Prime and Composite Numbers

• A number p is called a prime number if it appears exactly twice in the multiplication table.

In other words, the only multiplication problems with positive whole numbers that have answer p  are "what is 1 x p?" and "what is p x 1?" The first few prime numbers are 2, 3, 5 and 7. For example, 7 is prime because the only way to get 7 are 1 x 7 and 7 x 1.

The number 1 isn't prime because it only appears once in the table.

The number 6 isn't prime because it's there four times: 1 x 6, 2 x 3, 3 x 2 and 6 x 1.

• Numbers like 4,6,8 and 9 that appear more than twice in the multiplication table are called composite numbers.

Every whole number that is bigger than one is either prime or composite.

One word of warning on my definition is that it only works when you make the multiplication table big enough so that p x 1 and 1 x p are in the table. The number 14 only appears twice in a standard multiplication table as 2 x 7 and 7 x 2, but it would be there four times if you used a bigger table that also included 1 x 14 and 14 x 1.

****End of the Excerpt**

That is an exact excerpt of what the book says. That is how the chapter on prime numbers starts. :huh: that is not right. I feel like they could have and should have used the Sieve of Eratosthenes instead.

ETA: I'm going to extend the excerpt for all of 7.1

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I haven't actually seen Glenn Ellison's book, but the way the OP describes this sounds like the way Miquon develops the Sieve of Eratosthenes. Schwartz(an endowed chair of math at Brown) does the same thing in "Counting on Monsters" before moving on to Euclid's proof of the infinitude of primes.

Could you elaborate on why this is a "problem"? For an older kid, moving straight to factors might be faster but for a 1-3rd grader it seems that a sieve approach is fine... it might be even better to use geometrical examples, impossible rectangles and all that..

But the book is aimed at 3-6 graders, not 1-3 graders. I like the geometric idea too and actually I think sides of rectangles is a great way to discuss factors.

I actually went and looked up the preview for this book on amazon. He does begin by mentioning that 7 is only the answer to 1x7 and 7x1. But then his definition is "A number p is called prime if it appears exactly twice in the multiplication table". Now, immediately afterwards, he then continues and says "The only multiplication problems with positive whole numbers that have answer p are "What is 1xp" and "what is px1"?", which is correct -- but I really don't like making that an incidental remark following a really unusual definition. I think it would be just fine to follow up the usual definition with the observation that a prime number appears exactly twice in the table.

I will say that my original comment was going solely off OP's remarks and I am pleased to see the customary definition included immediately afterwards.

I also agree with OP that I don't really like counting 1xp and px1 as two separate problems. Something that's supposed to challenge and extend elementary students ought to be discussing commutativity.

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The idea is not developed as the Sieve of Eratosthenes or as anything else. The idea is not developed at all It is just stated exactly like this.

*** I'm including EXACTLY what the book says***

Chapter 7

Prime Numbers

As you were working on your multiplication table you may have noticed that some numbers like 24 come up as the answer to multiple multiplication problems while others like 7 are only on the answer to two very trivial problems, in this case "Whats 1 x 7?" and "Whats 7 x 1?". If so you were on your way to discovering a concept that has fascinated mathematicians since the time of the ancient Greeks: prime numbers.

7.1 Prime and Composite Numbers

• A number p is called a prime number if it appears exactly twice in the multiplication table.

In other words, the only multiplication problems with positive whole numbers that have answer p  are "what is 1 x p?" and "what is p x 1?" The first few prime numbers are 2, 3, 5 and 7. For example, 7 is prime because the only way to get 7 are 1 x 7 and 7 x 1.

The number 1 isn't prime because it only appears once in the table.

The number 6 isn't prime because it's there four times: 1 x 6, 2 x 3, 3 x 2 and 6 x 1.

• Numbers like 4,6,8 and 9 that appear more than twice in the multiplication table are called composite numbers.

Every whole number that is bigger than one is either prime or composite.

One word of warning on my definition is that it only works when you make the multiplication table big enough so that p x 1 and 1 x p are in the table. The number 14 only appears twice in a standard multiplication table as 2 x 7 and 7 x 2, but it would be there four times if you used a bigger table that also included 1 x 14 and 1 x 1.

****End of the Excerpt**

That is an exact excerpt of what the book says. That is how the chapter on prime numbers starts. :huh: that is not right. I feel like they could have and should have used the Sieve of Eratosthenes instead.

ETA: I'm going to extend the excerpt for all of 7.1

OK. Yeah, that's not cool. A discovery component, followed by a imprecise definition, followed by more formalism is great(even if the more formalism gets kicked down the road)... a sloppy definition with no real derivation with no follow up isn't cool :(

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Oh, never mind this post. My mistake.

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ETA I just feel that I should say that I disagree with the idea that mathematically talented students are some how more deserving of "accurate" explanations than those students who are not mathematically talented. I believe that all students deserve clear and coherent instruction no matter what the discipline is. Mathematically talented students may deserve stronger problem sets so that they can develop their talents and hone their skills, but everyone should get the same reliable and accurate explanations, in my opinion.

Yes and no. There are levels of formalism and nuances of definition that may be inappropriate for a beginning student but perfectly appropriate for a more advanced student.

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Yes and no. There are levels of formalism and nuances of definition that may be inappropriate for a beginning student but perfectly appropriate for a more advanced student.

Can you please give examples of what you mean? I can not think of any instance where I would understand the need to withhold a definition from one group of students and not another.

I can understand needing to explain the definition informally or review it more often with one group of students, but with hold it just because you don't think that the students can take it?

I don't think that this is ever done in any of the countries I am familiar with, I would like to see how this works in your experience.

ETA: I assume we are talking about students at the same level of experience with a topic. Not one class of grade 1 and one class of grade 3, right? :confused:

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Thank you for the review. I have the the book, but haven't opened it yet. Since I'm more visual, it sounds like a lot of work for me. I may just stick with zacarro. :)

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Thank you for the review. I have the the book, but haven't opened it yet. Since I'm more visual, it sounds like a lot of work for me. I may just stick with zacarro. :)

Do you have the workbook and answer key also?

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ETA: I assume we are talking about students at the same level of experience with a topic. Not one class of grade 1 and one class of grade 3, right? :confused:

Sorry, I was gone over the weekend and unable to access the internet.

I am thinking about students who are the same age but at different levels of achievement. For example, in a standard classroom, a teacher may have students who are all grade 3 technically, but some of them are quite good at math and should really be working ahead, and some of them are still working on grade 1 level even though they have been promoted up.

I don't have a good example of differing definitions from elementary level because (quite honestly) I haven't taught struggling learners at that level. So here's an example from calculus. This course is frequently taught at (at least) 3 different levels -- an "applied calculus" class for students who are business or biology majors, a "calculus" class for everyone, and a "honors calculus" level for students who are talented in math. The way that limits and derivatives are defined is going to be different.

For example, in the "applied calculus" class the best definition given is probably going to be along the lines of http://tutorial.math.lamar.edu/Classes/CalcI/TheLimit.aspx-- this is also the first definition given in the "calculus" class. The more standard mathematical definition as http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx will be given towards the end of the section on limits in the "calculus" class if it is covered at all, and probably be skimmed over. However, in an "honors calculus" class (or indeed in the older books I have) the epsilon-delta definition will be given much earlier and then examples to clarify the meaning given. They will also be expected to actually use this definition. This definition, however, is so abstract that most of the students in the other classes will find it of very little use.

Ideally I would postpone such topics for struggling learners in the first place, but the current educational system won't allow us to do that.

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Thank you for that. I was wondering what you meaned by that comment. I thought you meant some times teachers or books do not teach the real definition of a thing to "slow" students which made me shocking gasped because I can not understand that practice.  I guess that this could be a western American thing but my parents would have been so angry if they taught incorrect teachings in my school when I was a pupil. If schools taught wrong things like this on purpose, there would have been another revolution in the streets. Its okay if some kids can not make the connection from the abstract definition to the applied algorithm, but as far as I know, everyone at every level would have had the correct definitions.

I had noticed that Saxon doesn't teach many definitions clearly or in the most natural order, but I think that is because the teacher is there to teach the lesson to the young ones and then they practice. I can not believe that NO ONE would tell children the real meanings of things in maths. Or any other subject.

I absolutely do not approve of the "definition" of or "teaching of" prime numbers in Hard Math. It is just wrong, unclear and wrong. There is no reason to not explain truthfully what a thing is. It is better to not teach it, than to teach wrong.

Sorry, I was gone over the weekend and unable to access the internet.

I am thinking about students who are the same age but at different levels of achievement. For example, in a standard classroom, a teacher may have students who are all grade 3 technically, but some of them are quite good at math and should really be working ahead, and some of them are still working on grade 1 level even though they have been promoted up.

I don't have a good example of differing definitions from elementary level because (quite honestly) I haven't taught struggling learners at that level. So here's an example from calculus. This course is frequently taught at (at least) 3 different levels -- an "applied calculus" class for students who are business or biology majors, a "calculus" class for everyone, and a "honors calculus" level for students who are talented in math. The way that limits and derivatives are defined is going to be different.

For example, in the "applied calculus" class the best definition given is probably going to be along the lines of http://tutorial.math.lamar.edu/Classes/CalcI/TheLimit.aspx-- this is also the first definition given in the "calculus" class. The more standard mathematical definition as http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx will be given towards the end of the section on limits in the "calculus" class if it is covered at all, and probably be skimmed over. However, in an "honors calculus" class (or indeed in the older books I have) the epsilon-delta definition will be given much earlier and then examples to clarify the meaning given. They will also be expected to actually use this definition. This definition, however, is so abstract that most of the students in the other classes will find it of very little use.

Ideally I would postpone such topics for struggling learners in the first place, but the current educational system won't allow us to do that.

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• 5 weeks later...

Review Part II: This part deals with only the second part of the book which includes topics on

11 - Modular Arithmetic

12 - Long Multiplication

13 - Combinatorics

15 - Regular Polyhedra

16 - Unmultiplying and the Prime Factorization Number System

17 - Fractions

18 - Probability

19 - Division

20 - Fractions Part 2

21 - Decimals

and the only chapters we worked are the ones that look like this. I, mama, read the whole book but it was a while ago since I had forgotten this book because we returned it to the library. We have not worked to get the book again because it was not much left for us to do in that book, but I am grateful to the book. It provided my babyish son a great experience with "hard" math. He has much confidence from doing work from a "hard math book" that it is noticeable growth in him.

I decided not to do the chapter on modular arithmetic with my son. It seemed like it will be a better topic to learn about later. I do not know if that was the BEST decision but it was a GOOD decision for us because of what happened when we tried the chapter on combinatorics.

I have to say that the chapter on combinatorics--as written--would not be understood well by my sons head. The language was trickier for me to make sense of (I'm ESL) and its not a topic that I am fluent with, so I struggled to see the whole truth in that chapter and I didn't trust my self to teach "the gaps" that I know that the author leaves when he writes on math (The author is not clear or precise so I didn't want to be unclear and imprecise while teaching my son, especially when I did not know what I was leaving out)

But a great thing happened when I was confused: my son thought that any math that mama can't understand must be the most fascinating!

He became interested in combinatorics and so I found another source and we have been working out of Combinatorics for the 3rd Grade Classroom. Its a good resource to have and my son loves it a lot and he likes that we are learning it together. But he still gets mad when he asks a question and I do not know the answer or the explanation and so have to study it first.

My son loves shapes and geometry so the chapter on Polyhedra wasn't even enough for him. I found two more resources that we used when we worked from that chapter: Math Is Funs: Regular Polyhedra and 3D Polyhedron Shapes.The most special part of learning about regular polyhedra was of course making them with candy and tooth picks. Of course since we do not have candy in the house much little sister had to eat the math right away making big brother very angry and the fight created a very big fuss. So we wound up doing 3 days of candy math and now all of the kids love polyhedra. It was fun to declare Yes or No to the Polyhedron quiz when the kids were learning about the curved shapes not being polyhedron.

What else is especially interesting because it is very difficult to read and pronounce these big words but my son has been motivated to read and spell more math words so that he can be more independent with his reading.

In conclusion: I'm glad that I took the time to read this book. I'm glad that I took the time to take my son through the book--after the second math competition that he was in he felt very badly about his maths. I told my son that he was good at math, but a bad reader (because he's so lazy about books) but he felt that he was just bad at math too. Since he is being able to work through much of this book he thinks to himself--"Hey, I can do hard math! All of my studying must be paying me back." and his confidence has coming back. Whats extra is he wants to better reading so that he can do good in maths contests without me there.

Even though I do not approve of many of the the ways that the author explained something when making this book, I am very grateful to him. This book was a good "next step" for us. This book is perfect for a kid who works at a good 3rd grade maths book but might not have the best confidence. This book, will mostly cover things that a 3rd grader will know about and it isn't the best "main text" but if nothing else, will expose your child to some interesting topics that probably aren't in their math book or that their teacher won't show them without a request. I would not use this book for ANY arithmetic--addition/subtraction/multiplication/division are better taught by most other books. But as an "extra text" for special topics: Base-8, Tessalations, Logic Puzzles, Area/Perimeter, Modular Arithmetic, Polyhedra and just confidence and working on "hard problems" this book is very valuable.

My son has found a completely new topic that he is interested because of this book: Combinatorics. Also this book gave us a good stepping stone for learning more geomerty because of Polyhedra and has caused many good discussions (and a few bad). My son really enjoyed this book and I'm not sorry that we spent so much time on it.

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• 2 years later...

All - I have just joined and already asking questions!! But at the same time I feel obliged and honored to give my opinion. My son's 9 and GT. I was gifted this book and frankly my work load is usually 14 hr work and 3 hrs. commute. So, neither I have the time or much \$ to research and just started using this book, 4 months back. I also have the workbook and answers.

The good part: For my son at least, a teacher was not much required. He started off with chapter 2 - Base 8 only because the chapter reads What if Simpsons were real!! On his own he grasped almost 80% and then followed thru with the worksheets. Chapter 3 - adding in your head, Chapter 5: Addition Puzzles, 6: Multiplication tables, 8: Subtraction, 10: Area, 4: Tiling, 10: Polyhedra, 19: Division and 21: Decimals. All of these he understood himself about 80% and he did the worksheets.

>>> What I understood is - if a child is a good reader, careful reader the material presented here can be self taught. I do understand the approach by Ellison may not be acceptable to many against specific areas however in today's world where time crunch and availability is a major bottle-neck having such a book is awesome.

>>> I carefully looked at all the worksheet answers, that was my job. Trust me, when I say this - but textbook is one thing the worksheets are another. It actually made my son think and think hard. I found him many, many times going back to the text book and returning with a rather grumpy face. In US, students are used to repeat what was taught. The work book actually made him think!! It was simply put: not easy. Frankly, if I did not have the answer book I would have struggled for quite a few. Example - FAT + CAT = CLEO. (its in the text book). This addition puzzle made me think, think hard. In work book, at least twice as difficult.

The bad part: The chapters which are normally NEVER touch in 3rd. or (perhaps) 4th. grade school like 7: Prime numbers, 9: Distributive property, 11: Modular Arithmetic, 13: Combinatorics, 16: Unmultiplying prime factorization number system, 18: Probability, 19: Advanced fractions he had trouble and his grasp was 40%. So, I believe in these topics perhaps the author wrote the subject matter a bit too complex. I also agree the typeface used in the book leaves a lot to be desired!!

>>> Here, I completely agree with the OP. Quite a few areas I ended up going about it, my way, in terms of explanations. Again - the work book is a bit on the tougher side.

>>> Word problems are a bit scant everywhere.

Overall - my son has a rather love/hate relationship with this book. Loves it because he has realized it has made him smarter and he has won a few things in school competitions. Hates because its not easy and groans when it comes to the work book.

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