Excellent list, Ray. Perhaps also check out AOPS Intro to Algebra as well.

I wanted to add that I bought the Blue Series Place Value units from Math Mammoth to supplement a curriculum that I was using for the last school year. I thought the MM units were well done and well thought out. They were helpful and clear. I think MM Blue Series would be a good supplement to any curriculum because you could focus in on areas that needed more practice. We used Singapore Standards Edition Levels 2 and 5 last year. Overall I was happy with them. My favorite books from Singapore remain the IP and CWP, though. They are much more interesting than the standard curriculum if you enjoy problem solving. ;) Good Luck :)

:iagree: This really becomes evident at the graduate levels. When I was working on my doctorate in math, the group of students (as a whole) that had to make the largest jump from undergraduate to graduate maths were the American students. The students from China, Korea, and Russia who I worked with had much more solid math backgrounds than most of the American students - the introductory graduate math courses were mostly review for them. I really liked graduate level math. The focus on proofs was so logical and made so much sense. Also seeing how the different fields of math can be expressed in different ways was inspiring. It touched more on creativity and problem solving skills than early math to be sure.

I love your question, and I agree with the physicist. Yes, a child can be helped to enjoy and thrive at math. I think some of it depends on your (the teacher/parent's) attitude towards math. If she sees that you enjoy it or take an interest in it she will be more likely to as well. I have been able to turn a teenager around in math. She was not my child, but a student I tutored at a request from a computer science professor while I was an undergraduate student in college. She went from not liking math nor doing well in math to being on the Dean's List in her high school. My thoughts are that for a student to do well in math it is helpful for them to not be willing to give up on difficult problems and also to not be afraid of failure. Math can get tricky, but it is those who are not afraid of it and are unwilling to give up that succeed. :)

In the beginning of the school year, the first two weeks can be the toughest. After several weeks of a schedule, we usually have a routine down that helps things run more smoothly. For example, each child knows what is coming next and the routine helps them to understand what is expected of them. When I make schedules I usually allow extra time for certain subjects - like math or languages. These subjects can have questions from previous days' assignments and its best not to rush through or put rigid time limits on them. Usually we don't need the extra time but it is helpful to know that it is there if necessary. I know it can be hard to relax when you are trying to juggle various abilities and subjects. If you prioritize subjects which are most important to you, I think it makes it easier. How rigorous to make the content depends on the child. You can tell by their behavior. If a child rarely makes mistakes on a subject and usually gets 95-100% on everything, it is probably too easy. I'd add in something more difficult. If every problem or a large majority of problems are a struggle to get through, it is likely too hard or not the right approach. I would then re-evaluate or slow things down a bit.

It depends on the child. My 10 yo daughter can calmly withstand long periods of math, latin, reading, etc. She comes out of it with a smile on her face, and then will usually ask me questions about what she has just learned periodically throughout the day...like you can tell she is still tossing it around in her mind. :) My 5 yo old wiggles away after about 15 minutes of math, reading, etc. When designing a schedule, I'd take into account the ability and toleration/frustration level of each child. No one schedule fits all. That is one of the benefits of homeschooling - that you can tailor it to the individual child. A solid education should challenge them and even push them out of their comfort zone occasionally, but it should not frustrate them so much so that they end up dreading any subject. I seek the balance for each individual child.

For my daughter last year in we combined Singapore 4 with the Saxon middle levels. I don't recommend doing that because in our case (for her specifically) I had to adapt the Saxon material so much that it seemed pointless and was not a good match. Live and learn. I had very good results mixing Saxon 1-3 with Singapore K-2, however. For grade 4, with my son I plan to do Singapore SE 4 with the IP4 and CWP4 (which would both be the US Edition). Good supplements with Singapore Level 4 could be MEP 3 or 4 or Math Mammoth 4 (which looks similar to Singapore but more like extra practice.) I have not seen the RM 1-3 levels, but I really like RM 6. For example, for this school year my daughter did Singapore SE Level 5, IP 5A, and then moved into Russian Math 6 and IP5B and CWP5. Russian Math goes deeper into the concepts than Saxon did, and it has great explanations. She is happier with this year's combination. RM 3 may also be a good supplement with Singapore 4 based on the positive experience my daughter has had with RM6. I hope you find what works for her. :)

Hi, Snickerdoodle, I'm not sure if you wanted a solution or not, but here is mine: Note: [ ] = unit Rachel: [ ][23][42] Jane: [ ][23] Sandy: [ ] We are given that the total pencils for all three = 124. Therefore: 3 Units = 124-23-23-42 = 36 Which implies: 1 unit = 12 pencils So: Sandy has 12 pencils. And Rachel has 12+23+42 = 77 pencils. Together they have 89 pencils. Hope that helps. :)

Before the difference is 47. After Jason gives 15 marbles to Bob the amount will change by 30 (that is Bob's count will go up by 15 and Jason's count will go down by 15 = net change of 30 marbles.) 47-30 = 17 Now Jason has 17 more marbles than Bob.

Another idea are the Teacher Guides. The HIG were not out yet last year when I would have needed Level 5. I bought the TGs for Level 5 last year and had not used the HIG nor TGs before. I found the TG to be useful, and I'm glad I purchased it. It had relevant suggestions to aid me in presenting the concept and directed me to extra problem solving in the back. I think my daughter benefited from me using it. :)

Math Mammoth looks gentle and cost effective.

My 4th grade (pre-algebra/algebra ready) daughter is doing Russian Mathematics 6. It sounds like something your son would like. The problems go into more depth than Saxon and non-IP Singapore. RM has better formal math definitions, language, and explanations than both Saxon and Singapore in many cases. There is a small amount of review at the end of each chapter, but nowhere near the levels of review that are in Saxon. There is a B set of problems which are at the end of most sections which are more equivalent in depth to Singapore IP problems and in some cases go into more depth. There are only answers to the first three chapters (no solutions manual) of the book posted on the Perpendicular Press website http://www.perpendicularpress.com/math6.html, but the translator of the book from Russian to English stated that he'd have the rest of the answer key out by the end of the summer. Because of the depth of the problems, it can take awhile to grade the chapters that have no answer key yet. We don't skip any problems, though. We are really enjoying the book. The first edition - what we use, is out of print, though. Now there is a second edition coming out. I don't know the differences, but you can purchase the PDF version of the second edition at the website. You may also consider starting out in NEM 1 from Singapore. Good Luck.:)

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Yes, I adapt. If it is legitimate to learn (automatize) the math facts by using the Right Start games (which I own), then using Saxon math tricks should be egually legit. :D

I am sorry that happened. I would not use Saxon if my children did not respond well to it, either. My 10 yo daughter last year used some of Saxon 7/6. She did not like it. She is now happier doing Russian Mathematics 6. It goes a bit more deeply into the concepts, but does not have the continuous review. She liked the earlier levels of Saxon, but not the middle levels.

The weakness is the way that Saxon presented this "oddball" set of numbers - referring to them as a set of numbers as that is somehow odd. When I taught the lesson, I did not refer to the group of numbers as "oddballs". ;) My children had no trouble picking up both ways - with the "tricks" that Saxon uses to teach the math facts and the regrouping as taught in Singapore. The "solid regrouping strategy" that I think you are referring to (for example: 6+8=4+10=14) is really not that hard to teach nor understand when added to the way Saxon teaches the math facts. The more ideas or ways to see the math facts the better.

I remember this section for the "oddballs" - in other words - they had no trick for these. I remember thinking this was a weak spot in Saxon as well. I had my son use manipulatives to figure them out. We also did something similar to what you described. For 6+8, I showed him that we want to make 8 into a 10 by taking 2 away from the 6 which leaves us with 4 (6+8=4+10=14). This confused him at first, but then after showing it with a few more examples from the other "oddballs" he understood it. For these types of weaknesses in Saxon, I just do my best to explain the concept behind them. All curricula have strengths and weaknesses. I have been very happy with Saxon 3 this year. I think Saxon does an overall good job of teaching the concept behind the ideas in the Saxon 1-3 levels that I have used. Saxon is time consuming, but I have found that with math you reap what you sow. For some children, spending extra time rather than limiting the amount of time spent on math is what is best for them. Others don't need that much time. For my child that used Saxon 3, we also use Singapore level 2. Perhaps this is why I have not had the types of frustration with Saxon that many have had. We do Saxon 3 only 3 days a week and the Singapore 2 on Thursdays and Fridays. I would get bored with using only one curricula. The only time I would not combine curricula for math is if it was overly frustrating one of my children. In that case it would be better to focus on one and then add in another as a supplement only rather than doing two full curricula. Both of my children have done extremely well on every standardized math test they have ever taken - including the one for this year. Whether the credit goes to Saxon, Singapore, or just there own ability is anyone's guess.

I think it depends on the child. Some children really enjoy learning new languages. For example, since September my daughter has completed Latin (LC1), Spanish(Learnables 1), and Hebrew (Shalom Uvrachah). She even requested to do French for the rest of the school year. I printed off free French vocabulary words to keep her occupied during the times when she used to have a language lesson. She was not confused, but I did keep them separate as courses. I can see differences in my own children as to how much they can handle when it comes to languages, so it really does depend on the child.

I'll share what my son (age 7) did this year. This is how I combine the two: He did Saxon 3 on Mondays, Tuesdays, and Wednesdays. Singapore Level 2, IP2A, IP2B on Thursdays and Fridays. For the days we use Saxon 3, he would only do certain sections of the meeting book: the oral skip counting on most days, and sometimes I'd check the other areas to make sure he knew them. Doing the meeting exactly as stated would have been way too much review for him. Then he would do one side of the worksheets and usually one lesson per day (although sometimes I'd combine 2 lessons into one day). It seems like we skipped the first 20 lessons because he had Saxon 2 last year and did not need the review. For Singapore 2, he was able to move through the material quickly - usually 2 or more lessons a day. He is now finishing up the IP2B workbook. He usually does about 7 to 10 pages of the IP per day. He sometimes asks for help on the "Take the Challenge" sections, but does the rest independently. I should also mention that we did our drill sheets at different times of the day than the regularly scheduled math to keep it from feeling overwhelming. This pace worked for him; I'm not saying it would for everyone. I have been very happy with this particular Saxon/Singapore combination. I have found Saxon levels to be at least a year behind. For Saxon 2, I'd combine it with Singapore Level 1. Your best bet with Saxon or Singapore is to take the placement tests though to be sure. Good luck. :)

Thanks for all your valuable advice. I am still undecided. My two favorites right now are Henle I (since it is recommended in LCC and by Cathy Duffy and SWB.) and Latin Prep I which seems to be a favorite of many on this forum. I know that Henle was written long ago, but Latin has not really changed. My daughter seems ready for this even if we have to go slower at first. Latin Prep looks more fun and equally rigorous. She may enjoy this more. Can anyone compare these two any further?

FWIW, my parents did not push me towards math - even when I was in high school. They did put me in gifted programs from an early elementary age, but other than that they did not push me towards any particular subject. I did not REALLY start liking math until I was at university. From there on - it felt like I could not get enough math. :D There is plenty of time for your son to explore math in a fun way. If he is happy with you accelerating him than go with it. :)

I think it is great that you are encouraging your son to dream big and taking him to be around others who enjoy math. Enjoying math is key to sticking with it long term and being around others who enjoy it is helpful.

I am curious if anyone has used Latin for the New Millennium? http://www.bolchazy.com/prod.php?cat=latin&id=5602

First Form Latin appeals to me, also. According to the Memoria Press website: Completion of First Form Latin is equivalent to one high school credit in a foreign language. I am not sure whether this would be a better fit than Henle, though, since my daughter has demonstrated that picks up Latin quickly without needing much review. The website also says a 5th grader could begin in Henle. On the other hand, FFL looks more visually appealing than the Henle text and is apparently written for middle school level students. If I bought FFL, I'd likely also buy Henle I since it has been around for a long time and has a solid reputation.

The way I taught "regrouping" when using Saxon was with using dollars. That is how the book teaches it, and we added play money dollars for manipulatives. When using Singapore, I purchased a place value activity kit from Lakeshore Learning and used place value blocks and a place value mat. I bought an extra set of ones, tens, and hundred blocks to make sure we had enough for regrouping. Seeing the above examples in different ways was enough to solidify the concept. I would suggest writing down on the board what you are doing - for example, 10 = 10 ones, 100=10 tens. Then I would also show the steps on the board while you demonstrate it with manipulatives. Good Luck. :)