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Ways to Tweak Saxon/How to Use Saxon Successfully?


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So I teach at a 3-day a week co-op/school for homeschoolers. It's great and I'm enjoying it. But, they use Saxon Math and many of the students are struggling. I'd say about half of the kids in each grade aren't really understanding math at the conceptual level. But the overall curriculum choice is not my immediate concern. I'm looking for tips to supplement or adapt Saxon Math to remediate the areas they're struggling in for my own class, which is Algebra 1/2. (I opted my own kids out of the math)

 

Right now a few of the issues we're dealing with are:

- a lack of understanding of basic algebraic equations (like how to isolate the variable on one side to solve the problem),

- geometry concepts such as finding volume on complex word problems (Saxon has some doozies!),

- fractions (we spent two days reviewing fractions in Fall which helped clear up some issues but they still freak over fractions when included in algebraic equations).  

 

How can I make the Saxon Algebra 1/2 program work well for us? Is there anything I could change or supplement in it to help the tricky areas? 

 

Also, there are SOO MANY problems! But very few to practice the current lesson's new concept. So they are being asked to move on before mastering the previous one. And I have to keep to a specific pace because the co-op uses Seton Home Study as the basis and they require you to get through the entire program in 36 weeks, which means I MUST do 4 lessons every week and a test. How do I somehow keep the busy work in check while making sure they have enough practice? 

 

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I don't have any curriculum suggestions. Just the three concepts that every student I ever had struggling in algebra had missed.

 

1) "you take what you know, to find what you don't know, to tell them what they want to know." You write down all the information given, write what you can calculate from it, and find out what you can in that situation. Then, look back and see how that information fits the question. Then make sure you answered the question!

 

2) "all numbers can be done and undone." Did you multiply on one side? Divide on both sides to "undo" it. Have a fraction? Fractions are division! So, multiply to get rid of them. Have "stuff" in the fraction? Do or undo it, then undo the fraction.

 

So 1 and 2 would work on getting the variable on one side of the equation. "Undo" all the stuff to get the variable on its own. Once the variable is isolated, is it the final answer, or does the variable need to be reinserted into another problem to get the final answer, particularly word problems?

 

3) "when in doubt, draw it out." The problem says it's a square. If they ask for help, my first question is, "where is your picture of your square?" The majority of the time, they can do it from there. Even three dimensional shapes, it's possible to draw something. I still drew pictures when I took calculus last time. It works!

 

There is a series on Netflix that goes into the history of Maths, and included in one of the episodes includes how someone figured out the volume of three dimensional figures. Maybe you could watch that scene in class or as homework. Understanding where these crazy equations come from sometimes helps in the application of them.

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I don't have any curriculum suggestions. Just the three concepts that every student I ever had struggling in algebra had missed.

 

1) "you take what you know, to find what you don't know, to tell them what they want to know." You write down all the information given, write what you can calculate from it, and find out what you can in that situation. Then, look back and see how that information fits the question. Then make sure you answered the question!

 

2) "all numbers can be done and undone." Did you multiply on one side? Divide on both sides to "undo" it. Have a fraction? Fractions are division! So, multiply to get rid of them. Have "stuff" in the fraction? Do or undo it, then undo the fraction.

 

So 1 and 2 would work on getting the variable on one side of the equation. "Undo" all the stuff to get the variable on its own. Once the variable is isolated, is it the final answer, or does the variable need to be reinserted into another problem to get the final answer, particularly word problems?

 

3) "when in doubt, draw it out." The problem says it's a square. If they ask for help, my first question is, "where is your picture of your square?" The majority of the time, they can do it from there. Even three dimensional shapes, it's possible to draw something. I still drew pictures when I took calculus last time. It works!

 

There is a series on Netflix that goes into the history of Maths, and included in one of the episodes includes how someone figured out the volume of three dimensional figures. Maybe you could watch that scene in class or as homework. Understanding where these crazy equations come from sometimes helps in the application of them.

 

I've been meaning to watch that Math series on Netflix! It's even on my Queue, lol! 

 

I like the "all numbers can be done and undone" language. I've of course explained that concept but never using that language and I like the simplicity of it.

 

The drawing out is such a problem too. I can definitely focus on insisting on that too. These kids are so used to "just do what the textbook says" kind of math that they balk at having to think about it too much. And I get panicked thinking how many problems they're supposed to complete if multiple problems require drawing it out and spending a good bit of time on it. As it is they spend 1 hour on instruction MWF and are taking 3 hours to finish their homework on Tues and another 3 hours on Thurs. That seems absurd when my boys take 30 minutes per day on Singapore Math and my daughter takes 60 minutes per day on Math U See. 

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That is a crazy amount of time to do the homework! Hopefully they will see that drawing it out will make it go faster since the thinking part will come faster.

 

I hope these weird tools help. Honestly, they came out of desperation with one highly intelligent young lady who just couldn't get it. I blurted them out the first time.

"what did you just say?!"

"Uh, gimme a second. I'm not exactly sure."

Then we wrote them down. She went from an F eight weeks into freshman algebra and graduated high school with a B in trig/pre-calculus. She wrote the rules in the back of the graduation announcement she gave me. 😂

 

Edited because I left it unattended in the vicinity of a three year old and emojis are fun.

Edited by Elizabeth 2
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So I teach at a 3-day a week co-op/school for homeschoolers. It's great and I'm enjoying it. But, they use Saxon Math and many of the students are struggling. I'd say about half of the kids in each grade aren't really understanding math at the conceptual level. But the overall curriculum choice is not my immediate concern. I'm looking for tips to supplement or adapt Saxon Math to remediate the areas they're struggling in for my own class, which is Algebra 1/2. (I opted my own kids out of the math)

 

Right now a few of the issues we're dealing with are:

- a lack of understanding of basic algebraic equations (like how to isolate the variable on one side to solve the problem),

- geometry concepts such as finding volume on complex word problems (Saxon has some doozies!),

- fractions (we spent two days reviewing fractions in Fall which helped clear up some issues but they still freak over fractions when included in algebraic equations).  

 

How can I make the Saxon Algebra 1/2 program work well for us? Is there anything I could change or supplement in it to help the tricky areas? 

 

Also, there are SOO MANY problems! But very few to practice the current lesson's new concept. So they are being asked to move on before mastering the previous one. And I have to keep to a specific pace because the co-op uses Seton Home Study as the basis and they require you to get through the entire program in 36 weeks, which means I MUST do 4 lessons every week and a test. How do I somehow keep the busy work in check while making sure they have enough practice? 

 

But that's how Saxon works: each new concept introduced in little increments, continued to be taught and processed and developed while the next concept and the next are introduced and processed and developed. Students are not supposed to master one concept and then move on to the next. It is why every.single.problem needs to be done in every.single.lesson. There is no busy work. Every problem is important.

 

This is what our Janet in WA wrote about Saxon:

 

Saxon involves an element of the spiral approach -- regular review of previously taught topics -- but Saxon’s approaches review very differently. When a student learns a new concept in Saxon, he practices it with only a few problems -- rather than with a full problem set, as in most math curriculums. Then, Saxon spreads the practice problems for that concept out at the rate of one or two a day, for the next 20 or so problem sets, along with problems from many other previously learned concepts. So it isn’t exactly review -- it’s the equivalent of a problem set of 25-30 problems, spaced out over a period of many days. When that concept is dropped from the daily problem sets, it will reappear periodically throughout the rest of the book - which is the true review in Saxon.

What makes Saxon really different -- incremental -- is that concepts are not taught “whole.†There are no units or chapters that cover, say, fractions completely, and then move on to another topic. On a particular day, a student may learn a small “increment†of a concept -- say division -- and practices it for a few days before adding another “increment†of the division concept. Meanwhile, the next day, he may learn an increment of, say, fractions -- again, practicing that increment for a while before adding another piece to the fraction puzzle. So the student ends up practicing both the fraction “increment†and the division “incrementâ€, along with other “increments†every day. How long the student practices the “increment†before adding another in the topic depends on the difficulty -- and newness -- of the increment. Saxon often follows a difficult new “increment†with several easier, or review, increments from other topics to give the student time to practice that difficult increment without distraction from other difficult concepts. There are no units or chapters in Saxon -- just a seamless whole.

 

This may sound like chaos, and many have abandoned Saxon with just that reaction. But it’s not chaos. It’s ingenious. Because Saxon hasn’t just chosen these “increments†willy-nilly. They are carefully chosen and presented, and offer something unique -- the opportunity for the student to see how *all* of the “increments†and concepts of math are intimately related day after day, from the very first page of the book. Because when the child learns that increment of division, and then that increment of fractions, Saxon takes the opportunity to show the student how those two concepts are related -- both in the lessons and in the problem sets. It carefully and constantly matches and juxtaposes concepts both in daily lessons and in problem sets. When it gets to Algebra and above, it does the same thing by combining algebra, geometry, trigonometry, etc. into the same seamless whole. The student learns a little algebra, then uses it to learn a little geometry, and so on.

 

My sons have thrived on this approach, though I had a difficult time accepting it at first. They love the variety from day to day, and within the problem sets. And they’ve benefited from having to change their math gears often to tackle all the different concepts from day to day and from problem to problem. What is a big turn-off to many is just right for many students -- including mine.

 

 

 I guess it isn't possible for you to change the math text, so if you want to make Saxon work, the best way is to do it the way it was written: Do the lesson with the students orally, then assign the practice set, all of the problems in every lesson. It's how to succeed in Saxon.

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But that's how Saxon works: each new concept introduced in little increments, continued to be taught and processed and developed while the next concept and the next are introduced and processed and developed. Students are not supposed to master one concept and then move on to the next. It is why every.single.problem needs to be done in every.single.lesson. There is no busy work. Every problem is important.

 

This is what our Janet in WA wrote about Saxon:

 

 

 I guess it isn't possible for you to change the math text, so if you want to make Saxon work, the best way is to do it the way it was written: Do the lesson with the students orally, then assign the practice set, all of the problems in every lesson. It's how to succeed in Saxon.

 

Yes, and I understand that's the method behind Saxon. But we've been doing the program exactly as recommended and written, yet the students are drowning. They don't 'get' math at a core understanding. As in, they can do the procedures when you tell them what to do but struggle to apply it in real situations/word problems, which seems odd because Saxon has TONS of word problems and we often go over them in class. I have 1-2 who are making A's but many others are failing most tests the first time around. And I have been assigning the entire problem sets because I'm aware that it's how Saxon works, hence the 9 hours they're spending on math every week. Seems absurd when my kids, and many others, spend half that time learning math with other math programs and get the same scores on standardized tests.  

 

I'm not going to agree with Saxon's spiral math method from a pedagogical viewpoint. I just need ideas for how to make it click for my students who aren't succeeding with it as written, know what I mean? When the answer isn't simply to switch to a different curriculum, as it would typically be for a homeschooling family who just picked Saxon and found it didn't suit them. 

 

If you do the lesson orally together in class, assign the entire practice set, check the answers, give the weekly tests, and the kids don't succeed....what then? 

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I never used Algebra 1/2 but did teach 8/7 (and several previous years) and Algebra 1, which bracket it.

 

One thing that was extremely helpful in 8/7 was to pause occasionally and put all the rules onto one sheet of paper.  So, for instance, how do you multiply and divide complex fractions? How do you raise exponents to another power?  How do you multiply or divide them?  

 

Or even just the rules about 4 functions with both negative and positive numbers or combos thereof.

 

Then I let my student use that sheet for a while, until she was remember this consistently.  87 is very incremental, and I imagine that 1/2 is as well, and quite broad.  It's important to scaffold the students into getting their arms fully around the material, instead of losing the increments from two weeks before.

 

Also, I kept bringing her back to a model.  If something involved, say, converting from a fraction to a decimal or to a percent, I would encourage her to quickly write out an equivalency that she was certain of, and check her method against that one.  For instance, .5 is the same as 1/2 which is the same as 50%.  How do you get from one to the other?  Use that EXACT METHOD to get from a more complex one to the desired form.

 

Lastly, I taught a version of two column work that I kind of made up.  It's similar but not identical to geometric proofs.

On the right goes the stuff that you know--the givens, the initial relationships, etc.  That's also where you write the definition of your variables.

On the left does the work that you are using to solve the problem, starting with an equation or equivalency from the right hand column and gradually adding material as needed.  Then at the end, you double check to make sure that you have not accidentally stopped in the middle of the problem--that you have actually answered the question.  Only then are you finished.

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My oldest is in public school 6th grade and I am just learning about math options.

 

Some kids take a one-year course "consolidating previously-learned math including...." before taking Algebra.

 

Some kids take Algebra I over two years instead of over one year.

 

So my question is how kids were placed into this class. Have they really learned what they need to learn to be in this class?

 

My second question is if really some of these kids would benefit from taking Algebra I over two years.

 

I don't know, it is just something I wonder, bc I have just looked at the forms lately (about how they determine placement for 7th grade math).

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Question: Are your students solid on their basic math facts and skills? Just because they hit the age for Pre-Algebra doesn't always mean they are ready for it. If

they are struggling with remembering basic math facts and other basic math skills, then they will struggle the whole way through higher math. Go back and remediate.

Are the parents noticing any gaps that may be causing problems?

Khan Academy may help if you can identify those trouble spots to concentrate on. Also A+ math was recommended to us as a site to print your own math sheets. I haven't used that one yet though.

If that is not the issue they may find Art Reed's DVD series helpful. Saxon is tough, but there are few math programs that can compete with it.

Another option is to have the kids go back and review the lessons for the problems that they miss or don't understand, (those little numbers next to the problems).

Sometimes is just takes a few exposures to the same concept for them to "get it".

Could you split the class? That way the faster kids won't be held back by the ones who need more instruction.

We did 87 then pre-algebra, kind of over kill, but pre-algebra was a breeze.

Hope you can find something that will help.

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...As it is they spend 1 hour on instruction MWF and are taking 3 hours to finish their homework on Tues and another 3 hours on Thurs. That seems absurd when my boys take 30 minutes per day on Singapore Math and my daughter takes 60 minutes per day on Math U See. 

 

For many years I've taught math, usually Alg 1 or Pre-Alg, to homeschooled students using a school-type text.  I expect that homework be done, for about an hour a day, for five days a week, in addition to our twice-a-week class time.  That could be homework M-F, or they can skip one or two of those days and work on Sat and/or Sun.  However, I caution that they should be careful not to stack two days of homework in one day.  It's just not as effective, learning-wise.  In a pinch, if they must, I suggest they do a day in one sitting, say in the morning, and a day in another sitting, say in the evening.  There are always those students who are still learning time management and try to stack stuff, and it always shows in their work, and I patiently, pleasantly, point that out.  

 

I would suggest that you encourage your students to divide their six hours of homework done Tu/Th into five (or six) different days of homework.  For me, I teach Mon & Thur, so it often looks like this:

M- teach three lessons, give three days of homework (MTW), Th-teach two lessons, give two days of homework. (ThF)

For some students, who are busy during the week and prefer to work a bit on the weekends, if their parents agree, I do it like this: 

M- teach two lessons, give two days of homework (TW), Th-teach three lessons, give three days of homework. (Th/F/Sat or Sun)

Either way, they can choose to spread Thursday's assignment over Thursday, Friday, Saturday, and Sunday in whichever way works for their schedule.  

 
Either way, sometimes I teach ahead a bit so that I don't have to teach three lessons in one day from scratch.  I find it useful to spend the last ten minutes of class "previewing" the next lesson or two, which helps them take it in better when I come back to it during the next class and go more in depth.  So they could get a super-quick preview on Monday, a slightly longer preview on Thursday, a proper lesson on Monday, then they do the homework.  At that point they've seen the material three times, in increasing complexity, before they have to work with it.
 
You've got the luxury of three days, so you could teach two lessons, and assign two lessons each time.  So on M teach lessons 1&2, assign for homework M- lesson 1, Tue, lesson 2, to be due Wed.  On Wed, teach lessons 3&4, 3 to be done W and 4 to be done Th.  On Friday, teach lesson 5 & 6, with the homework being lesson 5 (to be done Friday night, or on the weekend if they choose), but give them the homework for 6 as well, in case they'd like to get ahead due to a busy week.  
 
High school students generally do almost an hour of instruction a day, then a significant homework assignment in the evening.  They also work on the weekends.  Homeschoolers should not expect to get the same level of learning without the same level of work.  Your students are putting the time in, but all in a big chunk, which is just not conducive to learning the material.  They need time to try something and let it sink in before tackling the next lesson.  Regularly trying to do two-three lessons in a day is really not ideal.  Spreading it out will be much better for understanding and retaining the material.  Yes, it means they will have homework on a co-op day.  At that level, I don't think that is an unreasonable expectation.
 
I would also encourage you to deviate from the text where necessary.  You are obligated to teach the MATERIAL, not be a slave to the text (I assume?).  When I taught ABeka in a co-op situation, I regularly deviated from the text when I thought I could give the students a better experience with the concepts by pulling material from elsewhere.  I regularly decided to skip things I thought were not a useful way to spend precious co-op class time.  And I regularly substituted homework problems with ones I thought gave a better experience with the material.  Set the goals for what you want the students to learn, then use the text as a tool but don't be afraid to use something else as part or all of the lesson if you feel it meets their needs better.
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Unfortunately this may not be the problem of Saxon. Co ops have exactly two types of homeschoolers - those whose parents follow up, check homework, ensure learning and require the work to be done.

 

And those who don't.

 

Both major homeschool academies here have almost a 50/50 spread across the board from 6rh grade to high school. 50% do the work and have parents who are checking all week and keeping kids accountable and teaching. 50% come with literally nothing done because they forgot and their parents never really truly check up.

 

If these kids were doing their daily lessons every day and getting them checked with mom and going back and re

Learning what the missed there is no way they'd be confused about fractions.

 

I'm

Not a huge Saxon fan (though we have used 6 years of it) but I strongly suspect that Saxon isn't your problem

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PS this is also why very few co ops and homeschool one day per week class centers do math. It's nearly impossible because there are so many kids that just won't do the work. I would finish out the year and move on.

 

Edited: I just saw that this is 3x per week. Is this a homeschool school ? Like as in a real school with transcripts and that provides grades and issues report cards? If it is you need to bring the issue to the principal and have a letter sent home -if it's a real school they agreed in good faith to do the assignments and therefore should be prepared for disciplinary action from the school if the moms aren't checking up.

 

:)

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... I have to keep to a specific pace because the co-op uses Seton Home Study as the basis and they require you to get through the entire program in 36 weeks, which means I MUST do 4 lessons every week and a test. [/size]

 

This right here is part of the problem.  You are not being asked to take the kids where they began the year and build on that foundation and teach them a year's worth of material.  Instead, you are being asked to teach from a textbook, at a certain pace, regardless if they are ready for it and regardless of the pace at which they can understand it.  That's a huge problem.  That's, frankly, removing the benefit we have as homeschoolers to pace ourselves and cover material based on the needs of the specific student.  This is an issue to bring to the parents and to the co-op leaders.

 

Unfortunately this may not be the problem of Saxon. Co ops have exactly two types of homeschoolers - those whose parents follow up, check homework, ensure learning and require the work to be done.

And those who don't.

...

 

If these kids were doing their daily lessons every day and getting them checked with mom and going back and re

Learning what the missed there is no way they'd be confused about fractions.

...

 

I agree to some extent.  But kids at the pre-algebra level are also at the level where they need to be responsible for their own work - or lack thereof.  They need hand-holding on time management - they should NOT be doing all of the work on Tue/Thur - that is not a recipe for success.  They need to have a planner, and they need to be led through using that planner to decide when to do the homework so it fits in their schedule.  They need some kind of accountability for the homework - for example, have a few of them put the solution to a selected problem on the board at the beginning of class then talk their peers through it.  At that age, I give my students full access to the answers, including worked-out solutions, and I expect them to check their own work periodically as they go through it.  What is your method for ensuring that this is done?  For a small group I can just ask, and they will be honest with me because I don't scold, I help them figure out how to do it better next time.  I have the benefit of not being tied to an external pace, so I can adapt somewhat to the students' needs and schedule.  For a larger group, like you have, you may need something more formal, like having parents sign the checked homework.

 

The parents can be part of the solution also.  They need to know there's a problem with their child, NOW.  They need to understand that you need to keep a certain pace and can't spend time on remedial work.  They need to understand that the consequences if the child fails the class - presumably that the child won't get the credit.

 

If, say, fractions is the main issue, then as a PP said some work converting fractions to decimals and mixed numbers, and simplifying them, can be of benefit.  However, this work would have to be done on top of the rest of the work, which will be challenging.

 

Is there a "study hall" time period at co-op when you can be available for extra help/instruction for those who need it?

 

If you plan to teach again, I would strongly advise you to insist on a rigorous placement test, plus a list of the child's previous work, plus an interview with child in which you set the problems and have them talk through how they are solving them, plus a frank interview with the parents as to prior math work including struggles, etc.  Classes go most smoothly if all of the students begin at more-or-less the same level and can work at more-or-less the same pace.

 

Another option for next year would be to choose a text that can be taught and assessed at several levels.  (McDougal Littell comes to mind.)

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Once students get behind in math there is no way to continue without doing some intensive tutoring. How many kids are in your class? Is it possible to have them working at different levels? Plowing ahead in Saxon may result in dragging some of these kids over the finish line but it will be discouraging and they will hate it. I would address the co-op about this issue and figure out a way to allow the kids who are doing well to move on and tutor the kids who have fallen behind. Perhaps they can get more volunteers and split the class.

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Since shelving the Saxon and using a different book isn't an option.... have you considered the Key to ___ series? Key to Fractions, Key to Geometry (really pre-geo), Key to Algebra (more like prealg) They are skinny little workbooks and inexpensive. Their simple explanations help with the conceptual and there's plenty of extra practice. Being cheap and little should make them more other parent friendly.

 

I'll also add a vote for Hands on Equations. I'd make large cardstock pawns to demonstrate to the whole class so they can do it together. Getting a set for each kid would be pricey. There are inexpensive apps they can use on the side.

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Saxon has a reteaching workbook that you can buy and copy.  I would go through each students next test and copy all the lessons they missed.  I would assign the reteaching sheets as extra homework.  I would definitely let the parents know what concepts each child needs to work on.  The other pointer I have is to have each child take the test twice on test day.  Have them compare their answers and choose the right one.  This is a way to eliminate silly mistakes and/or computational errors.  My class did so much better, once I started to have them to correct their tests this way.  It also helped me to see what concepts were they weak on vs. what were just computational errors.  At this point, I wouldn't feel like it was my fault if they add, subtract, multiply or divide incorrectly.  They should have that mastered by now.  I've taught Saxon for years and never loved it. I will not be using it with my own children.  I also second the hands on equations.  Love that program.

 

 

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Saxon has a reteaching workbook that you can buy and copy.  I would go through each students next test and copy all the lessons they missed.  I would assign the reteaching sheets as extra homework.  I would definitely let the parents know what concepts each child needs to work on.  The other pointer I have is to have each child take the test twice on test day.  Have them compare their answers and choose the right one.  This is a way to eliminate silly mistakes and/or computational errors.  My class did so much better, once I started to have them to correct their tests this way.  It also helped me to see what concepts were they weak on vs. what were just computational errors.  At this point, I wouldn't feel like it was my fault if they add, subtract, multiply or divide incorrectly.  They should have that mastered by now.  I've taught Saxon for years and never loved it. I will not be using it with my own children.  I also second the hands on equations.  Love that program.

 

Do you know if they have reteaching masters for upper levels? I thought these were for the elementary grades only.

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Do you know if they have reteaching masters for upper levels? I thought these were for the elementary grades only.

hmm.... I've taught the middle grades Courses 1-3.  They have reteaching masters.  I am not sure if the old series does.  I much prefer the course 1, 2, and 3 series over the old series. They are much more complete and teacher friendly.

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My Father's World sells a schedule where they've minimized the number of problems to avoid repetition. We used it, but only when my kids scored 90+ on the exams. I might work with that, but assign the other problems as practice or review. We only used the schedule until half way through algebra 1/2, then it's every problem every day.

 

We've used Saxon for years (pre algebra through advanced math so far). We use the Art Reed DVDs which I'd recommend highly. Students child purchase them to use at home. They're not long and easy to understand.

 

Are the kids doing the work at home? Reading the lessons before class? Working the practice problems before class? If not, then they can. They might not understand it all, but it should help them.

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I'm not sure what grades course 1-2-3 correspond to.

It is Saxon's middle school series that they created for schools instead of homeschool.  It is much more teacher friendly.  It corresponds to 6/5, 7/6, and 8/7.   Course 3 is really a pre-algebra for 7th or 8th.  Most 5th graders who are good at math, but not amazing can handle course 1.  

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Saxon lessons take FOREVER to complete when a student is placed too high. Mixed problem sets are much harder to pull kids thorough when they do not understand the math.

 

Homeschooling Saxon fans often have their children back up and repeat a few problem sets or start the book over when lessons take too long. Problem sets are meant to be EASY and mostly review.

 

Not much should be all that new. The previous year should have introduced the topics enough, that the student isn't just now learning this topic from scratch.

 

Those geometry problems truly are brutal to students that have not worked up to them. They can be fun when viewed as puzzles when there is less pressure and other homework. But when kids are just expected to do a book because they are a certain age, they are just brutal.

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