jjgarner Posted November 1, 2014 Share Posted November 1, 2014 I have some questions and am looking for insight on scheduling and sequencing of Art of Problem Solving math. Our daughter will complete Singapore Math 6B (US edition) in her 6th grade year, and then we are seriously considering moving on to the Art of Problem Solving curriculum. Here is our current plan, although this could change depending on our daughter's pace through the next couple of years. I'm just trying to create a general roadmap. I would love any feedback from others who have or are using Art of Problem Solving. Here's our general plan - probably pretty typical: 7th grade - AoPS Prealgebra 8th grade - AoPS Intro to Algebra 9th grade - AoPS Intro to Geometry 10th grade - AoPS Intermediate Algebra 11th grade - AoPS Precalculus 12th grade - AoPS Calculus What about the "extras?" We could also add AoPS Intro to Counting and Probability between Intro to Algebra I and Geometry. I've heard that it works well completing Intro to Counting about halfway through Intro to Algebra, after finishing quadratic equations, and then picking up Intro to Algebra again until the end. Any experience or advice on this? Also, we're also wondering when and where we could fit in the Intro to Number Theory (after Geometry?), and the Intermediate Counting and Probability course (after Intermediate Algebra)? How is it possible to fit it all in in 6 years? Are the extras like Counting & Probability, and Number Theory essential? How long does it typically take students to finish each textbook/course? I've read that the online courses fly, and I'm not sure if we'd do those or work through the textbooks on our own. I would love any backup available though, as I'm not overly confident in teaching higher level math by any stretch. With all our daughter has on her plate, I don't see how we could do more than 1 - 1 1/2 hours of math a day. We do school year-round with breaks for holidays. Thank you so much in advance for any insight and advice you may have! Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 1, 2014 Share Posted November 1, 2014 The time for finishing the textbooks varies greatly between textbooks, and between students. Intro to Algebra is the text with the most material, and many students take two years to complete the text. It takes a very motivated and ambitious student to complete the entire text within one school year - I would not plan on that. NT and C&P are not parts of the traditional high school sequence and are not prerequisite for any subsequent courses. They are just fun. Fitting in NT and C&P is possible in different situations: - the student starts young and has more than 6 years - the student is exceptionally talented and able and willing to do extra math - the student completes several texts in one year - a young student hits a wall in algebra and needs to take a detour through one of these subjects to develop maturity for the harder parts of the algebra text - a student is more interested in NT and CP than in completing calculus in high school Here are our personal experiences: DD completed the entire Intro to Algebra text in one year plus summer. She took one year for geometry, and did both Intermediate Algebra and precalc in 10th grade because she had a strong reason to do calculus in 11th. She did not have any interest in C&P and NT, but wanted to take a calc based physics course in 11th grade. So, we tailored her math sequence to her goals and we eliminated some topics from Intermediate Algebra and Precalc that are not necessary to be covered at this level in high school. DS began in 6th grade with Intro to Algebra and took two years to complete the text; in between he took a one semester detour for C&P. He took one year for geometry, and will take one year to do Intermediate Algebra. Quote Link to comment Share on other sites More sharing options...
Arcadia Posted November 2, 2014 Share Posted November 2, 2014 My boys get bored with just algebra so what works for them is DS1 - int algebra, intro geometry, int C&P spread over 2.5 years including summer. DS2 - intro algebra, intro geometry, intro number theory For example last week DS1 opt to do geometry so he did geometry all week taking a break from algebra. DS1 did C&P last year to cover required portions of California algebra 1 since we were with a charter last year. He does like C&P anyway. Quote Link to comment Share on other sites More sharing options...
Julie of KY Posted November 2, 2014 Share Posted November 2, 2014 I think it is very hard to "plan" your progression through AoPS. It is so hard to predict how a student will do. Of all the books, my oldest found Intermediate Algebra the hardest. Geometry is often hard for kids, but he loved that book and whizzed through it. Some options: 1) You can overlap some of the core books. You can start the algebra book after you get through the square root chatper in prealgebra (the rest of that book has more to do with geometry, stats, counting, probability); You can start geometry while doing the algebra book, etc. 2) You can do the Number Theory and/or the Counting and Probability books concurrently with any of the other books. We would stretch out the end of chapter review in a core book while meanwhile doing a chapter of number theory or counting and probability. Quote Link to comment Share on other sites More sharing options...
jjgarner Posted November 3, 2014 Author Share Posted November 3, 2014 Thank you to those who have responded so far with advice and shared your experiences with using Art of Problem Solving. It is very helpful to us as we look ahead. I can imagine it's hard to truly plan out an AoPS progression, as it can work differently for different types of learners with different types of goals, time constraints, etc. I really appreciate you taking the time to write and share what has worked for you and your kiddos. Do you all think the Counting and Probability, and Number Theory courses are essential to getting the most out of this curriculum? I would love to include them in some capacity if time allowed. I can imagine those courses would only help to strengthen one's math and problem solving abilities, plus they do seem fun! :-) Thanks for the tip too regarding allowing more than one year for Intro to Algebra. I see that the online course for Geometry is shorter in duration, so theoretically that first high school year could maybe be spent on completing intro to Algebra, and beginning and finishing Geometry??? We'll see how it goes. Thanks so much! Quote Link to comment Share on other sites More sharing options...
maize Posted November 3, 2014 Share Posted November 3, 2014 Listening in here :bigear: DD11 just started AOPS prealgebra. If we stick with her grade level according to local school cut-offs, she is in fifth grade (but on the older end). If she finishes prealgebra this year she would have plenty of time for some extras--I think I might try the CT and N&P books concurrent with Introduction to Algebra and Introduction to Geometry, just spreading the whole thing out over several grades. But I don't know how things will actually work out. I see no need for her to take calculus before 12th grade, but there is the possibility she would choose to accelerate through the high school years and graduate at 17 rather than 18. Which would leave less time for extras. She is good at math but it is not a passion, and I do not foresee her choosing a particularly math intensive field. My guess is she will not need math beyond college calculus and statistics. She does enjoy AOPS so far, she likes the challenge of figuring things out. Quote Link to comment Share on other sites More sharing options...
Arcadia Posted November 4, 2014 Share Posted November 4, 2014 Do you all think the Counting and Probability, and Number Theory courses are essential to getting the most out of this curriculum? In terms of essential, algebra is essential to the science progression in particular physics. C&P and NT are nice enrichment and broaden the math curriculum from just algebra and geometry. Precalc and calculus are entertaining by themselves. Calculus would affect science later on. (my opinion is based on being an ex-engineer. A mathematician would probably think differently) My kids didn't do the online courses as they prefer to set their own pace. I think if you get the C&P and NT books and don't mind how much your child complete out of each book, then you won't need to stress about completing everything in 6 years. Quote Link to comment Share on other sites More sharing options...
kiana Posted November 4, 2014 Share Posted November 4, 2014 In terms of essential, algebra is essential to the science progression in particular physics. C&P and NT are nice enrichment and broaden the math curriculum from just algebra and geometry. Precalc and calculus are entertaining by themselves. Calculus would affect science later on. (my opinion is based on being an ex-engineer. A mathematician would probably think differently) My kids didn't do the online courses as they prefer to set their own pace. I think if you get the C&P and NT books and don't mind how much your child completes of each book, then you won't need to stress about completing everything in 6 years. Nope, even as a mathematician, you're right. Algebra and precalculus and calculus affect science. Quote Link to comment Share on other sites More sharing options...
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