Hi again homesweetschool and 4myboys. I’m going to do my best to answer your questions succinctly.
homesweetschool, you asked how to progress through more advanced fractions and what happens after fractions. You can find a detailed scope & sequence on pages 47-48 of the math handbook. I won’t list it out here because of that but, in general, after that introduction to fractions we see to complete the idea of division in the DVD, we have Weights and Measures, introductory Decimals, Factors, and Fractions. The next two years we have more advanced work in all of these areas following a review, ending with some business math. 7th and 8th grade also have Geometry and Algebra is begun in 9th grade with some business math continuing through the high school years.
How is it all approached? Lessons are still short, no more than 30 minutes. Oral work is still an important practice in the upper grades. Problems are interesting and aimed at reality while long and boring calculations are excluded. Emphasis is still placed on understanding rather than “getting through.”
Now I’ll combine in 4myboys son who is making minimal progress with fractions. I might suggest reading Nursery Examples of Fractions found in “The Parents’ Review” by Mrs. Boole, Vol. 8, 1897, pgs. 76-82. These can be found online at Ambleside Online and might help you understand some of the difficulties your son is having. One of my boys loves to be on Khan Academy in his free time and one day he was having problems understanding what Mr. Khan was teaching in regards to fractions so I listened along and said, “Remember when you were making bookshelves with your dad…” and he stopped me right there and told me not to go on because that made him “get it” and he could continue working the problem. That link to reality is pretty important.
Okay, I’ll be bold since you’ve both asked for advice. There is not a perfectly written CM curriculum currently for sale (that I know of) but, Strayer-Upton Practical Arithmetics, Second Book (beige book) combined with either Ray’s New Practical Arithmetic or A New Junior Arthmetic by H. Bompas Smith for the factoring portion (or another source of your choosing) does a very good job of it. They are highly scripted and you can work them orally with your children. We have a stainless-steel refrigerator in the kitchen that I use as a dry-erase board and my kids sit at the kitchen island for math lessons. Strayer-Upton has a built in review making it really handy. Just remember, as I’ve said in another thread, Strayer-Upton can have terribly verbose and confusing instruction at the beginning of each new portion. Those are best skipped and I feel confident that Charlotte would have skipped them while her students were guided in discovery themselves. The problems are carefully graduated and have a combination of interesting, real-life questions (i.e. [and more advanced] gluing a 1/16″ layer and two 3/32″ layers of veneer to a 3/8″ board will result in what total of a thickness?) and abstract questions.
Okay, I’ve got to go for the time being but will be back.
Best,
Richele