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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]Examples of compacted integrated math: 
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html[/quote]

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is  disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.[/quote]

Ding dong - did you open the second link?  :lol:

Integrated math can be compacted, just like any other sequence.

[/quote]

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.[/quote]

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.  :lol:

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche? 
[/quote]

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

[/quote]

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
[i]"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."[/i]

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math [i]and[/i] language.

[/quote]

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB  is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

[/quote]

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this: 
[i]"AP Calculus AB focuses on topics that are taught in the college-equivalent [u]first-semester calculus class[/u]. AP Calculus BC focuses on topics covered in [u]both first- and second-semester calculus classes[/u]."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. [u]All topics in the eight units of AP Calculus AB are included in AP Calculus BC[/u]."[/i]
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence. 
[/quote]

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; [b]applications of integration[/b]. Infinite sequences and series. [b]First-order ordinary differential equations.[/b] Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.[/quote]

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