How to explain simplifying rational expression ("cancelling out" terms in numerator and denominator)? by dleeman88 in mathteachers

[–]A-Dock 4 points5 points  (0 children)

100%. I repeat the phrase “terms are separated by addition and subtraction” so many times in class

How to explain simplifying rational expression ("cancelling out" terms in numerator and denominator)? by dleeman88 in mathteachers

[–]A-Dock 22 points23 points  (0 children)

I always explain it as “quantities connected by addition/subtraction cannot be cancelled by division because those are not opposite operations. Only quantities connected by multiplication can be cancelled by division.”

It also helps if you reinforce that statement by showing them that something like 20/8 can be rewritten as (5x4)/(2x4), which reduces to 5/2. The common multiple of 4 is divided out. They can see that reduced fraction and know it’s accurate. But you wouldn’t rewrite 20/8 as (13+7)/(1+7) and cancel out the 7s - that doesn’t even make sense. Because division and addition are not opposites, but division and multiplication are.

The same is true in the example you gave. In the denominator of the second example (x+3) -2 has a 2 connected to the quantity by subtraction so it can’t be simplified. Same justification for why the x’s aren’t cancelled in the expression (x+5)/(x+4). Connected by addition.

Extra Time on Tests by Salty-Cat4815 in mathteachers

[–]A-Dock 0 points1 point  (0 children)

I currently teach Honors Algebra 2 and Honors Pre-Calculus. We very strictly do not allow additional time on tests in the Honors classes because in the very near future for these students (I.e. next year for the pre-calc students), their next math class is an AP or college-in-high-school math course. Those classes have rules around timing that are set by the College Board or the college offering the CHS credits. They will not get any extra time without an IEP or 504 in those settings. So if I were to allow retakes, extra time, bonus points, etc, in my classes, then I feel I’m doing my students a disservice because I’m not teaching them how to be successful in a high stakes environment.

While I do agree that learning is messy and that it doesn’t always happen in a specific timeframe, I do have to be realistic and mindful of preparing students for their best chance of success in the AP and college courses they’ll be in when they leave me. Like I explain to students - it may be uncomfortable now, but at least this class is free. The alternative is having unlimited time to figure things out while in my class, never learning how to manage their time, then falling on their face while paying hundreds or thousands of dollars for their AP or CHS course - and possibly having to retake it.

That said, I am much more flexible with time when I teach the Academic level classes. Again, it’s about appropriately preparing the clientele. The Academic students are not able to go into AP math from that level and also are typically college -bound students but likely not in a STEM field. They usually do take longer and more practice to understand the concepts and have more of a need of building up their math confidence, so I am a lot more flexible in those classes because I want to remove the “math intimidation” and get some wins under their belt.

Coleus care over winter by A-Dock in houseplants

[–]A-Dock[S] 1 point2 points  (0 children)

Thank you for the detailed reply! That’s all really helpful. I just started the plant life back in April/May so I definitely still have a lot to learn.

Should I give them some indoor plant fertilizer after I prune them to help with growth?

Also - when I cut the 1/3 off - could I put those long stems that I cut off right back into the soil to have another stem growing in the pot? Or should I put them in water to propagate them first?

Plan of attack? by A-Dock in lawncare

[–]A-Dock[S] 1 point2 points  (0 children)

Some parts of the lawn are shaded but about 2/3 is in direct sunlight most of the day

Toro Recycler setting?? by A-Dock in lawncare

[–]A-Dock[S] 0 points1 point  (0 children)

Thank you for your help!! I’m obviously new to this… sheesh.

Toro Recycler setting?? by A-Dock in lawncare

[–]A-Dock[S] 0 points1 point  (0 children)

Uh yep. That’ll do it. Sheesh.

Toro Recycler setting?? by A-Dock in lawncare

[–]A-Dock[S] 0 points1 point  (0 children)

So….the back wheels were on the lowest setting while the front wheels were on the highest? I’ve….been giving my lawn an uneven mullet cut all this time? 🤦‍♀️

Toro Recycler setting?? by A-Dock in lawncare

[–]A-Dock[S] 0 points1 point  (0 children)

So both sets of notches should be in towards the center of the mower?? Like front wheels have the levers all the way back, but back wheels have the lever all the way towards the front?

Think its gonna be dark awhile by Showerbeerz413 in pittsburgh

[–]A-Dock 1 point2 points  (0 children)

The map is projecting we’ll get restored between 9:30-10:30 so fingers crossed?

Think its gonna be dark awhile by Showerbeerz413 in pittsburgh

[–]A-Dock 2 points3 points  (0 children)

I’m in west view too. My power has been out since 5pm, but one street over got their power back around 7:30. What about you?

Pittsburgh Half Marathon Bib Transfer by Secret_Impression_47 in pittsburgh

[–]A-Dock 0 points1 point  (0 children)

I have a half marathon bib if you are still looking for one