You're comparing different things. In the ratio 2 girls : 3 boys, the fraction form is 2 girls / 3 boys. What you're thinking of is a ratio of girls to students: 2 girls / 5 students So 2/5 OF THE CLASS is girls and 3/5 OF THE CLASS is boys. 2/3 here is just girls to boys - not to the class. HTH... units are really useful!

Those "safe places" are dreadfully dangerous. They're the Bermuda Triangle of the house! I believe ours is still in the amazon box hanging out in our bedroom. We have so many amazon boxes hanging around, it's great camouflage. Could that be an idea?

I agree with this. Unfortunately, I hear so so so so many times from my students (I teach developmental math at a cc) that they are just told the mnemonic and not told why. In some cases they've been told things completely wrong (I heard from a district math specialist that she SAW a teacher tell students they didn't need the distributive property because they could use order of operations.) I see PEMDAS as a mnemonic introduce problems - even with slashes: P/E/MD/AS. It may be just given the type of student I see, but I shudder any time I hear someone say PEMDAS. Some students manage to use it correctly - but we're only talking about 4 steps to remember. I don't see a need for a mnemonic for that. (And I see the problems with it every semester!)

I've seen it really cause problems. I've had students argue with me about it because MD means multiplication first. It's slower to walk through the steps... but the mnemonic can get them in trouble later. Don't put up roadblocks... even though you are tempted now! Purplemath is also a good site for explanations. Some of math IS simply that "common agreement is this, so this is what it is". I recently read an explanation/discussion of order of operations that strongly disagrees with the way I explain it given that it breaks down with numbers like fractions, decimals, and irrational numbers (you can't talk about multiplication as repeated addition for instance). But I think that looking at order of ops as shortcuts helps give a reason for WHY the convention is what it is and not "just because" :) (And I just managed to multiquote! Yea! :D)

I explain it as shortcuts. This works at a basic level... there's a bit more to it higher up - but this explanation works for getting an understanding of why. Say you have 5+3x4 We do the multiplication first since we see multiplication as a shortcut for repeated addition... so if we were to expand the problem, it'd be 5+4+4+4 Exponents are a shortcut for repeated multiplication, so you'd expand the exponent as multiplication, then expand it as addition. Parentheses (or symbols of grouping) simply say DO THIS FIRST! So, order of operations is (1) Symbols of grouping (DO THIS FIRST!) (2) Exponents (shortcut for multiplication) (3) Multiplication and division as they appear left to right (multiplication is a shortcut for repeated addition... and division doesn't exist... only multiplication... which is why you'd do division before multiplication when reading left to right) (4) Addition/subtraction left to right (similarly, subtraction doesn't exist...only addition (define subtraction as addition of the opposite)). Thinking of the operations as shortcuts does help with WHY the order is what it is - and I really hate the mnemonics because they don't explain why at all - and they have students arguing multiplication before division rather than seeing them at an equal level.

Yes, you're overthinking this :) A ray is defined by an endpoint and ANY other point on that ray. In your example, you have ray XT and ray XB making up angle TXB. You could make a case that this is the only angle in the illustration based on the definition... but I've never encountered this. Instead, you'd simply talk about rays XT and XB and wouldn't use points A and S since they're irrelevant for the angle. The angle is made up of rays XT and XB - NOT AB and ST because an angle has to have the rays at the common vertex. A ray is defined based on two points with one as the endpoint. (points are undefined) So in your example, if you wanted a different angle, you'd just use rays XA and XS (for instance) to get angle AXS. It's all in the definition. From the points you mentioned, you can construct any number of rays... but only some of them will form angles. Based on definition, I'd argue then that with ray AB and ST, you don't have any angles since you don't have a common vertex.

Mathematically, it is correct that an angle is defined as the union of two rays - definitely NOT line segments. (Confirmed in two of my texts. As a general rule, use the definition of the text you're using...as long as it's correct... some things are in flux - like the definition of natural numbers or whole numbers.) However, both definitions I have have the angle emanating from the same point, so it would NOT make sense to have the two rays not having the same endpoint. Sounds like a poor illustration and bad example. You'll talk about angle A from rays AB and AC (with A as the endpoint of each ray) or about angle BAC or CAB, but they do have to have the same endpoint.

It was tough when we started it. For a couple days I made my son do the problems with base ten blocks to SEE what was happening. Then I let him use the algorithm but any errors and we'd be back to the blocks. They really helped.

I got the Extra Practice books for 3 and 4. My son needed extra practice with long division in particular. I don't think the EP books have enough extra problems though, so I've been also using Spectrum workbooks. I've bought materials for 5 and decided to try the Tests book instead of the EP books. I think that'll work a bit better for us. I don't intend to do all the tests. In some cases, I may not use any tests. I think they may be a useful reference and provide some extra practice at a similar difficulty level to the text. If the cartoon characters are an issue, you might cover them up with a post-it before starting any of the work.

:grouphug:

Not me :(

Thanks for posting. I knew my husband understood me when he bought me Crystal Line without asking me... he saw it published and knew I'd want it. Crystal Singer is one of my favorites of hers.

Even if you view the Bible as completely literal, how do you handle the fact of translations? That's what I just DO NOT GET about literalism. My folks are both ministers (ELCA). They both had to learn Greek to read the New Testament and my mom has a study Bible that has four side by side translations. For me, this is just a huge disconnect.

I haven't heard anything... :toetap05:

:iagree: (apart from 2nd ETA) :) I let my son read Ender's Game and he was able to handle it fine, but I wouldn't let him read Hunger Games yet. I think they're good books, but it'd disturb my son for now. It is a series I'd recommend prereading.

Your undergrad degree is what my husband majored in... way back when there were the Big Six accounting firms. (We went to UCSB. Miss the bike paths something fierce.) Two weeks before graduation he said he wanted to switch to a film studies major. :glare: I managed to talk him out of that one. He's much happier working with computers than he would have been with accounting.

:lol: I managed to stick it out... but it was touch & go for a while! I was ever so unimpressed by my education courses. (I do hear that some programs are good, but from my experience, I'd be in favor of doing away entirely with colleges of education.) Undergrad: math & English majors Grad: MAT - math (Masters of Arts in Teaching) Yeah... I at least avoid the questions of "Are you qualified to teach?" or "How will you handle upper-level math?" Still get socialization ones though!

:iagree: I got the book about a year or two ago because someone posted saying it had one of the best recommendations on how to keep a lab notebook. I like the back & forth discussions too. It helps me think through things I may not have considered otherwise.

:iagree: And if you look at the WWS samples, if your child were able to do the work there, you wouldn't need to be doing WWE - they'd already have those skills.

:toetap05: Thanks. Just spent time on youtube. Dratted additional links. Grump. I just bought one of his Teaching Company series. Really looking forward to it.

Our library has it... I'm 5 in queue. Thanks :)

I'm getting some of that by learning Latin with my son. Would math be a topic that interests you? Discrete math is a branch that has some questions that are pretty simple but that draw you in.

I don't know how well it might work for you, but I've been very pleased with Pearson's MyMathLab software. It's the same that's at the Interact link. They may or may not have something similar for working problems for physics. I have seen students who do the homework do better in the course. Of course, I am working with lower-level students (no courses that are transferable), but the program does avoid the issue of students just copying. And I also assign quizzes that are basically pretests. The questions are shuffled around and student scores on tests are generally within 10 points of a quiz score.

Update... I sent an email this morning and got a reply... They're planning on shipping either tomorrow or Monday. Thought those of you waiting might like to know :)

No! No! No! No nuts in our house AT ALL!!! This completely ignores the request NOT to bring anything and would put my child at risk. Don't cross that line. And unfortunately, some allergies ARE that severe that this would result in an ER trip.