vonbon
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Posts posted by vonbon
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Threads like this are one of the many reasons I love this board. Most HS boards/groups I've been part of would have looked at me like I had two heads for asking a question like this and say it obviously doesn't matter.
I never thought to wonder about this...but I'm glad I know now! Thanks for asking it, OP.
Maybe this is one reason I'm not connecting with a ton of parents / homeschoolers IRL. :laugh: Two heads!
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On a phone so if this sounds curt my apologies.
Rows come first, then columns. So 4x7 is four rows of seven each. The multiplier is the number of rows, multiplicand is the number of columns.
So 4x1 is a column of four; 1x4 is a row of four.
Keeping this in mind helps in much higher math; I suspect knowing that it goes rows then columns would have helped me earlier as well.
The reason 3x4 and 4x3 can be different is because the numbers occupying the spaces in the rows and columns might be different. So if it is three cows by four cows, no biggie.
However if you have a matrix of cows and pigs, the arrangement could be different. Let's say you first ask your pigs and cows to line up (from a straight line) in three rows of five (3x5). They are in a line that goes pig pig cow cow cow pig cow pig cow cow cow cow pig pig pig.
The matrix looks like:
Pig pig cow cow cow
Pig cow pig cow cow
Cow cow pig pig pig
Is not the same as lining them up 5x3 from the same line:
Pig pig cow
Cow cow pig
Cow pig cow
Cow cow cow
Pig pig pig
Notice that even if you turn the second matrix 90 degrees to look the same as the first, the arrangement of cows and pigs is different.
This becomes important in statistics and computer programming.
I think I love this...It could be very helpful...
But I'll have to look at the multiplier / multiplicand and adjust this? Hmm....
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More importantly, who has 28 oranges? Did that many come in a bag? ;)
Looking at your picture, I would say 7 rows because rows go across to me (think crossword puzzle if nothing else) and columns down. But if I actually had 7 rows and 4 in each row sitting in front of me, I would describe it as 7x4. That's just me. I don't have anything to back this up, just this is how my brain works.
We'll be going into multiplication soon, just barely touched on it. We bought the Times Tales DVD download. So basically I'm saying I don't have a BTDT experience to share, just thinking that you may be overcomplicating it. Of course, I don't know what higher math is affected by swapping things. The highest math I took was trig.
Our friend has orange trees and brought us a couple of huge bags of them awhile back. I kept one in the garage because it had about 50 oranges in it and it's cooler in there. :laugh: We're finally through the second bag!
So yesterday at the breakfast table we did...orange math! We pretended to pick them, haul them to the table in a sack, and then we divided them up between ourselves. It worked well to truly let Division sink in to our brains and then we moved on the the concept of "Division with a Remainder" with the oranges, leaving an extra one as a remainder. My kids quickly said, "Yeah, but you can just cut it in half and split the remainder." So...that leads to another upcoming concept in Singapore: Fractions.
Math with Vitamin C!
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I'm going to weigh in on the "please be kind" part. You have asked an excellent question, and I want to encourage you to keep asking questions of this sort on these boards. You are doing your students a great service by being completely 100% clear on what is going on with even these basic operations. Good for you! If you encounter another topic along these lines, please keep asking; the pp's and others will provide lots of great ideas.
I'm going to add another bit that may or may not be helpful. In addition to arranging your counters into a 4x7 array, you can take those same counters and arrange them into a 2x14 array. Or a 1x28 array. Because all those operations provide the same result.
Have fun and go deep whenever possible!
Thank you! "Please be kind" is because I have a tendency to "go deep" in many areas of life and it can tend to drive people a bit nuts, especially those who are more pragmatic or who do not want to or don't have the time to slow down and analyze or ponder. I prefer not to skim the surface with most things. I understand that this tendency can be tiresome to some and sometimes I sense that it can be taken as being pretentious. That's not my motivation--I don't have time for that! ;)
When I can clearly conceptualize things in my visual brain and grasp them through and through on a deep level, it gives me more confidence that I'm teaching correctly and laying a good foundation of number sense with my kiddos.
We are just getting into this: "In addition to arranging your counters into a 4x7 array, you can take those same counters and arrange them into a 2x14 array. Or a 1x28 array. Because all those operations provide the same result."
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My DS has also recently started multiplication and I've found it easier to teach that the first number is the number of groups. That's because I want him to really focus on the groups, not the amount in each. Since we are also doing division at the same time its helped to remind him to separate the number into groups. Groups, groups, groups. I'm finding it helps to separate his thought processes away from adding and subtracting to thinking in groups by always saying the number of groups first. When you look at a picture or real life arrangements you notice the number of groupings first. So, first number is groups. Later when this becomes more automatic it makes sense to explain it both ways, or either way.
Are you in Singapore 2a? IIRC, the illustrations went both ways, at least it seemed that way to me and how I naturally looked at the groupings.
BTW, I'm not an expert and this is my first child. Its just what I've found to be true for the very beginning of multiplication/division.
I like what you and other posters are saying about groups and then what's contained in each group, I get "Milk x 3"; very helpful example (above.) This is helpful. I'll try to phrase it that way: "We have 4 groups and there are 7 in each group." I can see using this verbiage too: "Seven groups of four." It's probably best if a student can hear it said or see it written all sorts of ways and get the concept.
We're just a few units into Singapore 2B. I like it a lot, but sometimes I go "off road" and use manipulatives, Family Math, or just fun, real-life examples or what I call "story math" (outrageous word problem stories with silly drawings and colorful characters made up on the fly) to get away from the pages upon pages in Singapore and to casually "test" a bit and see if DD truly understands what she's learning there. I get a bit restless using just straight Singapore TM, text, and workbook.
No expert here and this is my first child as well. :)
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Yes, the labels will matter. The dependent variable is graphed on the y axis and the independent variable on the x axis.
Y is a function of x..or y depends on x, symbolically y=f (x). The elementary teachers here do discuss that in words with those who are interested when they do their data unit, without going to symbols.
OK, I remembered something like this. Probably from research work (science degree but haven't worked in that field in a long time.) And now I'm remembering that this doesn't come up until middle school / high school math...so we have a while. :)
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(Note: in equally many places, 4x7 is read this the OTHER way, to mean "4 taken 7 times", or "4 sets multiplied by 7", so in this version, 7 is the multiplier and 4 is the multiplicand (set)). So reading it either way appears to be correct; just teach it consistently to what fits with your math program. It appears the way I initially labeled with multicand 1st and multiplier 2nd is more typically US; labeling with multiplier 1st and multiplicand 2nd is more typical to UK and Canada.)
Great! Thanks for this as well. I didn't want to confuse people, but I almost put this as part of my question in the OP. It seems like sometimes I'll come across a video or website or something out of the UK on math and will hear them say things in an opposite order than commonly said in the US. So I guess you have to consider the source and the way it's phrased.
We're using Singapore. I'm sure the TM goes into this somewhere, but I really appreciate the replies, as it's saved me a lot of time trying to find a reputable source that addresses this exact issue for both primary and higher maths.
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Technically, yes, it does matter. And it comes into play in higher math levels. For a seven-year-old (am I reading that right?), it really doesn't matter, and actually, learning the fact that multiplication is commutative is a good thing to learn at that age.
OK, super! Thank you! Yes, she's 7, so my question is probably more to put my own mind at ease and make sense of it. This has been nagging me for about a month now. Reading your response, I see that I can probably let this go for now unless I'm writing out or setting up an array with manipulatives. Then, I might as well be accurate about it. But for DD, I will focus on getting the commutative property across.
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Not a mathy person, but I'll just toss in that while the product (answer) is the same, the order does mean something a little different -- the first number is the "multiplier", the second number is the "multiplicand" (set):
Lovely! Thanks, Lori D. I was googling earlier today to figure out those labels: multiplier, mutiplicand. I knew they existed--just couldn't remember them. I'll go back and read your entire response more thoroughly. Thank you!
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More to the point of the OP's question, when dealing with multiplication at this level, whether it's written 4x7 or 7x4 doesn't so much matter from a pragmatic perspective - the product is the same. However, at a deeper conceptual level, it's nice when the student actually understands that "4 groups of 7" (4x7) is distinctly different from "7 groups of 4" (7x4).
This sums up my question exactly--thanks. I think on "a deeper conceptual level" about many things in life. Somehow straightening this concept out in my head will help me teach my daughter, even if she doesn't yet need to know it. Thank you!
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Hello Fellow Boardies!
Can someone who loves math help me out with this? DH7 and I are exploring multiplication. She is understanding the basics and figuring problems out with a variety of methods (mental math, adding, using counters, counting by 1's, 2's, 5's, fact memorization, etc.) I kind of let her arrive at the answers in her own way and then introduce other possible ways of solving things.
When I lay out counters in an array or write out a problem, does the order of the numbers matter?
For example, we have 4 boxes with 7 oranges in each box. Should that be written 4x7 or 7x4?
I know that for the answer / product, the order doesn't matter (Commutative Property.) But I would like to be labeling things accurately if it will be important for her in higher math concepts in the future. I am trying to lay a good / accurate foundation / number sense.
How would you label this array below in regards to rows and columns? I would say this is 7 rows and 4 columns. 7 rows with 4 in each row. So would it be incorrect to "label" it on paper or with words as 4x7?
x x x x
x x x x
x x x x
x x x x
x x x x
x x x x
x x x x
Does it matter if you label it 7x4 or 4x7? Is it just a matter of personal perspective? Should I be matching up rows/columns in arrays with how the problem is written?
Also, when you begin to talk about columns and rows (like in populating tables via Excel data or the x and y axis) at some future point, will the order of the numbers matter? Or would one just assign the labels of X and Y to the data and plug it in accordingly?
I might be mixing concepts--sorry. Please weigh in with any helpful thoughts and please be kind. I've never taught 2nd/3rd grade math before and I think I'm mixing in things from basic up through college math and science data. My main goal is to lay a good foundation for future math but I'm not super-adept at higher math myself. It's all a bit fuzzy. Thanks.
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I agree that fall is a really pretty time on the Coast.
The North Coast seems to lend itself to roadtripping because some of the beauty is just going along and seeing what seasonal things you happen upon. Could you spend a couple nights here and then another couple there, for example? Many of the towns north of SF are really intriguing, unique, beautiful, and worth seeing (including Santa Rosa, IMO) but most tend to be smaller than Santa Rosa and, for most people, I think you're not going to find 6-7 days worth of things doing in any one small town. To me, the beauty is in seeing the region vs. staying in one spot.
If you don't want to drive a ton, you could use Santa Rosa as a hub and do some day trips to Sonoma, Napa, Petaluma, and also to towns around the SF bay or use 1-2 days in towns around SF (Sausalito and a Bay cruise, for example.) There is lots of hiking, kayaking, etc., as another poster mentioned. You can arrange trips for freshwater or ocean/bay kayaking. Pt. Reyes is a must-see, IMO. Lots of wildlife and rugged coast mixed with lighthouses and pastoral farms.
I wouldn't rule out the wine country even though your daughter is 17. There are a lot of historical and artistic aspects that are interesting to anyone of any age. In many wineries, there's a lot to see (caves, art, architecture, etc.) that appeals to people who are not wine tasting. It's very beautiful country and there is a lot to see from an agricultural tourism standpoint (grapes, small farms.)
If, on the other hand, you are not opposed to driving some miles (like 4 hours up), you could consider heading further north to the Lost Coast and the Redwoods. Obviously a ton of natural, wild beauty, hiking, and majestic trees. Eureka is kind of a hub for some wildlife enthusiasts, as there is a university there with zoology/natural resources studies, a research vessel for marine biology, and it's surrounded by marshes with visitor centers for bird watching. You can see some of the best redwoods and elk north of there. Kind of a haven for a true biologist type who likes spotting and checking out wild things (like my DH.)
You can't go wrong with Santa Rosa as a starting point. You'll find lots of beauty and fascinating, new experiences on your trip! The hardest part will be shoehorning it all into 6 days! :)
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I re-read your post. One trick I use is, if we buy junk food (rare), I have DH lock it up in his work truck, which requires a key and walking a ways in the dark at night...flashlight, shoes, etc....All of that adds up to a good-enough barrier to generally keep my paws off of it. Is there some way you could "hide" that stuff from yourself at work? That's hard if it's in a common break area-- Out of sight/out of mind?
A co-worker of mine used to grow his own vegetables. He'd bring in humongous bowls of fresh green peas in the spring--best work snack ever! He'd bring in carrots and other fresh stuff from the garden and put it in the common area. People loved it! Maybe you could counteract things by bringing in veggie trays so it's not all junky stuff?
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When I exercise really hard and fairly consistently, the bad food doesn't appeal to me as much and I'm not as hungry in general. I actually end up craving healthy stuff (lettuce, broccoli, apple, etc.) and water after a workout. I also crave lean protein and fewer carbs. Fatty, sweet stuff doesn't really appeal when I'm in good workout pattern and actually tends to gross me out.
One thing that stands out is that the workouts have to be pretty thorough and challenging; for me that means working out with other people. I wouldn't push myself hard enough alone. Just walking (though good exercise) doesn't seem to have as much of an effect for me craving-wise, though some exercise is definitely better than none!
This type of healthy craving never happens when I'm not working out. Meaning, I don't find this to be true when I'm sedentary. If I get into a sedentary pattern, the further away I get from consistent exercise, the more I start to crave bad stuff. Bad stuff begets more bad stuff and I'll yo-yo between sweet and salty. Caffeine seems to cause me to crave sweets when the buzz wears off.
I buy bulk packs of gum and mints. Sometimes I'm not really hungry and that's enough of a sweet.
From experience, I think shift-work and insomnia or lack of sleep play a huge part with hormones and cravings. There are some good TEDtalks on sleep deprivation; very informative, good info and I think shift-work and cravings were mentioned.
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Oh, I just saw pinkmint's post; sorry.
Yeah--agree with a few posts above too...I don't tend to get struck to deeply emotionally when a celebrity dies because I never knew the person.
But I do think he added a unique flavor and style to the field of music. I suppose when someone passes, people tend to reflect on what contributions they made to the world.
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Didn't read all of the replies, but wanted to add that I read an article that explained why there are not very good YouTube videos, in general, of his music (other than the fact that most of his popular music was released before YouTube existed.) Apparently, he was very much in favor of privacy and copyright laws. It stated he was very opposed to the sharing/ripping off of music on the internet, bootlegged videos, and was not a fan of technology (iphones, Facebook, etc.) other than the technology he used to create music. So, in those ways, I think he was a very artistic person and probably did most/much of his work for the pure art form that it was, vs. placing more emphasis on commercial gain. Refreshing, considering all the things happening in "music" now that basically equate to $$$ vs. any real, unique talent.
Also, the article stated that much of his art has never been released.
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More votes for the following previously-mentioned spots:
Capitola / Aptos / Soquel with Manresa, New Brighton, Rio del Mar, and Sunset Beaches in those areas. You can camp at some of the beaches in the area, but would need reservations pretty far in advance, normally. There is a wide range of hotel and beach house options, from resort-style $$$$ to Best Westerns at $150 to $200-ish/night in the high season to cheaper, seedier mom-and-pop motels. You can easily access Monterey from these areas (40-minute drive), which has great tidepooling spots that are fascinating but not for swimming, and of course, the Monterey Bay Aquarium.
I've never stayed at these, but they're intriguing and right on/at the beach/pier at Capitola:
Capitola Venetian Hotel https://en.wikipedia.org/wiki/Venetian_Court
Avila / Pismo / Morro Bay I'd say the same for these for accommodations--a range of quality and rates. Pismo Beach is like 13 miles long or something and popular with campers and 4x4 people (jeeps, motos.) The beach area around the pier is classic laid-back California with surf shops, clam chowder, swings on the sand, people fishing from the pier, kite-flying, etc. Avila's been updated in the last several years with more upscale shops. It has a smaller, cute pier and the beach is nice for bonfires, etc. Morro Bay's got a harbor with sportfishing charter boats and some nice beach for walking, driftwood hunting. IMO, they're all unique and beautiful.
I grew up near and went to college in these areas. You will see 4-year-olds splashing and playing the water for hours at a time. The Pacific is cold, but you can boogie board, shell hunt, and play for a long time without truly getting cold. YMMV but we've always found that the cold wears off and somehow you develop an immunity to it after a bit of time/exercise/playing. For surfing, yes--wetsuits.
Most of the hotels I've seen on the coast have a swimming pools/hot tubs.
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'Hue' brand available on Amazon. IMO, they're not "cheap", but they are the things you listed. I air dry them so they don't fade.
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I'm considering beginning Latin either next year or at some point in the future with my 7yo. Looking into various curricula and reading old threads to gain some insight...
Song School Latin's site says it offers both Classical and Ecclesiastical pronunciation options in/on all books/audio/video products.
Which pronunciation have you chosen to study and why?
I'm also curious about our exposure to Latin in church (Catholic.) Some songs are in Latin and, after previewing some of the SSL DVD chapters online, it seems that the Ecclesiastical pronunciation is what is used in church (sorry if that's stating the obvious.) Can anyone confirm this?
If we chose to go the Classical pronunciation route, would my daughter's experience be like mine in church? I'm fluent in Spanish so I recognize some of the Latin words in songs and writings but I've never studied Latin itself so I don't know how to actually pronounce them. Or would it be better to choose Ecclesiastical so that it matches up with what we sing in church? (Hope this makes sense--)
What about professional applications in the long run (science, medicine, theology, law, etc.?) Or learning romance languages? Is one pronunciation better than the other?
Thanks for any insight!
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Well, I thrive on novelty. The most energy-creating, happiness-inducing situations and skill sets for me are those that I am encountering or acquiring for the first time-- It's a bit like controlled, happy mania for my brain.
Once I figure something--anything--out, then it's like, "Meh...next." It just kills me to do some things the same way twice. I suppose I do follow some routines because they're proven and help me to focus amidst distractions (like paying bills, washing the car, etc.)
Maybe seeking novelty covers up weaknesses and fear of commitment, etc. It does make it hard to "master" things. But at the same time, it's just so darn fun to do things in new ways.
I almost never make the same recipe twice and many times just gather up appealing ingredients and sort of cook in a "choose your own adventure" way. Drives my foodie-gifted-cook DH nutso. Sometimes I really don't even know what it'll end up being until halfway or most of the way through. If I use recipes, it's almost always to combine 2-3 "ideas" and make it my own way.
Many things in life are this way for me. To do otherwise (to follow a path I've already taken) can feel like death sometimes. Just can't bring myself to do it one.more.time that way. Even in simple things like mental math or cleaning the house. It's just sort of a soul death to repeatedly follow a routine.
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Ditto on FLL and WWE together--really enjoying it. You might check out another thread currently going on, as there's been some discussion of FLL/WWE:
http://forums.welltrainedmind.com/topic/602328-la-quandry-for-2nd3rd-grade-anyone-else-in-this-boat/
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Just want to list 2 titles that are really helping us "newbies", in case anyone else might benefit from them. They're pretty good resources, but consider the ages of my kids with the first one (7 yo, 4 yo), as it might be a bit basic for older children or those more experienced with the Mass. The second book listed is great and straight-forward, an all-in-one place to find prayers; I'm going to use it for myself too:
A Child's Book of the Mass by Puntel and Roberts
The Catholic Children's Prayer Book (Saint Mary's Press)
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The above description of Abeka is intriguing...will have to check that out because I've sort of longed for something that was all-in-one vs. my eclectic approach that takes more time to prep.
And now I'm worrying about the "jot and tittle"!!! :ohmy: Is that the problem--DD is not going to retain a bit of this FLL? Hmmm..... :huh:
(following)
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Help me brainstorm about school next fall - please be gentle
in The Chat Board
Posted
I'm sorry for what you're facing. I don't have a reply to help, but wondering if you might receive more ideas from the Learning Challenges board or General Ed board vs. Chat?