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Math Word Problems (Or Forcing a Square Peg in a Round Hole)

My nine year-old has more homework than usual this week. That’s OK. Since I homeschooled my oldest sons, I know all too well how to teach a third grader, but every once in a while the explanation seems to elude me.  His weakest (and therefore most detested) subject is math, so I wasn’t surprised that he balked when we began the two pages of word problems. The conversation that ensued while we worked through the problems was actually quite comical.

Me (reading from the assignment): Write and solve a word problem in which you must find an unknown partner.

Aidan (a little confused): You mean like I have to do in gym?

Me (containing my smile): No, Honey. This is different. The teacher is asking you to create a word problem similar to the nine that we just worked through. Finding an unknown partner means you’re only given a portion of the information and you need to use math to find out the portion that you weren’t given.

Aidan: Does it need to be a subtraction problem?

[He sees no useful reason he should ever have to do subtraction, especially if it involves borrowing from the *neighbor*.  Wait until he opens his first checking account!]

Me: Let’s assume the answer is YES since the previous nine problems all involved subtraction.

Aidan (enthusiastically):  I know! There were 15 kids in costumes. Six kids wore ghost costumes.

Me (excitedly thinking he’d caught on quickly): Good, Aidan! I’ll write that part down for you. Now you need to end the word problem by asking a question. What would your question be?

Aidan (very confidently): The question part is really easy, Mom!  How many kids wore werewolf costumes?

Me (mental face palm): Ummm.  No. How could I answer that, Aidan, since there are still nine kids that I don’t know about?

Aidan: Easy. I could tell you.

Me (growing more confused than HIM!): Tell me what, Aidan?

Aidan: I could tell you that eight of the kids wore werewolf costumes!

Me: But eight werewolves plus six ghosts only equals 14 kids. I thought there were 15 kids in costumes.

Aidan (more than ready to make his word problem work):  OK. So let’s say that the other kid dressed as Darth Maul.

[sigh]

It’s fun to hear how Aidan processes things. He’s not a neuro-typical third grader since he navigates life with high-functioning Autism, but he is very academically adept. That said, our math lesson gave me reason to pause tonight to explain to him that somewhere in our conversation, he went off-course. It wasn’t about werewolves at all when we began the word problem, but once he introduced werewolves into the picture, he was focused on  making it work.

How often do we find ourselves doing the very same thing, whether it be with a school assignment, a work situation, or a life circumstance? After using a half page of paper on one algebra problem, it becomes obvious that the direction in which we are headed is not right. But who wants to rework that entire problem? It seems more time-efficient to chalk it up to a great, albeit failed, attempt and be thankful it was only worth five points while moving on to the following problem. At work, we find that the implementation of  a new product did not provide the company with the long-term benefits we anticipated. Rather than giving voice to this fact, we force the new product to fit into the business while we listen to our peers grumble under their breath. In life we find ourselves accumulating debt. As the interest becomes higher than the principle, we begin to realize that our credit card debt is too high, but it’s so much easier to open a new credit card and start with a zero balance than to reign in our spending habits and pay off the balance on the first card.

As we worked through Aidan’s math word problem that evening, we had to return to the base problem to ascertain how to best address it. Avoiding the problem, or simply adding new factors, was not working – no matter how hard he tried forcing that square peg into the round hole!

What are the square pegs in your life? Are you working through issues where you’ve introduced too many factors? Or are you simply ignoring that the issue exists at all? Unfortunately, the issues that are not dealt with remain, needing correction and seeking closure. Left open and uncorrected, they haunt us unceasingly.  Face the issues in your life; correct them; bring closure. It will feel fa-BOO-lous!

Philippians 3:13-15
Brothers and sisters, I do not consider myself yet to have taken hold of it. But one thing I do: Forgetting what is behind and straining toward what is ahead, I press on toward the goal to win the prize for which God has called me heavenward in Christ Jesus. All of us, then, who are mature should take such a view of things. And if on some point you think differently, that too God will make clear to you.

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It CAN Always Get Worse!

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How was your week? Mine felt unbearably long and there were many times I was sure Friday evening would never arrive – or if it did, I would somehow miss it amid the chaos of life. The proverbial nail was driven into the casket this evening as my six year old spilled his milk on the peanuts I had just spent two hours shelling while our four month old puppy pounced excitedly between his rawhide bone and the sweet, dripping kitchen table unsure which way to run in the 1.5 square feet of space available. Admittedly, bedtime could not come soon enough – if not for the young ones, for me.

OK. It can always get worse. When I’m tempted to feel tapped, I try to remind myself of that fact. For example, Rasputin, the iconic Russian religious advisor to the Romanov family, definitely dealt with greater grievances. Hated by many in a country where he held significant influence and power (not an unusual feat in and of itself), he experienced trials and tribulations beyond what I’d wish on my worst enemy. Rasputin was stabbed, poisoned, shot three times, clubbed, and drowned – and with the exception of the stabbing, it all happened in one evening!

I can’t top that. More importantly I don’t even want to try! Incomplete homework assignments, piles of laundry, sticky floors, dinner dishes, spilled milk, and puppy poo all plague my week, but I can tackle those consistent challenges that attempt to derail my days. And much like Rasputin, I don’t go down without a good fight. But his life, and subsequent death, serve as a stark reminder that it can always get worse!

So how did you say your week went?

I’m Normal. What Are You?

After a full day of playing with Legos, Matchbox Cars, Wii, and various outdoor toys, the time had come for Owen’s best friend, Alex, to go home. As we  entered the van for the fourteen mile drive, Alex chose to sit in the far reaches, the very back seat – because providing additional challenges in a conversation can make it extra interesting, right? As I chatted with Alex over the expanse of empty seats, our conversations flowed easily, especially considering Alex is only five years old and doesn’t really know me very well. We were, however, trying our best to listen to each other over the noise of both the engine and the road.

When Alex told me he was learning Spanish, my curiosity was piqued.  See, Alex is Asian – but beyond knowing THAT, I have no idea what Alex’s heritage is, so the following conversation ensued:

Me (trying to peer into the rear view mirror to occasionally establish eye contact):  That’s really cool that you’re learning Spanish, Alex.  What is your ancestry?

Alex (pausing, not quite sure of the meaning of the word):  Ummmm ….. I don’t know.

Me (trying to help him out with both an explanation and a prompt): Ancestry means lineage or where your parents and grandparents came from. Are you Korean?

Alex (quickly): No.

Me: Are you Chinese?

Alex: No.

Me: Are you Vietnamese?

Alex: No.

Me (now floundering as I was running out of options): Japanese?

Alex: No.

[Since Alex was so sure these options were not part of his ancestry, it struck me that Alex might KNOW his ancestry and I need only quit prompting him. So I continued my line of questions in a new manner:]

Me: If none of those are part of your lineage, then what ARE you, Alex?

[Alex’s reply was quick as a wink and sure as a boy could be, causing me to really hear his answer.]

Alex (simply):  I’m normal.

Touche, Alex.

Pause for consideration, Reader. How do you see YOURself? It occurs to me that we all too often view our differences in a manner that set us apart from others, in both a positive and negative manner. If you’re seated across from a potential employer in a job interview, that may be a necessity to secure employment.  More often, however, we need to look for commonalities that enable us to be ONE with each other.  At the tender age of five, Alex seemed to understand that commonalities make for both a confident person and a more peaceful community. Additionally, it is what Christ calls us to do.

1 Cor 12: 24-26:  But God has so composed the body … 25 that there may be no division in the body, but that the members may have the same care for one another. 26 If one member suffers, all suffer together; if one member is honored, all rejoice together.

Are you normal, Reader? It IS a more excellent way!

Knee-Jerk Notions

Gorilla Glue is probably one of the best modern-day inventions.  It seems to be an oft-thought of solution for a vast number of situations that occur in our household based upon it’s ability to create a permanent bond between an almost limitless variety of items.

When the top of my coziest slipper found it’s way free of the slipper’s sole last year, my first thought was … Gorilla Glue! Without any hesitation (or much forethought), I placed an ample supply of the product in between the two surfaces of my slipper. My second thought wasn’t far behind … Pressure! Knowing this product worked best under pressure (just like me), I decided to place my foot into the slipper and apply that pressure while I navigated through my Facebook messages that evening.

It worked like a charm. Really, it did. But it did MORE than intended. While it did, in fact, stick the sole to the slipper top, it ALSO stuck my foot to the inside of the slipper proving that this was probably not my most brilliant moment! So what went wrong? As I pried the outer epidermal layers from the skeletal remains of my right foot, I realized that there were definite drawbacks to swift solutions, even when the issue at hand was of minuscule magnitude.

After initiating my knee-jerk notion of using my foot to apply the pressure required of Gorilla Glue, these were the lessons learned:

  • The first solution is not always the best;
  • Some solutions can be more painful than others;
  • Planning for all potential outcomes is always wise.

Often I learn lessons without the loss of body parts. Other times valuable lessons are somewhat elusive, albeit more permanent than Gorilla Glue bonds themselves when they come with a cost. While I quite liked the sole of my foot as it was, I must admit … I enjoyed the softer, callous-free foot while it lasted.

Knee-jerk notion: Could Gorilla Glue double as a spa treatment?

Thinking Outside the (Crayon) Box

Owen, my sweet-as-pie six year-old, loves to be creative so it never surprisesme to find him sitting on the floor surrounded by crayons and paper, sometimes adding scissors and glue to the mix. Recently he invited me to join him as he conceptualized his next great feat of artistic expression. Quite often I look for an out, deferring him to one of his older brothers as a potentially better partner in craft. On this particular day, however, I decided to color with him, elbow to elbow.

Owen: Mommy, want to color with me?

Me: Sure, Honey. Could you bring the paper and crayons to the table please?

[He arrived at the table with the paper and immediately left the room in search of the crayons. It took him longer than usual to return and I will admit, I was growing a bit impatient as I sat there pondering what to make for dinner, thinking about the homework I needed to tackle with his brother, and feeling somewhat dismayed at the depth of debris stuck to my sock from the unswept kitchen floor. After quite some time Owen returned to the table with the crayons and a proclamation.]

Owen: Here are the crayons, Mommy! I broke them all in half so we wouldn’t have to fight over them!

(Sigh. We each took our half-set and began to color, him a bit more contently than me.)

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The first thought to cross my mind as we bumped elbows and noses while we colored was that I would probably only fight to the death over the yellow and pink crayons, at least one color of which he would likely have no interest in using anyway!  The second thought to cross my mind was that we would soon be buying a new box of crayons. Fortunately this was just a small set that needed replacing.

Looking at Owen’s actions in hindsight, a few thoughts pop out beyond the fact that I happen to be bugged by the chaos created by broken crayons. Owen thinks much differently than I do. Given that there is a vast age difference, that doesn’t entirely shock me – but I also see a difference in how he thinks in comparison to how I thought at his age. Growing up in a small town in a one-income household, possessions were both few and treasured. To break something of value intentionally would have been far beyond my comprehension of sanity and respect for personal property!

In that regard, many children today show a lack of appreciation for the items they own. Elaborate gifts for birthdays and Christmas have become the new normal, the expectation rather than the exceptional blessing they should be. Because they happen to be part of the modern day culture, for example, many teens feel that iPhones, game consoles, and cars are inherent to who they are, essential for their happiness, and indispensable in their daily activities. As a result, the value of the expensive toys, iPhones, and game consoles is lost, as broken items are typically tossed rather than repaired. Even those broken crayons have value though. They just await an art project of new proportion and different dimension.

On the other hand, I absolutely applaud my six year-old for his ability to both anticipate a problem and create a solution before coming to the table! Owen saw his limited resources and realized immediately that product distribution might pose a challenge. That showed ingenuity beyond the capability of many adults who are no longer able to think outside the crayon box.

I held my tongue that day deciding instead to instill in his being a sense of harmony as we colored shades of scarlet and tints of teal, creating a masterpiece previously unparalleled in his short history.

http://dailypost.wordpress.com/2012/10/15/weekly-writing-challenge-a-splash-of-color/

Owen

Owen

“Can I have a cookie?” he asks with a gleaming ice-cream grin!

[I’m guessing he doesn’t need more sugar!]

Fait Accompli: Vegan Pasghetti

For weeks now, my five year old has been asking me to make Pasghetti for dinner. Of course, he REALLY intends to say Spaghetti but has said it incorrectly for so long that we don’t even bother to correct it any longer!  We just join him in his mispronunciations!  😀

The only problem with conceding to the wishes of one kid, is that it typically runs contrary to the desires of another kid.  This was the case last night.

Owen:  Mommy, can you pleeeeease make Pasghetti tonight? We haven’t had that for a really long time!

Me: Sure, Honey. I’m hungry for pasghetti too!

Isaac:  Really?  Do I need to eat Pasghetti? Can you at least give me a small serving? You know how I feel about Pasghetti, Mom!

Thought Bubble:  “OK. It’s 2 p.m. and I have nothing else planned. I DO need something to feed the troops this evening and Pasghetti would be quick and easy. I’m going to count that as a consensus. After all, we got 2.5 yes votes. Curt and Aidan are not here so can’t really weigh in on the vote. And I consider non-votes to be YES votes anyway!”

Me:  Yes, Isaac, we’re having Pasghetti. Sorry, Dude, but it has been a while and the littles have been asking for it pretty constantly.

I walked to the pantry to take a quick inventory:  Ragu (Roasted Red Pepper and Garlic Flavored) – check.  Whole Wheat Pasta – check. Fresh Garlic – check. Mushrooms – check.

A full 90 minutes after that conversation, I got the dreaded phone call from my husband inquiring about dinner.

Curt: I’m picking up hamburger so we can have Pasghetti tomorrow night.

Me:  Ummm …. we’re having that tonight.

Curt: But we have no hamburger.

Me:  Correct.  It will still be good though.

Thought Bubble #2:  He knows the vegan in me won’t eat the meat version and he’s generally been very supportive of my choices. He enjoys most of my vegan dishes without complaint that they are free of dead flesh, but I’m sensing that he wants the traditional meat-laden Pasghetti. Ugh!!  I have nothing else planned for tonight and I am HUNGRY!

Curt: We could eat pizza and you could just have whatever you want tonight. Then we could make the Pasghetti with meat tomorrow night.

Me: (Sigh ….. and a very pregnant pause) I suppose I could have peanut butter toast before training at karate tonight.

Curt:  OK. Go ahead and make the Pasghetti tonight. I’ll buy burger for next time.  The boys and I will have pizza tomorrow night instead of tonight.

Thought Bubble #3:  Whew.  I hate last minute changes!

I DID make Pasghetti last night, hurrying into the kitchen to begin it before anyone with substantial input could change their mind!  Fortunately I also found a package of TVP (textured vegetable protein) in the pantry to give the dish the texture that the men were missing. I hadn’t tried it out in anything yet and was worried I’d create a dish so horrid that I’d never be allowed another chance with vegan Pasghetti!  Other additions to the sauce included fresh garlic and mushrooms, along with some additional flavors from my plethora of spices that are lined up in my spice cabinet alphabetically for quick retrieval.

In the end everyone gave it a thumbs-up …. even the naysayers that approached this dinner with fear and trepidation!   As I cleaned the kitchen and washed the dishes, I noted how very little remained as leftovers.  That was telling. 🙂  As was this comment this morning:

Owen:  Do we have any Pasghetti leftover for my lunch today?

Vegan Pasghetti  . . .  Nailed it!!!!!!!!