Ahhh summer is here!  Well not officially for a couple weeks, but the strawberries are ripe and fresh corn has been spotted in the stores. We saw this sign at a local farm stand:
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I decided I’m going to wait for corn prices to come down a little before we buy some, and moved on to the next produce display. Wanda stayed back to study the sign for several minutes and finally asked “What does that mean?”  What is obvious to an adult can be such a puzzle to a 5-year-old. Upon closer inspection it hit me that this sign is a multi-faceted math learning tool for kids! Here was an opportunity to talk about money, fractions, adding, multiplication, rounding, and decimals, not to mention the concept of a “dozen”. Wow!

Step by step we read the prices and I explained what each line means. We talked about how a price that ends in “.99” should always be rounded up to the next dollar. She thought it was so weird that they don’t just sell it for 4 dollars or 7 dollars (I agree with Wanda).  I asked her to figure out if you pay more or less per ear of corn if you buy a dozen or a half dozen. This was a tough problem, so we worked it out together. Again, she thought it’s so weird that the more you buy the less you pay per piece of corn. Now there’s a great lesson in marketing as well as math!

This brief but educational exchange at the farm stand is the perfect example to support my “math is everywhere” mantra. I encourage you to look around next time you go out with your kids – whether it’s the farm stand, grocery store, gas station, the mall, or even a walk in the park. Can you find signs like the one we saw for corn? Can you see geometric patterns in the things you see in nature? Does your child know what all the different numbers at the gas station pump mean? These everyday activities are all opportunities for mini math discussions. Once you start to incorporate these math conversations in your day, you may soon find your child will do the same. So go ahead and call me corny, but I really believe every 5 minutes you spend doing math with your child really counts! π
 
Kids are fascinated by big numbers. “What comes after a trillion?” “How much is a zillion million?” “What’s the biggest number in the world?” “Is there such a thing as a kajillion?” Even kindergarteners are often familiar with “infinity”. Did you know a one followed by 100 zeroes is called a googol? 

Well, my daughter set out to write down one of the largest numbers in the world. She started right after breakfast:
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As you can see it starts with a 1. She was so determined to keep writing this huge number that she nearly missed the bus. That was not pretty. She ended up taking the paper to school so she could finish it during free time. By the time the afternoon bus dropped her off I had forgotten about the Big Number but the first thing she did when we got home was announce “I finished my number.” Here’s the rest:
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Now that’s a lot of zeroes! Looks like she was losing steam near the end, but no one can deny she achieved her goal of writing a really big number. I can only imagine what her teachers thought of this little project. In any case, I found this amusing (minus the morning fight just before the bus came), and I certainly admire her stubbornness determination to complete the task.
 
So, what is your child's concept of a "really big number"? Here's a homework assignment: ask your child(ren) to write or draw a picture of a really big number and see what they come up with! If you get an answer you'd like to share, leave a comment (don't forget to include your child's name) or send me an email: jennifer@mathmeup.com. Have fun! π
 
Ramona is learning how to write her numbers. After you get past zero and one though, they seem way more difficult than letters! As I mentioned in the previous post, her current focus is the number 3.  I watched her get a lesson from Dad one day:
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A few days later I was making lunch and she ran to the kitchen shouting “I made threes!” Here’s what I saw:
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I thought this was an adorable effort, but couldn’t help but mention that, well, they’re all backwards. I thought she might argue with me (she’s 3 years old after all) but to my surprise she accepted that there’s room for improvement here. Ramona loves to trace things, so I made some “dotted” 3’s for her to practice writing them this way:
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I don’t have all the pictures to prove it, but let’s just say we’ve been practicing 3’s diligently for awhile now. Most of this practice is self-motivated because Ramona actually enjoys writing (probably a result of constantly wanting to catch up with the bid kids). She often sits on her own to make letters and numbers, so don’t get the impression that I make her do this stuff!  Anyway, I think she finally got it. To verify, I asked her to draw me some 3’s this morning:
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Yep I think she got it! Next up, number 4...  π
 
I bring you another car activity today. I think I need to start a new category for “Car Math” because lately this is the place we end up having some of our most productive math conversations (and plenty non-math conversations as well, we just drive around a lot…*sigh*). First, I bought these window crayons:
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Then, I put them in the car and forgot about them for a couple weeks.

Then, one drizzly day we had a 15-minute window of wait-time in between school pick-ups and I remembered about the window crayons. Brilliant!

When I showed these crayons to the girls their faces lit up like the sunshine that was missing from our skies that day. When I said yes, they are allowed to draw on the car windows, you would have thought it was Christmas morning right there in our minivan. They were so ecstatic! Not wanting to break the celebratory mood, I hesitated before asking Wanda “Do you want me to write some math problems on the window for you to solve?” To my surprise she answered “Yeah!” and at that moment I too felt as if Christmas came early this year. So, here she is working out her problems:
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Her sister joined in the fun too. We’ve been working on the number “3” so she practiced a few times:
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When the math lesson was done, I let them go crazy and draw whatever they want.  We only spent about 5 minutes doing math/number activities, but it was completely painless and the girls were happy to participate just because of the novelty of the window crayons.  Since they were so enthusiastic about doing the math, I didn’t mind letting them ‘express themselves’ with the Window Crayons for the remainder of our wait. I should admit though, when it was finally pick-up time I could barely see out the window behind me!

Yeah, the windows were a mess, but a little Windex took care of the “art” later that day. It was a good excuse to wash the car windows anyway, no doubt they needed it! π 


 
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This one snuck up on me, but it’s been a great way to pass time in the car and sneak in some math skills. Like most moms, much of my day is devoted to drop-offs, pick-ups, practices, lessons, etc., so we are in the car more than I care to admit. A few weeks ago on the way to gymnastics we decided to keep track of traffic lights. This wasn’t a planned activity. It was actually Ramona who pointed out we hit 2 green lights in a row, and from that point on we tracked traffic light colors all the way to the gym.

Would you believe there are 17 traffic lights between our house and gymnastics class?! Sheesh! On that first trip we counted 9 reds, 8 greens, and 0 yellows. On a subsequent trip we counted 7 reds, 9 greens and 1 yellow. We now know there are 11 lights between Preschool and Target, and 10 lights between home and Kindergarten. Boringly, there’s only one light between our home and the local elementary school (and it’s always red when we get there!).

There’s so much to love about this light-counting game… where to start ?!

1.      Counting light gets everyone engaged in the same activity. This just feels way more positive than the bickering that tends to erupt in the back seats when we aren’t working together.

2.      Light counting gets your kids actively involved in data collection. It’s not trivial to remember the number of greens, reds, and yellows while you’re on the road (try it!). It may be easier to assign a color to each passenger. For a longer trip you might need to keep a tally with pen and paper (preferably not the driver). You could even keep a log in the car to compare results after making the same trip several times.

3.      Within a few trips your kids will have memorized the total number of lights between your home and all your common destinations. Not that this is important to know these things, but I find many kids enjoy this sort of trivial information.

4.      Counting lights provides a nice segue into the world of data analysis and statistics. Once you have counted reds, greens, and yellows for the same trip several times, your kids will develop expectations about how many reds, greens, and yellows are typical. Help them determine the average number of red (or green) lights you encounter for each trip to soccer practice. Then ask questions like “What do you think are the chances we’ll get all greens today?” Or all reds, or only 1 green, or 3 yellows, etc.? Watch your children transform into budding statisticians!  

Now that we’ve become a traffic-light-counting crew, the kids actually get upset when we forget to count. They get excited when we go to a new place and can track lights on a different route. They cheer for the color they’re in charge of counting. Have you ever felt relieved to get a red light? This game can make you feel that way! And of course, the thrill of hitting the rare yellow light can be so exhilarating.

Best of all, traffic light counting is for all ages. Even if you don’t have kids, or your kids are in high school, just try it on your next few trips. You may be surprised how easy it is to get caught up in this simple diversion. π 

 
Hi my friends. So sorry to leave you alone for so long. The preschool newsletter is done. I can move on with my life! Here's a little post that has to do with big numbers:

Seven Billion
I found this poster inside a National Geographic magazine on our coffee table:
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We don’t subscribe to National Geographic so I don’t even know where it came from, but anyway this fascinating picture is called “The Face Of Seven Billion”. It is actually a sort of chart. The face you see is made up of tiny human figures, 7000 of them to be exact. Can you see it better here?:
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How about now?:
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Each human figure represents 1 million people. 7,000 of them together represent the 7 billion people in the world. Yikes! So many people! Let me tell you, the kids actually “got” this. Well, I take that back. I don't believe they grasp the magnitude of 7 billion, but they "got" how the chart works and they know that there are A LOT of people in the world. I explained the poster to my 7-year-old one time and he understood it well enough to repeat the meaning behind the chart to his little sister who also “got” it for the most part. The 3-year-old, not so much….

I commend National Geographic for creating this interesting, informative, and artistic presentation of our world population, in a way that is impactful even to a child. I must tell you that the back of this poster contained so many more intriguing facts and charts. You really should check out the interactive version on the National Geographic website.

By the way, the arrangement of these 7,000 tiny people creates an image of the most “typical” person on the planet who happens to be a 28-year-old Chinese male. When my kids stepped back and saw this face for the first time they exclaimed “It’s Daddy!” OK, it kind of looks like him, but in fact he’s much older than this “typical” guy. And for those who know “Daddy” I think you’ll agree with me he’s anything but typical! π
 
Is there some law of nature that states as soon as winter is safely behind us, our calendars must automatically be filled with countless activities, meetings, classes, conferences, sporting events, trips, and celebrations? Everyone has come out of hibernation to make up for all that winter downtime. Due to the sudden upswing in activity around here, I’m a bit backlogged on my writing – so much to blog about, so little time! As soon as I get the Kindergarten newsletter done, I’ll have more time to document the math we’ve been up to.

Despite our busy-ness, we still find time for numbers. Just for fun, here’s a glimpse into a typical morning around here – “arts & crafts” with Ramona:
Enjoy! π
 
We have short bits of down-time between weeknight activities. On Mondays everyone is home from school by 3:45pm and we have to leave for Karate at 4:10. On Wednesdays we’re all home by 4:15pm then we depart for gymnastics at 5. Normally this in-between time is spent doing homework, playing, snacking, making dinner, whining, fighting, etc… but sometimes all our “stuff” is done and we’re left sitting around waiting for departure time.

It’s times like these you have a choice that goes something like this: a) read a magazine while the kids play their DS, b) turn on the TV, c) force your son to practice piano 15 more minutes, or d) play a math game! I freely admit option a and b are good for me many an afternoon, and option c was really just for the tiger moms out there, which leaves option d as a fine choice for those afternoons when everyone is getting along and you find yourself with a few ounces of patience left and 20 minutes to kill.

We encountered this situation a few days ago, so I pulled out a game that’s been sitting on the shelf for months:
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Math Bingo! Since we never played before I wasn’t sure how hard this particular version would be (keep in mind the players are 3, 5, and 7 years old), but I figured we could wing it. And so we did, and it worked! I made a rule that you can’t yell out the answer, you have to raise your hand and wait to be called on:
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The other rule was that someone had to help Ramona:
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Some of the problems were a little challenging for our age group, but we muddled through:
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We completed 2 rounds and before we knew it, it was time to leave for karate class. Twenty minutes, 20 fairly challenging math problems under our belts.  And guess what, no lie, this was actually fun! Kids love it when you sit down and play a game with them (even a math game, I promise).

If you are interested in obtaining this game for yourself, I’m sorry to report it’s no longer available in the $1 bin at Target, which is where mine came from. I saw it for sale on e-bay for $6.95, but honestly I don’t think you want to pay that much. There are tons of math bingo games out there, just google “math bingo” and you’ll be all set.  π
 
I recently attended a presentation on Teaching Math To Preschoolers, organized by our school district’s Preschool Parents Club. The speakers provided lots of ideas for integrating math into the lives of 3 -5 year olds, and one of the main points was this: Count! Count! Count! Count everything, all the time, and those numbers will sink in before you know it. As you can imagine, I bought into the count-count-count philosophy years ago so our kids are pretty much mad-counters at this point.  Today I want to share a counting game we’ve played a lot lately.

We often hold up our fingers to show how many items we are talking about. How many different ways can you show a number using the fingers on one hand? That’s the challenge I presented Ramona while we waited in the car at the bus stop. We started with the number 2. Well, there’s the obvious:
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But how about this:
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Or this?:
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Moving on to number 3:
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I have a soft spot in my heart for chubby, clumsy fingers. Some of these are pretty tricky for little hands. What good practice for improving finger dexterity though, don’t you think? The bus came before we got to 1, 4 or 5, so we tried some of those combinations at dinner (sorry, no pictures!).

When working with a preschooler, one-hand combinations are enough. For older kids, how about using both hands? How many different ways can you form the number 3 using the fingers on both hands? How about all the other numbers? See if your (older) kids can figure this out. With so many possibilities, how can you keep track of the combinations?

I am excited to let you know that my friend Jill’s son already figured out this problem. He devised a method where he assigned each finger a number, then worked out each finger combination and removed any duplicates to come up with an answer. She took a picture of his work so I hope she doesn’t mind if I share it with you:
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And guess what, Jill told me they did this at the dinner table. I just love spontaneous math lessons. Thanks Jill for sharing! π
 
Hi!  This is Chao.  I gave the kids these worksheets a few days ago.


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For Wanda, I made her do additions.  She's good with results up to 20, but gets confused about the tens.  So first I had her add multiples of ten to get used to the scale.  Then I had her add a double digit with a single digit without need to carry, like 56+3.  

Then I had her round large numbers to the nearest hundreds.  The kids have a hard time dealing with large numbers.  I want to show them that they are the same as single digit numbers.  It's just the scale is different.  I also want them to have a sense for numbers and understand that most of the time you only care about answers up to a certain precision.  Whether you pay $25,137 or $24,972 for a car is not important.