Bringing Math into March Madness

Never mind the complicated algorithms needed to get team seeds and brackets, here's a great way to sneak in a little math with your kids while rooting for your favorite teams.  Give your kids a possible score (let's say 14) and ask them to figure out different ways the team could have reached a total of 14 points (i.e. 2 points + 2 points + 2 points + 2 points + 2 points + 2 points + 2 points). Then follow up with, "Hey, that's 7 groups of 2 point shots, [7 x 2]..."  What a beautiful way to bring multiplication in!  Next, ask if there is another way the team could have gotten to 14?" (i.e. 3 points + 3 points + 3 points + 3 points + 2 points)

Simplify it a bit by saying that your team has, say, 6 points.  Then ask how many more points the team needs to get to reach 10 points.  Or, compare your teams score (let's say 10) with the opponent's score (let's say 15).  How many MORE points does your team need to score to beat the opponent?

Complicate it a bit by asking questions like, how many groups of 2 point shots did our team get if it has a score of 42?  How many 3 point shots did we get if the team has a score of 42?

Let the Madness be an inspiration for more Math!

Spring has Sprung -- Make it Meaningful and Measureful

If Spring has sprung in your neck of the woods, turn the glorious outside weather into an authentic learning universe! One ever-so-helpful activity that you can encourage your kids to do is measuring different plants and flower growth.  Measurement is notoriously tough for kids of all ages, so the more practice they can get, the better off they'll be.
It's sometimes tough to measure flora with a regular ruler, so let your kids pick a favorite ribbon or piece of string as their nonstandard measuring tool.  [This is also handy because they can measure the circumference of trees (the length around the tree) using the ribbon or string.]

Let your child pick what he wants to measure.  Is it the new dandelion emerging from the ground or a blade of grassing poking up through the crack in the sidewalk, or is it a bunch of different plants around the yard? Again, let your child choose!  Once your kiddo has picked what he wants to measure help him hold the string along the plant (or around the plant) and keep fingers on the two ends.  Lay the string or ribbon down next to a standard ruler, again keeping tabs on the two endpoints and help your child read the length of your specimen.  Depending on the age of your child, you may need to round to the nearest inch, 1/2 inch, 1/4 inch, etc.  This is also a great time to talk about the metric side of the ruler and how the lengths are the same, but the systems are just different.
Don't forget to record your child's findings (or let him do it!) and revisit the plant once a week/month to chart its growth!
Happy Measuring!! ;)

Pucker Up, We're Counting Kisses

Pucker up, Buttercup!  Valentine's Day may have come and gone (I think many of us may be a little thrilled by that), but 'tis always the season for kisses! A simple, fun and loving way to practice counting with your little ones is with kisses.  I tell Katie that she is going to 5 kisses and then we count each one as I give them to her.  Other times, she gets 10 kisses.  She loves getting the kisses and tries to "top" the number that I gave her by giving me one ore kiss.  So simple, and yet so effective!
For older kids, try counting your kisses by 2s, 3s, 5s, or ask your child to figure out how many kisses he will get by solving the expression you give him (I'm going to give you 4 kisses plus 2 kisses...how many kisses is that?)

Sing (and Type) the ABCs

If you're reading this blog, chances are you've got a computer.  Great!  Have you thought about using it to help your child learn her ABCs?  I'm not talking about video games or YouTube videos (though there are some really great, albeit additive, ones out there), I'm suggesting a more interactive "game" between you and your child (and your keyboard.

Simply open up a blank Word doc, enlarge the font and start asking your child to type the different letters.  Katie, my 2-year-old, absolutely LOVES this "game".  She sees me typing away and this gives her the feeling that she's doing the same thing.  I have her sit on my lap with my laptop on a lap board on top and ask her to type "B, for baby" or "C, for Charlie".  She really gets a kick out of seeing the letters she's typed appear on the screen and again, she's having so much fun that she has no idea that she's learning.  We stick with "caps lock" on as she's just beginning to identify letters, but soon enough I'll have her type in lowercase letters as well.

We play this splendid game with numbers, too.  Again, there's no reason you couldn't extend this activity to include spelling practice (type in the word, "bat") rhyming words (type in a word that rhymes with "bat", sums (type in the sum of 3 and 9) and differences (type in the answer to 10 minus 8), and so on.

Keep kids laughing and enjoying themselves, and you'll keep them open to learning endless amounts of things!

Homemade Number Cards

I was at Target earlier this morning and was so close to buying a pack of "Number Cards" for my 2 year old, since she is really getting into number identification and counting.  Luckily, before I checked out, I realized that I could save myself a few bucks and make math so much more meaningful just by making my own.  Do I really think she is going to know/care about the difference between factory-made and mom-made? I think not.  Rather than spend the $4.99 on the pre-made cards, I got a pack of blank 3 x 5" index cards.  All I need now is a Sharpie.  The nice thing about making these homemade cards is that I can:

1. go up to whatever value I want (we're at 30 right now),
2. decide if I want to write only numerals, or words and numerals, or even add pictures (see #3)
3. draw pictures of things that I know she will love! (right now she's in love with Max and Ruby, so I can draw 10 bunnies or 15 carrots or whatever)  The fact that the pictures will relate to something she loves will make the cards a positive thing that she really enjoys, as opposed to an isolated math threat.

The possibilities of these cards are truly endless.  We'll start with identifying and ordering from least to greatest, but from there, we could do so many different FUN (and educational) things with these cards -- all for the cost of a pack of index cards!

Remember, kids need to make connections to really make learning meaningful.  What does your child love? Find out and use that as the base for any learning opportunity!

Happy Educating!

Is Finger-Counting OK?

The question, "Is it OK for a child to count on his fingers?" came up recently.
My thoughts below...
In a word, YES!  When a child is just learning about the concept of numbers, it is fine for her to use her fingers. The keywords here, though, are " just learning".  

Young children do not have a grasp of the abstract value of numbers and their representation in symbols.  It is a very tough concept when you stop to think about it.  When kids are just learning, we try to encourage them to relate physical objects to the symbolic numbers.  As they mature, kids' minds can comprehend that the symbol for 2 (what we think of as the number 2) is really representing 2 objects (whatever they may be).  

-Why do some kids use their fingers when learning how to count while others don't?

Some kids use their fingers while others don't for a variety of reasons.  If the child was taught to count by only seeing her parents use their fingers, that child probably doesn't have many other frames of reference for what numbers can symbolize.  As a parent, we can certainly use fingers to count with our children, but we also need to make sure we count using books, toys, crackers, blocks, etc. so children see that numbers represent many different types of objects, not just fingers.

- Is a child who depends on finger counting at a disadvantage when it comes to mastering mathematical concepts? Why or why not? 

A young child who relies on finger counting is only at a disadvantage if he doesn't make the leap to the abstract.  If he cannot comprehend that numbers are used to count multiple items, he may struggle with higher level math skills.  We should strive to use finger counting in the most basic of math foundation building and then stretch our kids in other ways.  We certainly don't want children to think numbers "stop" at 10, (or 20 if they count their toes).  

- What suggestions can you give a parent who wants to help their child improve their math skills and lessen their dependence on finger counting? 

Try having kids count a variety of objects.  Start by counting fingers 1-10, and then repeat the process with blocks, books, toys, etc.  With the new objects (not fingers), introduce numbers 11-20).  Move slowly from 3D objects to 2D objects to see if your child can still count things that he cannot hold in his hand (but can still point to).  After that, have kids try to simply look at small numbers of things and "know" that there are 2 balls (instead of having to touch and count each one individually).  

Most importantly, exude the idea to your child that math is fun! A positive attitude about math, whether real or feigned, from a parent goes a long way in the long run.

Identical Snowflakes??! Possible, but Not Probable

We've all heard (and probably repeated) the old adage that no two snowflakes are ever the same.  I used to use the analogy all the time with my students when describing how each of us is also different and has our own special gifts and talents.  Well, I may have to amend my whole diatribe!

There is an article today in the Washington Post by Brian Palmer (http://www.washingtonpost.com/national/health-science/why-no-two-snowflakes-are-the-same/2011/11/07/gIQAlwZNLN_story_1.html) about the uniqueness of snowflakes.  It gets pretty technical at certain points, but according to his snowflake expert source, it is mathematically and statistically possible for two snowflakes to be identical; it is just highly, highly unlikely given the number of combinations of molecular arrangements. 

Palmer quotes Kenneth Libbrecht of the California Institute of Technology, "Now, it’s not a law of nature that no two snowflakes could be truly identical. So, on a very technical level, it’s possible for two snowflakes to be identical...[t]here are a limited number of ways to arrange a handful of bricks...but if you have a lot of bricks, the number of combinations grows very quickly. With enough of them, you can make a driveway, a sidewalk or a house.  Water molecules in a snowflake are like those bricks. As the number of building blocks increases, the number of possible combinations increases at an incredible rate." 

Palmer continues by explaining, "[c]onsider the math, which Libbrecht helps explain using a bookshelf analogy. He points out that, if you have only three books on your bookshelf, there are only six orders in which you can arrange them. (That’s 3 times 2 times 1.) If you have 15 books, there are 1.3 trillion possible arrangements. (Fifteen times 14 times 13, etc.) With 100 books, the number of combinations increases to a number that is far, far greater than the estimated number of atoms in the universe."

Like I said, it gets a little technical, but if you have 6th grader (or older) child, it's very likely that she's worked with combinations in math class.  While she's not going to be able to figure out the total number of snowflake combinations in the world on her own (Palmer shares that "Libbrecht estimates that around a septillion — that’s a 1 with 24 zeros — snowflakes fall every year."), this is a nice connection to make.

Happy Winter!

More Math Fun!

I had someone ask me again about ways to make math less scary for kids of all ages.  I find that kids get most overwhelmed when they lack a solid foundation; in other words, getting kids to understand and have number sense is my first suggestion.  Obviously, this is much easier when kids are younger, but even 8, 9, 10 year old kids benefit greatly from breaking down numbers and playing with them. 

Making math more into a game is a great way to build basics, but without the stress! One fun activity that you can do with your kids is to find some flat rocks and allow your kids to paint different numbers on them, one number per rock.  Vary the number range based on your child's age (maybe 1-5 for younger children and 1-9 for older kids).  If you don't have rocks, allow your child to pull 3, 4 or 5 playing cards from a deck of cards.  If you don't have cards, use scraps of paper.  The point is, kids see rocks/cards/scraps of paper as "game" pieces and all of a sudden, math is fun instead of stressful.

Ask him different questions about the numbers on the rocks/cards/papers and give him a chance to manipulate them to answer the questions, and more importantly, justify his reasoning.

Sample questions include:
"What happens when you add the number on this rock (e.g. 4) to the number on this rock (e.g. 3)?"  "Now, what do you notice when you add the number on this rock (e.g. 3 -- the 2nd rock from the first question) to this number (e.g. 4 -- the 1st rock from the first question)" -- the idea here is that your child will begin to see the Commutative Property of Addition, which states a +b = b + a.  You child will have to explain WHY 4 + 3 = 3 + 4.  Have him try multiple additions combinations to prove to you (and him) that this property always works.

"What is the largest number you can make with these three rocks (e.g., 7, 8, 3)?"  Assume your child chooses to manipulate the rocks to make the number 738.  Ask, "Great! Why is 738 better than 378?"  Then push further and ask about the place values of each of the digits in a 3-digit number.  Try to tease out that the number in the first place represents hundreds and the larger the number in the hundreds place, the larger the number overall.  "So, would it be better to have an 8 in the hundreds place, or 3 in the hundreds place? Why?"  "What is the value of the 2nd digit {tens}?"  "What is the value of the third digit {ones}?  Obviously, you want your child to get to 873, but be sure to praise and question each step along the way.

Ask your child to come up with her own questions about the rock numbers and let her "quiz" you.  See what questions and discussions arise, and go from there.

Good luck and happy math exploring!

Make Math (Even) More Magical!

We all know kids learn more when they're having fun (I feel like a broken record saying that over and over and over again), so let your little Einsteins go hog-wild with this fun math game!

Write each digit 0-9 on its own scrap of paper and have your kids crumple them up. 

Depending on the age/math proficiency of your kids, have them choose between 2-5 scraps from the pile.  Tell them their job is to use each of the numbers they have randomly chosen in a math expression, working toward some goal (largest sum, an even number, a multiple of 12) that you set.

So, for example, if you have a 5th grader, you may say to him, "Pick 4 scraps of paper.  Make (two) 2-digit numbers that, when added together, give you the largest sum possible."  If your child pulls a 2, 4, 1 and 5, let him play around with the numbers realizing that it doesn't make sense to make the numbers 24 and 15 (sum of 39), when he could make 51 and 42 and get a sum of 93.  Would changing the numbers to 52 and 41 change the sum?  Why or why not?

If you have a 1st grader, change the game to something like, "Pick 3 scraps of paper and add all of the numbers together".  While this may not seems exceptionally fun to adults, most kids will like the novelty of moving the papers around and the fact that they're written on pieces of paper instead of a math worksheet.

Other ways you can change this up:
- use a die or 2,3,4, dice to get your random numbers (kids automatically think "game" when dice are involved!)
- have your kids play against one another to get the largest sum and have them explain their thinking ("I made 42 instead of 24 because 42 is a larger number.  A large number plus another large number will get me a larger sum than 2 small numbers added together....")
- add more pieces of paper and have repeated digits
- let your kids set their own goals for the math expression
- have your kids pick 3 pieces of paper randomly and then have the option to choose which number they'd like to have for the 4th digit, depending on that round's goal

What else can you think of to make this math game even more fun!?

Math Phobia - Let's Cure It Together!



Math Monster, be gone!

 I taught 5th and 3rd grade for 7 years and am taking a little time off as I prepare to have my 2nd kiddo.  Someone recently asked my opinion about kids' math-phobia, its source and more importantly, its solution.  Here's what I think.

As you well know, many kids struggle with math.  I'm probably not going to get a whole lot of love from parents or fellow teachers, but one of the biggest disservices we do for our kids is teach them "tricks" to remember math algorithms.  As teachers, we are so pressured by making sure our kids do well on state tests that we look for a quick fix, and teach kids tricks that we assume they'll remember long enough to get them through the test-taking period. 

For example, when teaching kids long division, I've heard many fellow teachers teach their kids the saying, "Mom, Dad, Brother, Sister", which is supposed to help kids remember the steps,  "Multiply (Mom), Divide (Dad), Borrow (Brother) and Subtract (Sister)."  It seems like a great system until it's crunch time, the kids are under stress and have no idea if it was Mom, Dad, Brother, Sister or Sister, Dad, Mom, Brother or Uncle Sam, Aunt Patty, Grandpa, Cousin.  There's no meaning to which the kids can connect, and therefore, there's little chance the kids will remember the correct steps in the long-term.  Summer comes and goes and as the child enters the next grade, he's right back at square one as far as long-division proficiency.  So, his next teacher teachers him the saying "McDonalds, Dairy Queen, Burger King, Sonic" to "help" him remember the steps of long division and here we go again....

Our U.S. educational system is also very flawed (in my opinion) in that we spend small amounts of time on each of 6-7 math strands each year.  In Kindergarten, kids get a quick unit on number sense, geometry, patterns and algebra, etc., and then they see each of those units again in 1st-8th grade.  The problem with this is that there are so many units that each one is only touched upon for a short time.  There is a ton of breadth and not a lot of depth.  As compared with many Asian ways of teaching math (which focus on 1-2 strands only for the entire year), our system doesn't allow the investigation needed for kids to truly grasp what they are doing.

Unrelated as these two points may seem, they actually are very similar to one another.  My suggestion to parents and teachers who have math-phobic students is to start back at square one, and really spend time with your kids helping them to truly understand the basics of math.  If your child struggles with long division, I'd be willing to be that he doesn't grasp that it's really repeated subtraction.  (Have you ever sat down to think about division in that way?)  Asking a child to learn division, when he doesn't understand subtraction is like asking a kids to string together a compound sentence when he doesn't know the alphabet.  Without the proper foundation, his math tower (upon which more and more is constantly piled) is bound to topple. 

This all sounds great in theory, but what about reality?  My suggestion is to start small.  Kids know more than you (or they) think.  Obviously, the younger your child is, the easier it is for her to catch up.  If fractions are your child's nemesis, "catch" her talking about sharing half her cookie with her sister, or dividing up the pizza among her 4 friends.  Use real-life, meaningful scenarios to get your kids thinking about math.  Ask them tough questions and make the commitment to do some research yourself.  Do you really understand what it means to "borrow" from the hundreds place when solving a subtraction problem, or do you just cross out the 7, make it a 6 and put 10 on top of the 0 in the tens place? 

Kids are like dogs in that they smell fear.  If you grew up eeking by math class and clearly don't get it, I'm willing to bet your kids are going to hate math and try to slip through as well.  Maybe it's time for both of you to make the commitment to learn more about math than just the tricks that your teachers taught you years ago. 

Just "sum" food for thought!

No Muss, No Fuss, No Clean-Up: Fun Geometry and Communication Activity

Looking for another easy, low-cost, no clean-up activity? How about one that improves kids' communication AND geometry skills? Check this out!  Have your child draw a simple picture like the one shown here.  It requires little artistic ability from the child, which means there shouldn't be any stress involved.

 When she's finished drawing, DON'T LOOK at the image.  Instead, get your own sheet of blank paper and sit with your back facing her.  Her job is to describe to you her drawing in enough detail and geometric and positional language that you can draw your own version of her original image. 

For instance, she might start out by saying, "Draw a circle".  Well, without having seen the original, you may pick up the pink marker and draw a huge circle that takes up the entire page.  What she'll soon see is that she needs to say something like, "Draw a small gray circle with a black circumference."  Then she has to convey to you that there is a purplish-blue triangle hanging from the bottom left side of the circle.  But, she'll have to let you know that it is an equilateral triangle, as opposed to a bottom-pointing isosceles triangle or something else.  She also have to let you know that the triangle is similarly sized to the circle.  Next, she'll have to use her language to get you to draw the kite/diamond and the floating orange pentagon.

You can make up your own rules, such as the listening artist is allowed 5 clarifying questions, or the original artist is allowed to peak at the listening artist's work as it's being drawn so she can be more exact with her descriptions.
 
The possibilities are absolutely endless, and there's no reason multiple kids couldn't participate in this, if you're needing a little break.  One child could still be the original artist and a whole group of kids could be the listening artists.  Have fun! And, as always, happy learning!

Bubble Geometry

What kid doesn't like blowing bubbles? What teacher doesn't love it too?  Why? Because there is so much math embedded in this seemingly fun-only activity.  We all know kids learn more when they're having fun, so throw in this secret geometry lesson while your kids are blowing their hearts out!!

The object, of course, is to blow the biggest bubble.  Let your kids experiment with different shaped bubble-makers (homemade or store bought).  They can use wire coat hangers, string, or the wands that come with the bubble solution.  Here's the math part.  Once the bubbles pop, use the bubble ring that's left on the sidewalk and have a quick talk with your kids about the diameter, radius and circumference.  (See the definitions below for your refresher course.)  Get the rulers out and have your kids measure each of the three for each bubble they blow.  Have them make their own data sheets to keep the records straight. 

If you have multiple kids, you can make it a competition or have them work together in a team effort (which life lesson will you choose today?); if you have one child, see if he can "beat" his record with each successive bubble.  What improvements can your kids add to increase the size of their bubbles?

Your kids' math teachers will love you and your kids will be having so much fun, they'll do all the math you want just to keep making the biggest bubble! It's most definitely a win-win!

DIAMETER:    any straight line segment that passes through the center of the circle and whose endpoints are on the circle  (remember, the line segment has to start and end on the circle AND PASS THROUGH THE CENTER POINT)

RADIUS:  any line segment from its center or axis of symmetry to its perimeter  (think of this like a spoke on a wheel; the line segment has to have one end point on the center of the circle and one endpoint on the circle itself)

CIRCUMFERENCE: the perimeter (or distance) around the circle; you calculate this by (C=πd) OR (C=2*π*r)     (π = 3.1415)

Other ways you can embed math in this lesson:
- have your kids measure in centimeters and inches
- have your kids find the difference between each bubble's measurements
- have your kids research WHY bubbles are always spherical no matter what shape the wand is

Happy blowing!

It's Raining, It's Pouring....It's Math Time

It's raining here with no signs of letting up -- what a perfect day to do some math! As a teacher, I absolutely love(d) the NCTM (National Council of Teachers of Mathematics) website called Illuminations.  This site is full (absolutely exploding) with math games, ideas, objectives, activities for all ages and all math strands.  If your child needs extra help in algebra, there's a game/activity.  If geometry stumps your child, no problem -- they've got you covered.  And, when I say all ages, I truly mean, all ages.  We tend to think of Pythagorean theorem when we hear geometry, but don't forget that even preschoolers are practicing their geometry skills when they sort shapes and put them into patterns.  I highly, highly recommend this site to fellow moms, dads, teachers, whomever.  It's safe, free and educational.

Here's a screen shot of just one of the many activities: "Pan Balance - Shapes" -- a wonderfully rich activity that introduces kids to algebraic thinking without them even knowing it!  You definitely want to read each activities rules and explanations before playing and as always, you want to make sure your child is properly supervised.  This game's gist is as follows:  I learn that 2 red squares are the same "weight" as 1 blue circle.  In the next round, I learn that 2 red squares and 1 purple triangle are equivalent to 1 blue circle and 3 yellow diamonds.  From there, I can continue to figure out the value of each shape. I get to pick which shapes I place on which of the two balances and deduce their values from the results.  Amazing, isn't it?