Fun math trick to commemorate Swiss holiday

“Erste August” - August 1st - is Switzerland’s national independence day. Today the Swiss celebrate 615 years of independence with bonfires, lantern parades, great food and festive folk music.

Being Swiss, this is a fitting day to share a fun calendar math trick.

Swiss Chocolate Age Detector
(with Swiss clockwork precision)

1. Pick the number of times a week that you like to eat Swiss chocolate -- at least once but less than 10.
2. Multiply this number by 2. (Who can resist that creamy Swiss chocolate?)
3. Add 5.
4. Multiply it by 50.
5. If you already celebrated your birthday this year add 1756. If you haven't, add 1755.
6. Now subtract the year that you were born.
You should have a three digit number.

The first digit is the number of times you like to eat Swiss chocolate each week. The next two digits are your age!

This trick will only work in 2006. Here’s a little math puzzle for you to solve: how can you change the trick so that it works next year?

Thanks to my lovely web designer, Trisha Cupra of Australia, for the calendar trick. If you have a fun math game or amusement to share (or you just want to say “Grützi, I’m Swiss, too!”) post a reply or drop me an email. I’d love to hear from you.

Chuss!
Rita

Counting: There's more to it than 1-2-3!

This is a continuation of yesterday’s article, Quantification, which is just a fancy word for figuring out how much you’ve got. To recap, there are three developmental stages of quantification:

• Global quantification – child relies on perception.
• One-to-one correspondence – child matches objects one for one.
• Counting.

Check yesterday’s article, Quantification: How children learn to count, for a review of the first two stages.

Today we’ll focus on the third stage: Counting.

Counting is a not a trivial thing for little ones to grasp. There are three stages a child must come to understand.

1. Knowing the right order of the words. At this stage, it’s about the same as reciting a poem. It’s not the ABC poem but the 123 poem. This is called stable order counting.
   
   Have you ever observed a child count the fingers on one hand and end up with more than 5? They counted properly: 1-2-3-4-5-6, but they counted one finger twice. These children understand stable order counting – all the words were said in the right order - but they haven’t moved on to the next stage, which is…

   
   

2. Knowing that each object may be counted only one time, with one number word said for each object counted. This is an example of one-to-one correspondence: one word for each object.
   
   
3. The third stage is knowing that the last number represents the total. This is formally known as cardinality. This requires the understanding that the last number has two roles: the name assigned to the last item, and the name for the entire set. The pinkie finger is number 5, and the total number of fingers is 5.

To demonstrate the difference between one-to-one correspondence and cardinality, here’s a favorite story:

There was a little boy who was eating cookies with his mom. He counted them in the plate: 1, 2, 3. After he ate one his mom asked, “How many are there now?” “Three!” he replied. Mom asked how could that be, if he ate one? He said that he ate “1”, but not “2” or “3”.

This boy understood that there’s a word for each cookie, but he didn’t understand cardinality. The words for each cookie change when the quantity changes.

Fortunately for him, his mother accepted his answer and didn’t pursue a correct answer. These mistakes should be viewed as windows into a child’s knowledge rather than opportunities for correcting.

Once children grasp these 3 concepts:

• correct word order,
• one word for one object,
• the last word represents the total

then they start using counting as a method of quantification.

And so you see, counting is NOT as easy as 1-2-3!

To your child's success,

Rita

Quantification: How children learn to count

“It’s as easy as 1-2-3!” How often have we heard that phrase? Is counting really that easy? Let’s take a look behind the scenes at how a child learns to count. There’s more to it than you might think.

Today I’ll write about the developmental stages a child goes through which lead to counting. Tomorrow I’ll write about the developmental stages of counting itself.

Quantification is the formal name for the concept of figuring out how many things you’ve got. Counting is just one method of quantification.

There are 3 developmental stages a child goes through when learning to quantify.

1. Global Quantification. This is the stage where children are influenced by perceptions. They make a visual approximation of the quantity they’re trying to match.

• If a child wants as many goldfish as another, she’ll take a handful that seems to match the quantity.
• If she’s asked to take as many blocks, she’ll line them up side-by-side until her line is about the same length, without regard to the actual number of blocks.

2. One-to-one Correspondence. Children still use visual or tactile perceptions as in the previous stage, but in a more logical manner.

• Now the child will line the blocks up one-for-one, matching one new block for each of the original ones.

3. Counting. Children use counting as a method to quantify as they become comfortable with the first two stages, since counting relies on global quantification and 1-to-1 correspondence skills. Counting itself has several stages of understanding. Stay tuned for details in tomorrow’s Matinee Muse. :)

These stages will overlap, depending on the number of objects. A child who can count to 5 might use counting when there are only a few objects, one-to-one correspondence when there are more than a few, and global quantification when there are many objects.

Now what?
Now that you know the details behind your child’s ever-spinning gears, what do you do with this information? Give them appropriate activities! Here are a few ideas to spark your imagination.

Global Quantification ideas.

• Talk in terms of “more” and “less”, “many” and “few”, “big”, “little”, “tall”, “small”, “bigger” and so on. “Same” is a useful word, too.
• When your child helps with snack, toys, tea party or bathtub play, ask to have More or Less than them.
• Or, ask that every teddy be given the same amount.

Counting might not occur yet at this stage. If you're curious, you could ask, “How do you know (it’s the same)?” and observe how he answers. This will give you insight into the developmental stage he’s in. It’s an opportunity to listen, not necessarily to correct.

One-to-one correspondence ideas.

• Ask that every seat at the table get one plate, fork, cup, etc.
• Assemble a group of dinosaurs and give them each a piece of Lego dinner.
• Line up a row of blocks and put a shell on top of each.
• Gather 8 similar toys and give your child 8 pretend "coins". Trade a toy for each coin.
• Give your child 6 dolls and 6 hats. She will naturally pair them up.
• Put small rubber fruit counters on each square of a checkerboard.
• Place a goldfish on each square of a checkerboard placemat while waiting to be served.
• Place an object in each hole of an egg carton. The objects should fill the hole; otherwise your child might be tempted to put several in each hole.

You get the idea! Now it’s time to have fun with whatever you have handy that excites your child.

To your child's success,
Rita

Little Kids & Big Numbers

What’s the big deal with being able to count to 100 in preschool?

The beginning of February is when many schools celebrate their 100th Day of School. Since some of my blog subscribers have preschoolers, this blog entry is about the importance of big numbers for little kids.

I’ll say it as plainly as I can: I think big numbers are over-rated for toddlers. Unless a child has a rough concept of how many 100 is, it’s pretty useless to be able to count to 100. I consider it the equivalent of being able to recite a poem, the 1-2-3 poem. Until a child is able to grasp how much 1, or 2 or 58 is, big numbers just aren’t that big a deal. Counting to 10 or 20 is plenty.

What comes after 10?
Once a child can count to 10, the next step is to play around with the little numbers. What’s more, 1 or 2? Hmmm, if I were 2, that would be a terribly boring question!

How about: “I have 3 apple slices. You can have some, and I’ll have some. Would you like the bowl with 1 or the bowl with 2?” Of course this is not one of those math word problems to be done in their head; this is a real-life problem to be acted out at snack time.

This makes math part of a child’s daily life, and it uses the smallest of numbers. There’s really no need to jump ahead – even to 6 or 8 slices – until a child has a firm grasp of smaller numbers.

Having a solid grounding of how to manipulate small numbers will prepare a child for greater mathematical success than being able to recite to 100.

So the next time your friend boasts about how high their toddler can count, give them a smile and say “That’s nice!” but resist the pressure to compete. Big numbers are over-rated.

To your child's success,
Rita