Archive for June, 2010

Patterns in Nature — The Chambered Nautilus

Tuesday, June 29th, 2010



Discover the beauty of patterns in the natural world. Look at the structure of  a starfish or  a chambered nautilus? 


starfishA starfish has five points.  If we measured each point of the starfish, would they be the same?  Why is a starfish named starfish?  Is its shape similar to a star?  Does it have the same pattern?



chambered-nautilus-inside1If  we look at the structure of a chambered nautilus, we discover a nearly perfect equiangular spiral.   Why does each chamber become increasingly  larger as we spiral from the center?  Is it because the nautilus as it grows expands its living space, adding more and bigger chambers in an every increasing spiral?  The body, of course, would live in the biggest chamber of its “house.”


chmbered-nautilus-floatingLet’s look at the shell’s outer surface.  There’s a brown zebra stripe pattern on top and yet the bottom of the shell is white?  Why would this be?  Nothing in nature is random.  The brown zebra stripes on top act as camouflage.  Seen from the top by predators, the nautilus blends with the ocean depths.  When seen from below, it blends with the light coming from above.  Its shell is hard.  When the nautilus is threatened by predators, it withdraws into its shell and seals the door.  Did you know chambered nautilises existed 265 million years before dinosaurs roamed the earth?  These beautiful nautilises are described as living fossils.  Why?  Because they have remained virtually unchanged for millions of years.  So their beautiful design was perfect from the start!  In nature, patterns serve a function.  Patterns help the animal fool its predators and survive.

Our innate curiosity leads to discovery.  Stimulate your child’s curiosity by pointing out patterns in the natural world.  Explore the wonder of nature with your child. 

Although we now have the internet and can look up anything to explain the mysteries of nature to our children,  for a young child there’s nothing like books or magazines with photographs and illustrations to captivate his/her imagination.  A child turns the page at his own pace.  Best of all, he/she is there cuddled up with mom or dad.

Images  from, and

. Why all the artwork in my workbook?

Wednesday, June 23rd, 2010

teachildmath-coverWhen I wrote my Teach Your Child the Multiplication Tables workbook, I wanted to create the excitement of a circus.  I wanted each page to be as REAL as possible. I had my graphic artist, Rudy Rodriguez, create the cute circus animals and clowns.  I thought it fitting that Rudy the Ringmaster be named for him.

To make the times tables REAL, I used grids.  Children can immediately see how the multiples increase from 1 x 1 to 10 x 10.  This develops number sense.  On a grid, they can see that 5 x 5 really equals 25 squares.  Some children will quickly fill in the tables on the grid so I included circus figure watermarks for children to trace.  I wanted to entertain children as they learned the  times tables.


Children who have an aptitude for math often have an aptitude for art.  Because we were working so much with grids, I asked myself: Why not take the opportunity to teach basic drawing at the same time?   We included eight pages of “copy the circus character on the grid”.   I wanted a workbook that was also a fun activity workbook.  I wanted a workbook that children couldn’t wait to work in.


The first mom to receive a copy of my workbook took it with her on the family’s beach vacation.  She told me her son promised to work on it 20 minutes a day.  She knew she’d have to interrupt his afternoon each day.  But to her surprise her son came out of his room after his nap with the workbook in hand.  Rather than napping, he’d been filling it in.  “I never had to ask him to do his math homework,” she said.  “But to get him to nap, I did have to take the workbook away.”   At that moment, I knew my book would be a success!

Book Recommendation: BUNCHES and BUNCHES of BUNNIES by Louise Matthews

Friday, June 18th, 2010

bunches-and-bunches-of-bunniesFrom time to time, I’ll be posting about favorite children’s books.  Some will have math  stories and others will be favorite storybooks.  I want your child to fall in love with numbers and understand math concepts but I also want your child to fall in love with words!  

Reading to your children not only enhances their vocabulary but also stimulates their imagination.  If you have a passion for reading, your child will too!  Reading to your child is not only fun but creates a special bond between you and your child.  Please add your child’s favorite book in the Leave a Reply box below so that other children will enjoy these too.

        Here’s a  favorite multiplication book: 

    BUNCHES and BUNCHES of BUNNIES  by Louise Matthews, published by Scholastic with delightful illustrations by Jeni Bassett.

    Your child too will have fun reading about these cute, silly little bunnies while learning basic principles of multiplication.  Each page illustrates what happens when you square a number, that is multiply a number by itself  (1 x 1,  2 x 2,  3 x 3, etc.)   till we end up with 144 bunny relatives living in one house!  Each multiplication has a four line poem with a cute, memorable rhyme such as:       

                                 Count the bunnies at the ball,

                                 Rabbit partners, short and tall,

                                 Now the music comes alive,

                                 And 5 x 5 is 25.




Book Recommendation: ANNO’S MAGIC SEEDS

Friday, June 18th, 2010

annos-magic-seedsIf you haven’t come across Anno’s storybooks with their beautiful watercolor illustrations, you and your children are in for a special treat! 

See what happens to Jack when a wizard gives him two golden seeds and tells him to eat one and bury the other.   Jack’s planting these seeds introduces children not only to the concept of multiplying but also investing in the future.  As Jack reaps more and more abundant harvests, he marries and has a child.  When a hurricane wipes out his crops, Anno is able to begin anew because ten golden seeds have been saved. 

This enchanting tale entertwines literature, art and math concepts.  Parents and teachers will reap rewards with this book.  Why not stimulate interest in math by seeing mathematical concepts in an a enchanting “real world” storybook context?     The beautiful illustrations alone tell the story.  The youngest of your children too will be turning page after page.

Book Recommendation: 26 Letters and 99 Cents by Tana Hoban

Friday, June 18th, 2010


Many of you have come across Tana Hoban’s fun books.  Her 26 Letters and 99 Cents will delight your preschool to kindergarden child or even an older child who has trouble figuring out how to add pennies, nickels, dimes and quarters.  This book is in fact two books in one.  One book presents upper and lower-case letters beside colorful objects beginning with that letter. 

Turn the book OVER and numbers are pictured with pennies, nickels, dimes and quarters totaling that amount.  Your child is learning not only about numbers and  grouping but also  money.  While reading this book to your child, expand the lessons by having a pocketful of change on the table and having your child figure out how many ways to make 35 cents with all pennies, or all nickels or a combination of coins.  Your child is learning number concepts and addition.   Why not develop your child’s “number sense” at an early age?  This fun book will engage your child!

What are your child’s favorite Tana Hoban books?

Make Math Real!

Thursday, June 3rd, 2010









Yesterday, I tutored a 5th grade student in math.  Julie is a smart girl but sometimes lacks confidence in her math skills.  Her mother wanted her to work on ratios and percentages.  I decided the math lesson would be more “real” if we worked with cents, dimes, nickels and quarters to learn percentages.  After all, percent means per hundred.  Our lowly penny is a cent, meaning one-hundredth.  So it’s not hard to figure out that a penny/cent is 1% of a dollar.  You need 100 of these to make a dollar.  The math is written:  100 x .01 =  $1.  So one penny is 1/100 of a dollar.  Divide 1 by 100 and you’ll get 1%.


On the kitchen table, I scattered handfuls of pennies, nickels, dimes and quarters.   After we figured out a penny was 1% of a dollar, we went on to quarters.  Every child knows four quarters make a dollar.  We represented a quarter as a fraction:  ¼  and then divided 1 by 4 .and got .25 or 25%.    Two quarters represented  2/4 or 1/2  or 50% of a dollar.  Three quarters represented 3/4 or 75%.  With each of these computations, Julie handled the money, sliding it in place for the various math problems.  We then worked with dimes (its root word means ten) and nickels.  Interesting we have one coin named after the metal it’s made of.  As a child, I had difficulty understanding a nickel which is larger than a thin dime was worth one half of a dime!  So working with coins, we figured out percentages.


Then we turned to ratios.  I’d scatter an assortment of coins on the tabletop.  “How many of the 12 coins are quarters?” I’d ask.  We’d write the ratio:  3/12 and figure out the percent.  Then I had Julie scatter the coins herself and make up her own percentage problems. 



So when you have the opportunity, make math real by having real objects to illustrate the math lesson.