Archive for the ‘Developing Number Sense.’ Category

. 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.



Happy Valentine’s Day Book Recommendation: My Love for You by Susan Roth

Thursday, February 11th, 2010

How to express the depth of your love for your child on Valentine’s or for that matter any day  of the year?   Do you tell your child, “I love you as big as the sky” as I did with my children?  With this little counting book, you can express your love for your child as you teach numbers 1 through 10.

Through the eyes of a white mouse and a smaller brown mouse, you will journey on a wild-animal adventure.  The book begins: MY LOVE FOR YOU . . . Turn the page and read:  is bigger than 1 bear.  The next page tells you: taller than 2 giraffes.  And the next: larger than 3 blue whales. (Notice we’re developing good language skills in the use of comparative adjectives.)   The books ends with the sentiment that “my love for you is greater than all of these together . . .  forever.”

The illustrations in the book are delightful!  The landscapes are made of multi-layered, translucent tissue-paper collages similar to those your child will make in school.  These give the pages an amazing depth.  Some of the animals  are made out of construction paper. Explore with your child how the patterns on the 5 pythons are made out of simple  rectangles, squares and triangles.  Why not sit down with your child and construct your own as an art project?  Or maybe cut out two giraffes and apply small brown squares to  make a  giraffe mosaic?  This book will inspire you.

I recommend this book not only for its lovely sentiment (the two little mice can represent a parent and child, an older and younger sibling or simply two friends), the counting skills it imparts but also the art.  This charming little book will delight your child on Valentine’s or and other day!

Why is THREE written 3? Learn how numbers came to be with this cute YouTube video

Sunday, November 22nd, 2009
Have you ever wondered how Arabic numbers evolved?  Why do we use 1 for ONE, 2 for TWO, 3 for THREE, 4 for FOUR, 5 for FIVE, 6 for SIX, 7 for SEVEN, 8 for EIGHT and 9 for NINE?  Could the way numbers are written actually mean something?
You may remember Roman numerals: I, II, III, IV, V and so on.  When you look at these, it’s easy to decipher a pattern and break the code:


I represents ONE. II represents TWO.       III represents THREE. Rather than represent FOUR with four lines and FIVE with five lines, V was chosen to represent five.  FOUR was represented as IV meaning five minus one.  You subtract the smaller number on the left from the larger number on the right. The logic is apparent. Not so with our current system: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0.  Is there any reason FIVE is written as 5?  Is it a purely arbitrary notation or does its configuration actually mean something? Could these numbers too be based on a pattern?


Watch this YouTube clip:

to learn how our Arabic numbers were created and the logic behind them. Better yet, watch it with your child.   To open, copy and paste it on your url. Both you and your child will be amazed!


Approach math with a sense of wonder. Your child will be intrigued by its beauty and logic. 


 Who knew that even the way we write numbers 1-9 are based on patterns! You can count the angles in each one. There are THREE angles in 3 and so on.  In 0 there are no angles.  Amazing . . .

What does a trillion dollars look like?

Friday, July 17th, 2009

For those of you who haven’t seen this, check out this site.  Apparently, one million dollars fits into a grocery bag.  It is staggering to see what a trillion acutally looks like.  The graphics are amazing, easy for a child to grasp. 

Here’s the link:

Egg Carton Multiplication

Wednesday, July 8th, 2009

This fun activity teaches children the principles of grouping and multiplication. You will need:
A standard egg carton or muffin tin.
Dried beans, M&M’s or other small objects.

Cut off 2 of the egg cups so that you now have 10.
Count out 24 beans and ask your child the divide these in 6 cups so that the same amount is in each cup. When your child sees that 4 are in each cup, state the multiplication problem:   “If we have 6 beans in each of these four cups, how many do we have in all?”  Your child will answer “24”.  Now restate the problem as:  “6 x 4 = 24.”

Now have your child divide these 24 beans into 4 cups. State the problem: “4 x 6 = 24.” Your child is not only learning about grouping but also the commutative property of multiplication, that is, 6 x 4 = 4 x 6. The order of the numbers does not change the result:  6 x 4 = 24 and 4 x 6 = 24. 

Addition is also commutative:  6 + 4 is the same as 4 + 6. The order does not matter:  6 + 4 = 10  and 4 + 6 = 10.   Or 4 + 6 = 6 + 4. 

Now divide these 24 beans into 8 cups. Next divide into 3 cups.  Again repeat the multiplication problem: 8 x 3 = 24 and 3 x 8 = 24.
This fun activity is also teaching your child division as he/she is dividing 24 objects into 8 cups and so on. Your child will see that division is the inverse of multiplication:    24 divided by 8 = 3  and  3 x 8 = 24.

Continue this multiplication activity by counting out 12 beans and dividing in 4 cups etc.  It is probably best to do a few of these a day so the activity remains fun.  Activities such as this develop your child’s number sense.

Your kitchen is the heart of your home. It is also your “science lab” as this is where ingredients such as eggs, flour, sugar, baking powder and vanilla through the “magic of heat” become yummy cakes and cupcakes. Be sure to involve your children while baking.  Not only are they learning about measuring but also combining ingredients in certain proportions. By asking your child to help double your recipe, you reinforce multiplication skills. Your child will see the value of multiplication in every day life.

Learning to follow a recipe also teaches your child about fractions. More on this in another blog.