There are two rather sophisticated, fun and fantastic books that I want to tell you about this week.

The first is a book written by Barbara Kanninen and illustrated by Serge Bloch called Circle Rolls.

The main character in this book is a spunky, bespectacled Circle. That’s right, a circle—and all kinds of funny things happen when Circle starts to roll.

As Circle rolls, he smacks into Oval, who rocks because he is not perfectly round, and Square, who sits because his sides are straight. As Rectangle is bumped into, he stands and, as Triangle is smacked, he points. Then, as Circle hits the point of the Triangle, he POPS!  All kinds of crazy things happens when Circle pops and, soon, other shapes get involved.

This book is perfect for talking about the attributes of each of the shapes (the circle is round, the triangle has three sides and three points, etc.) In addition, the words rhyme. Rhyming helps children experience the rhythm of language. Through rhyming, they can anticipate the rhyming word, which will help them with making hypotheses, or predictions—an important early math and science skill.

My three-year-old grandson, Charlie, loves me to read this book with him—and we both laugh a lot when that circle POPS! Laughing and learning at the same time is a fantastic way to spend an early morning story time.

The second book is about a bunch of party-loving hippos called Hippos Go Berserk by Sandra Boynton.

Hippos Go Berserk starts with one hippo sitting all alone who calls two hippo friends to come over. Those hippos bring other friends and the party begins as the house fills up with hippos playing, partying and working.

They go BERSERK having a fantastic time all night long. When dawn breaks, the hippos start to leave in groups until just the one hippo is left, missing the other 44 that were with him all night long.

This is a great book for practicing counting, composing (adding) and decomposing (subtracting). It is also a just a fantastically fun book that children and adults of all ages love.

I highly recommend these two fabulous, fun and fantastic books that will leave you and your children laughing while you learn!

Below is a picture of a traditional “Shut the Door” game which asks children to roll the dice, count the pips (the dots on the dice) and then “shut” the numbered door shown on the dice.  When all of the doors are shut, the game is over.  There are ways to play this game individually or with others.  I especially like this one because it is a noncompetitive game that asks children to work together in order to meet the desired goal (all of the doors shut).

This version is played by as many as 4 children at once.  When children engage in this together, the play moves from being cooperative to competitive which is a natural progression as children get older.

Toy cash registers have come a long way since my children were little.  Ours had buttons with numbers and a big button that opened the drawer.  That was all.  Inside, there was space for the pretend money.  Funnily enough, I actually remember that the money that came with the register didn’t quite fit in the drawer.

Now they make cash registers that have small computers in them so that when buttons are pushed, the numbers come up on the screen.  Children can add up their shopping items and then total them.  Many of these new-fangled machines also have scanners that actually work.

The cash register is another great way to enhance the money experience for children.  They are usually a highly coveted item in the classroom, so it might be nice to have more than one around.

I saw this one on Pinterest.  It looks easy enough to put together and might be fun (it is also filled with math!)

Give each child an ice cube tray (this one has pumpkin shaped cubes) and fill a bowl with squishy eyeballs.  These are also available as bouncy balls.  Children take turns rolling the dice and then placing the corresponding number of eyeballs in their tray.  With younger children, the goal can be to fill their tray.  For older children, you can add another dimension by having the children fill their trays exactly.  That means they have to roll the exact number to fill the tray or they have to count out the eyeballs, fill the tray and then take away the remainders.  This way, they continue to play instead of simply waiting.

Count to tell the number of objects.

• CCSS.Math.Content.K.CC.B.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
  • CCSS.Math.Content.K.CC.B.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
  • CCSS.Math.Content.K.CC.B.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
  • CCSS.Math.Content.K.CC.B.4c Understand that each successive number name refers to a quantity that is one larger.
• CCSS.Math.Content.K.CC.B.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

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This entire domain is something I think most early childhood teachers focus on.  We count with children all of the time looking for opportunities throughout the day for children to develop this skill.  There are some interesting specific expectations here that I think are worth exploring- things you might not be thinking about, but should be.

The first part of this standard refers to “one-to-one correspondence” even thought the authors are not calling it this.  When a child counts one object to one number and understands that each object represents “1” and only 1 number name and quantity.  So when children set the table we ask that they put one napkin at each chair, and one plate, and so forth.  You may periodically have the children count aloud when putting each item in its place, to reinforce the concept of one item = one number.  The last number they arrive at is the total number of items they distributed.  So, if there are 5 chairs at a table and the child distributes 5 napkins and 5 plates, there are a total of 5 places for children to sit and eat.  That number is the same no matter what chair they started from.  Sometimes, you can be explicit about this by asking, “How many kids can sit at this table?” or “How many napkins did you pass out?” Follow this up with a prompting question, i.e., “If you put 5 napkins out, how many plates did you put out?  Why is it the same number?”  Explaining this, or putting it into words is going to be a work in progress, but the questions will encourage mathematical thought and exploration.

The next part sub standard is a much, much harder concept for most children.  Many children 3 and up, can tell you that 5 is more than 3, or 10 is bigger than 2, but understanding that there is an actual algorithm that 6 is one unit bigger than 5… that is highly complex.

So, let’s break this down.  If I can count, “1,2,3,4,5… and so on, I have memorized a specific set of words in a specific order that describes a mathematic algorithm of

1+1+1+1+1+1…. and so on.

That means that I have to possess an understanding of the concept of “1” or in other words, the “oneness” of something so that I can then make the leap to the larger principle that counting by ones is based on the addition of “1” to the previous number.  This is also true when we ask children to count by 2s or 5s or 10s.

As adults, it is hard to break down a concept that is seemingly very simply and something that we have had known for what seems like our entire lives, into this highly complex process.  Many teachers think that if children can count then they understand number.  That is patently untrue and is a disservice to them.

Simple addition will support this concept and by simple I mean adding 1 to other small numbers.  Put two fingers up on one hand and put one finger up on the other.  Have the children add the fingers together.  This clear and consistent approach to adding “1” will reinforce the eventual understanding that 1 more, means the next number in the sequence of numbers.

Keep those kids counting….whenever you can as often as you can.

This is one of those math  manipulatives that looks pretty straightforward at first, but on second glance, you can see how it can be much more complex as the children develop.

Put two elephants together and have the children add up how many links there are all together for some simple addition.  Turn the trunks to face one another an attach the links from both to create a visual idea of “all together.”

Sort the links by color and have the children only put the colored links on the elephants that match.

Ask the children to create a pattern while attaching the links.

Use the links as a developmental tool to support fine motor skills.