Stuck

One of the 11 Best Illustrated Books of 2011, Stuck by Oliver Jeffers would not be at the top of my list of books that can be used to teach traditional math concepts. However, I think it is a fantastic book for conveying the value of perseverance and persistence in problem solving. The story begins with Floyd getting his kite stuck in a tree then proceeds with his comical attempts to throw a variety of different items into the tree in his attempts to dislodge the kite.

TEACHING TIP:
Read aloud Stuck to your students then discuss the attributes that helped Floyd solve his problem. For example, persistence, trying alternative solutions etc. Relate these attributes to solving math problems. Later, when student face a challenging math problem, remind them of Floyd.


<a href="http://www.amazon.com/gp/product/0399257373/ref=as_li_ss_il?ie=UTF8&tag=bethsbook-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0399257373"><img border="0" src="http://ws.assoc-amazon.com/widgets/q?_encoding=UTF8&Format=_SL110_&ASIN=0399257373&MarketPlace=US&ID=AsinImage&WS=1&tag=bethsbook-20&ServiceVersion=20070822" ></a><img src="http://www.assoc-amazon.com/e/ir?t=bethsbook-20&l=as2&o=1&a=0399257373" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />

<iframe src="http://rcm.amazon.com/e/cm?lt1=_blank&bc1=000000&IS2=1&bg1=FFFFFF&fc1=000000&lc1=0000FF&t=bethsbook-20&o=1&p=8&l=as4&m=amazon&f=ifr&ref=ss_til&asins=0007263864" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>

Eat Your Math Homework

My favorite new book for the math classroom is Eat Your Math Homework Recipes for Hungry Minds by Ann McCallum. Students won't report to class claiming their dog ate their homework with activities such as the ones McCallum has cooked up. These tasty recipes can be followed at home or at school for a tasty snack of milk and math.

The recipes begin with "Fibonacci Snack Sticks" where children learn about patterns and sequences with a side of math history as they skewer a variety of ingredients to create edible patterns. Other recipes including "Fraction Chips," "Tessellating Two-Color Brownies," and Probability Trail Mix" will have students coming back for seconds.

Teaching Tip
Invite parents to join the class and assist small groups of children as they cook up some math.

[NOTE: I've provided links to both the hardcover and paperback versions of this book. You may want the hardcover for you personal library. I suggest multiple copies of the paperbacks so you have at least one copy for each small group.]

Teddy Bear Math

While I was away for the summer break a new book found it's way to my desk Teddy Bear Math by Barbara Barbiere McGrath. This book can engage children in a delightful exploration of counting, estimation, sorting, addition and graphing. The rhyming verse encourages readers to grab handfuls of Teddy Bear Counters for a variety of activities. Even if you do not have a set of Teddy Bear Counters for children to use along with reading the book I think it is a great addition to your classroom library.



An earlier book by McGrath, Teddy Bear Counting is a perfect companion to the new title. Together children will build Number Sense and develop counting skills.

Teaching Tip
Substitute beans as an inexpensive substitute for the teddy bear manipulative. I suggest dried white beans that can easily be spray painted red, yellow, purple, blue, orange and green then used for all of the counting and sorting activities.

Ten Flashing Fireflies

"What do we see in the summer night?
Ten flashing fireflies burning bright!
Catch the one twinkling there
Like a star.
One flashing firefly in our jar."

One of my favorite childhood memories is sitting on my grandmother's porch at dusk waiting for the fireflies. Some nights all of the cousins would happily run around and try to catch them other nights we would lazily watch as in unison they seemed to float into the tree tops.

Ten Flashing Fireflies by Philemon Sturges beautifully depicts this summer ritual in an imaginative counting book that is the story of a brother and sister catching and counting fireflies then releasing them back into the night.

Teaching Tip
Counting seems such a simple concept from our adult perspective, but for the young child learning to count can be a daunting task. For starters they must learn the number names and the counting sequence, then it gets more complicated with concepts such as cardinality (knowing that the last number said identifies the total number of objects in a group) and stability (knowing that rearranging the position of objects in a group does not change the cardinality). To help youngsters master these complex mathematical ideas we must give them many opportunities to count. Reading books such as Ten Flashing Fireflies can help. Luckily, children often like books read to them over and over again, so each time we read with them we can ask questions that help them learn to count. First, have them count along with the characters. Then, ask them to predict what comes next. For example, when the children have three fireflies in their jar then catch one more ask how many fireflies are now in the jar. Have objects available such as beans, pennies or some other small item and have children use them to represent the fireflies. They can add a bean to a jar (or pile) each time another firefly is captured. After reading they can count the objects again and again.

What other ideas might you have for using Ten Flashing Fireflies to teach basic counting concepts?

Welcome ISI Participants

Today I enjoyed a delightful morning with the Illuminations Summer Institute participants talking about my favorite topics: children, mathematics and literature. Welcome to those of you who have found your way to my blog following the workshop.

During the session I mentioned that my favorite source for guidance and inspiration about the integration of math and literature are David and Phyllis Whitin. They co-authored New Visions for Linking Literature and Mathematics. It and the two titles David co-authored with Sandra Wilde (Read Any Good Math Lately?: Children's Books for Mathematical Learning. K-6 and It's the Story that Counts:More Children's Books for Mathematical Learning) are fantastic resources. In my humble opinion the books are "must-haves" for every teacher's resource library.

In New Visions, the Whitins lay out a 4-part criteria that serve as a guide when selecting good math-related books. They believe the literature should demonstrate:

1. Mathematical integrity
2. Potential for Varied Response
3. An Aesthetic Dimension and
4. Ethnic, Gender and Cultural Inclusiveness

There are literally thousands of pieces of children's literature to sift through before you find the gems that make good resources for the elementary math classroom. This simple criteria serves as a great tool for identifying great books.

Favorite books? Advice?

Happy Saturday everyone! Welcome to all the new folks who have recently found their way to my bookshelf. Thank you for the e-mails that let me know you are enjoying your browsing. I welcome your comments, you can leave them here or write to me at bethsbookshelf[at]aol[dot]com

I would actually like to hear from you on something specific--this weekend I am preparing for a workshop that I'll give Monday morning to a small group of teachers who will be developing lessons for the Illuminations site. I am always eager for an opportunity to talk about children's literature and mathematics. As always, I have already gathered far more books than I will be able to share during the two-hour session. Help me edit myself down so I focus in on the best of the best. When someone asks for suggestions on great book for teaching math concepts what are the top titles in your list? Do you have any advice as far as what makes one book better than another to use during your math lessons?

Today I'll leave you with a few sources for teaching ideas:

The Wonderful World of Mathematics: A Critically Annotated List of Children's Books in Mathematics is the first teaching resource for math related children's literature that I bought for my personal collection. Now in it's second edition, this book is analyzes the content of more than 550 titles. Chapters organize the books by math topic.

Hand's on Math and Literature with Math Start is a fantastic new series written by Don Balka and Richard Callan that is packed with great teaching activities and reproducibles that extend the mathematics found in Stuart Murphy's Math Start series. Of course Murphy's titles can always be counted on to engage children in math concepts. Now this series by Balka and Callan help you extend the investigations with more hands-on activity ideas that explore the math concepts with more depth.

Who sank the boat?

Mr Grumphy's Outing by John Burningham and Pamela Allen's Who Sank the Boat? provide the perfect excuse to splash around in a cool tub of water on a hot July afternoon. In both stories the characters pile into the boats until they reach maximum capacity and ultimately sink the boat. As each new character is introduced children can make predictions of what will happen next. After reading the book children can investigate the sinking scenario as described below.



Teaching Tip
A lot of math and science can be explored with this activity. Give each child or small group a square sheet of aluminum foil (6" x 6") and ask them to shape the foil into a boat. Then children then place identical objects (marbles or bottle caps or pennies or paper clips etc.) into their boats until the boat sinks. The goal is to place the most objects into the boat before it sinks.

A detailed lesson plan for the foil boat activity can be found here. Extend the lesson by having different students use different objects then chart the results. Which objects needs the fewest to sink the boat? The most?

Patriotic Math

Like everyone else I am taking a long-weekend to celebrate the anniversary of America's independence. In the meantime, here is a source for patriotic math activities.

Math Wizardry for Kids

Although the school year has just ended and summer only officially kicked off last week, I've already heard from parents who are searching for ideas to help their children fill their vacation time with productive activities. First, planning a weekly trip to your local library is always a great idea. While at the library look for a copy of Barron's Math Wizardry for Kids, it is full of projects you can turn to respond to the child who is already lamenting, "Mom, I'm bored. I don't have anything to do!"

In Math Wizardry for Kids, authors Margaret Kenda and Phyllis S. Williams have have created a rich resource packed with dozens of creative projects that will not only keep children busy, but also encourage them to discover many of the mysteries and wonders of mathematics. The list of materials and clear directions are for each activity, accompanied by simple illustrations, empower children to work independently. I predict that many parents will enjoy completing projects right alongside their children.

Teaching Tip
Teachers will find Math Wizardry for Kids a handy resource for creative projects that students can do in and outside of class to reinforce math concepts and discover mathematical understanding for themselves. For example, Chapter 9 includes a project titled, "Build a Sun Clock." Students can use their sun clock to tell time as well as learn about measurement and angles.

Let's Hear it for the Girls

Last week I read an interesting post over at the math 4 love blog. The posting, When Girls Leave Math and What to Do About got me to thinking about books we can use that present girls as strong characters AND skilled in mathematics.

Danica McKellar, perhaps better known as Winnie Cooper from the television series "The Wonder Years" does a wonderful job of promoting girl math-power in Math Doesn't Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking A Nail and Kiss My Math: Showing Pre-Algebra Who's Boss. Her third title in this series is Hot X: Algebra Exposed! and is scheduled for release June 28, 2011. [Note: Hot X is available for pre-order from Amazon.com, click the book link here to learn more or reserve your copy.]

McKellar's books are breaking down stereotypes and demonstrating that girls can and do make great mathematicians. Her sassy and witty style not only teaches math concepts it also encourages young girls to tap into their own undiscovered math potential.

I mentioned novels yesterday that are worth noting again, Do the Math: Secrets, Lies, and Algebra and Do the Math #2: The Writing on the Wall by Wendy Lichtman who has created a young teenage heroine who uses math to solve life problem and mysteries.

Teaching Tip

From time-to-time we should all do some personal reflection and examine our teaching practices. Are we guilty of reinforcing the negative gender stereotypes? As role-models do we send subtle messages that it is okay for girls not to understand math? Parents, when your child asks for math homework help how do you respond? Rather than comforting a daughter that struggles with math with comments such as "I wasn't good in math either" parents can begin to send positive messages with responses such as, "I don't know, let's find out together." After all, parents are the most important role-models of all.

Official Start of Summer

The summer solstice has arrived, bringing with it the official start of the summer season. Yesterday we began or list of books for beach reading, long car rides, or simply reading while lolling in the backyard and sipping lemonade. On this day that is the longest day of daylight I hope that you and your children enjoy reading math.


Here are a few more titles to consider:

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan follows the travels and adventures of a mathematical wiz who uses his skills to settle conflict and give wise advice.

The Number Devil: A Mathematical Adventure is a rich mathematical fantasy that reveals both the mystery and beauty of numbers using a relatable character for readers age 8 to 80.

In Do the Math: Secrets, Lies, and Algebra and Do the Math #2: The Writing on the Wall author Wendy Lichtman has created a young teenage heroine who uses math to solve life problem and mysteries.



Teaching Tip
All of the books that I am listing this week would make good classroom read-alouds.

Welcome Math Jokes 4 Mathy Folks fans

Welcome to all of the first time visitors joining us today from Math Jokes 4 Mathy Folks.

You might be especially interested in this post from last month, "What ten things can you always count on..."? That just so happened to mentioned the runaway bestseller by Patrick Vennebush, Math Jokes 4 Mathy Folks.

I hope that you like what you see and bookmark this site so you can come back often.

Fun Summer Reading

Sometimes you just want to kick back with a good book and read. There are a number of books with a math bent that are also just plain fun to read. This week the summer soltice begins and many of us will be searching for books to read while soaking up the sun. Here are a few suggestions for books to tuck into your beach bag.

Crimes and Mathedemeanors by Leith Hatoutis is a delightful collection of short detective stories that will challenges teenagers and adults alike. The main character, Ravi, is a 14-year-old math genius who uses mathematics and physics to help the local detectives solve perplexing cases.



The Parrot's Theorem, an International bestseller by Denis Guedj is an interesting cross between mathematical history and a murder mystery combined with a charming parrot that will discuss math with anyone.



Finally, for younger readers, check out The Great Number Rumble: A Story of Math in Surprising Places by Cora Lee and Gillian O'Reilly. A book that aptly illustrates that math is indeed all around us.

KenKen Puzzles

For our final suggestions of fun resources to consider using while celebrating National Brain Training Week (June 11-17, 2011) we will look at KenKen puzzles. Just as with the magic square and sudoku puzzles discussed earlier this week, KenKen puzzles help children develop problem solving skills and number sense. Puzzles also help develop concentration.

Here are a few good sources of KenKen puzzles:

Will Shortz Presents I Can KenKen! Volume 1: 75 Puzzles for Having Fun with Math is recommended for children ages 9-12. Shortz has also published volumes 2 and 3 for the same age range of children. All of the titles in the series include a "Home and Classroom Guide for Parents and Teachers" written by Marilyn Burns.

KenKen puzzles are also available as a handheld game.

Teaching Tip
The bulletin board idea mentioned in the June 15 posing on Sudoku can be adapted for KenKen puzzles.

As an alternative, instead of incorporating the puzzles we have talked about this week into classroom instruction, consider just having number puzzle books available for children to enjoy in their leisure time. Parents might consider having a few number puzzle books available in the car to occupy children on long trips. Magic Squares, Sudoku and KenKen are a great way for children to enjoy math with out any pressure. Let's always remember to create opportunities for children to enjoy the wonder and beauty of mathematics.

The Art of Scale

In the spirit of full disclosure you should know up front that I have no books to share today. I'm taking a brief departure from the typical entry you find on this blog because I ran across two Web pages last night that fascinated me. I thought I would share them with you in hopes that you would know of a piece of literature or two that could be used along with these sites. I also hope that these resources inspire you to share your ideas for teaching scale.

SOURCE: Image of Swine Flu from http://www.lukejerram.com/glass/gallery

The above photo is one example of the dozen or so unusual glass sculptures created by Luke Jerram. Each beautiful piece is an authentic representation of some of the deadliest viruses on our planet. The sculptures are each about 1,000,000 times the size of the actual pathogen.

While exploring Jerram's Glass microbiology site I found a link to Learn Genetics and a depiction that is a great illustration of scale that can help you and your students comprehend just how small single cell organisms are compared to familiar items such as a coffee bean, grain of rice and a sesame seed.

Teaching Tip
I think both sites are great visual resources to use when teaching scale. What do you think? Do you see applications for these sites in your classroom? What resources and activities do you use to teach scale?

Sudoku

Continuing with our look at number puzzles in observance of National Brain Training Week (June 11-17, 2011) today we look at Sudoku, the number puzzle that quickly went from something no one had every heard of, let along pronounce, to becoming a global phenomenon. The traditional 9 x 9 grid Sudoku is easily adaptable for a range of age and ability levels. Books such as Will Shortz Presents the Monster Book of Sudoku for Kids: 150 Fun Puzzles begin with a short introductory lesson on solving Sudoku and entry level 4 x 4 grid puzzles before advancing to 6 x 6 then the traditional 9 x 9 grid puzzles.

In Sudoku Puzzles for Kids, author Michael Rios also modifies puzzles for children by only using the digits 1 - 6 in his puzzles rather than the typical 1 - 9.

Sudoku is accessible to even the youngest students with puzzles like those found in Kindergarten Sudoku by Peter Kattan and Sudokids.com Sudoku Puzzles For Children Ages 4-8: Every Child Can Do It. For Kids At Home or At School by Jonathan Bloom.

Teaching Tip
Carol A. Buckley describes a clever use of Sudoko in her November 2008 article, "Using Sudoku Bulletin Boards to Teach Mathematical Reasoning." Just as you can surmise from the article title, Buckley's idea is to create an interactive Sudoku as a bulletin board display. Using an enlarged 9 x 9 grid made of poster board mounted on a cloth covered classroom bulletin board, Buckley staples digit cards in the appropriate squares to replicate the given numbers of a puzzle she has selected from resources such as the books listed above. Velcro tabs are placed in the open spaces. Students use digit cards, with Velcro tabs on the reverse side, that Buckley makes available in an envelope positioned beside the grid. Throughout the day students can work individually or collaboratively to solve the puzzle. Once a puzzle is completed, Buckley can easily replace it with a new puzzle.

National Brain Training Week

In observance of National Brain Training Week (June 11-17, 2011) here are a couple of books that will give you and your students a good brain work out. What better way to put your mind through the paces than with number puzzles?

First let's ponder the challenges in magic squares. In Before Sudoku: The World of Magic Numbers Seymour S. Block and Santiago A. Taveres take readers on an engaging tour through time from the earliest appearance of the magic square (some 4,000 years ago in Ancient China) through modern times.

While Before Sudoku is more appropriate for high school students and adults, younger students will enjoy reading Ben Franklin and the Magic Square by Frank Murphy.

Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey by Paul C. Pasels may be most appropriate for the mathematicians among us.

Teaching Tip
Try this Magic Square Generator students can use to create puzzles to share. Or select one of these classroom ready worksheets of magic squares built from whole numbers, fractions or decimal numbers.

Hubert Horatio Bartle Bobton-Trent

WOW! How would you like to have that name? Hubert Horatio Bartle Bobton-Trent is a delightful character created in the mind of author Lauren Child. The humorous plot is along the lines of the classic parent/child role-reversal. Hubert Horatio's irresponsible socialite parents are squandering the family fortune. In his efforts to save the day the charming and resourceful Hubert learns that money isn't nearly as important as family.

Teaching Tip
Young readers will enjoy this tale that can be used as a starting point for conversations about money. If you want to follow the book with a continuation of the lessons on identifying, counting, and exchanging coins that we touched upon yesterday I suggest the "Coin Box" activity found on the Illuminations site. The activity was inspired by the article "Teaching the Value of Coins" published in the January 1999 issue of Teaching Children Mathematics. In the article authors Randell L. Drum and Wesley G. Petty Jr. address the fact that coins are nonproportionate models in terms of the value they represent and offer alternative, proportionate models that can be associated with each coin.

A dime doesn't buy as much as it use to

I've had money on my mind lately...not because of the economy, but because I've found myself in various conversations about children and money. Specifically, the topic has been concern that children are exhibiting increasing difficulty counting and exchanging coins. I think it has a lot to do with the fact that as our society evolves and depends more and more on digital commerce children have less and less opportunity to see the use of coins modeled in everyday life.

"Clink, clink, clink, clink...Clink, clink, clinkity... Money saved in a bank makes your brain think-thinkity!"

In You Can't Buy a Dinosaur with a Dime author Harriet Ziefert uses rhyming verse to tell the story of Pete and his experience in earning, saving and budgeting his allowance. Readers can join him as he saves, spends, and strategizes over future purchases.

Teaching Tip
If possible, provide children with an assortment of real coins to model the actions of Pete as they re-read the book. Encourage students to begin to save coins and create their own spending and saving plan.

And the winner is......

...Jen! Congratulations!!!!

Using the random number generator on random.org Jen was selected as the winner of the book Learning Algebra with Pizza by Dawn McMillan. Jen was one of the people that left a comment on the June 2, 2011 entry: More than Pizza and Brownies. Thank you Jen and everyone else who joined the conversation!

Congratulations Jen! You have one week to e-mail me at bethsbookshelf[at]aol[dot]com with your mailing address so I can send out your prize.

Growing Patterns

In April I shared several books and ideas for learning more about the Fibonnaci sequence. Here is one more title to add to that collection, Growing Patterns by Sarah Campbell. Using stunning photographs, Campbell explores the appearance of the Fibonacci numbers in nature.

Interestingly, the progression of the photograph layouts represent a Fibonnaci spiral. The text begins with a very simple pattern and advances to more complex mathematical concepts.




Teaching Tip
If possible bring an assortment of flowers, seed heads, fruit etc into the classroom for students to examine.

Discovery education offers an excellent lesson plan that includes a set of activity sheets that can help guide students as they investigate Fibonacci numbers found in nature.

Book Giveaway

Don't miss your chance to win a free book by commenting on my June 2, 2011 blog post. The contest rules are re-capped below:

Let's talk
I want to begin a dialogue with my readers so that I can learn from you and tailor blog entries to your instructional needs. To kick off the conversation I decided to offer a bribe, er I mean incentive, to encourage you to post a comment. Post a comment to yesterday's post by Monday, June 6, 2011 and you'll be in a drawing for a copy of Learning Algebra with Pizza by Dawn McMillen.

Here are the giveaway rules:

1. Leave one comment to the June 2, 2011 post anytime between now and Monday, June 6, 2011 at 11:59 PM Eastern Time. You are limited to one entry. The contest is limited to US residents only.

2. For this contest, I will pick one winner at random from the comments section of this post. The comments will be numbered in the order they are received, i.e. the first comment is #1, the second #2, and so on. The Random Integer Generator at random.org will be used to pick the number of the winner.

3. The contest winner will be posted by Wednesday, June 8th. The winner will have one week to email me to claim their prize.

More than Pizza and Brownies

Okay...I can admit it...I have food issues....a lot of people do these days. It seems that the 'go to' analogy for teaching fraction concepts is always food related. As I was going through my book collection and preparing my blog entries about fractions I realized that the majority of the stories we use have the characters portioning out food in fair shares. Given that obesity is a serious health issue in our culture, perhaps we educators we should be sensitive to the messages we send to children. For example, through our literature selections we can teach that fractions are more than just pizza, pies and brownies.



Toward that end, here are a few books that use non-food models to convey fraction concepts:

In Jump, Kangaroo, Jump Kangaroo and his friends separate into various groups to compete in Field Day exercises.

Eight messy bunkmates win the prize for the cleanest cabin in the funny fraction tale A Limpiar El Campamento! (Clean-Sweep Campers).

Readers of Polar Bear Math learn about fractions following the care of two baby polar bears born in a zoo.

In Go Fractions! the soccer coach and math teacher names his team fractions and the player numbers on each uniform are fractions. The team does share a food item in this story, but since the food is a healthy choice we'll include the title in this list.

Let's talk
I'd like to hear from you. What are your thoughts about using food models to teach fraction concepts? What about eating scenarios when teaching problem-solving strategies? It has been a while since I have been a classroom teacher, so I may be off-base. I want to know your opinion. Post a comment to this post by Monday, June 6, 2011 and you'll be in a drawing for a copy of Learning Algebra with Pizza by Dawn McMillen. (Yes, my attempt at irony!)

Here are the giveaway rules:

1. Leave one comment on this post anytime between now and Monday, June 6, 2011 at 11:59 PM Eastern Time. You are limited to one entry. The contest is limited to US residents only.

2. For this contest, I will pick one winner at random from the comments section of this post. The comments will be numbered in the order they are received, i.e. the first comment is #1, the second #2, and so on. The Random Integer Generator at random.org will be used to pick the number of the winner.

3. The contest winner will be posted by Wednesday, June 8th. The winner will have one week to email me to claim their prize.

More about fractions

Continuing our exploration of fractions let's look at Fraction Action by Loreen Leedy, a beginner chapter book of five stories that are useful for reinforcing concepts such as dividing geometric shapes into fractions, dividing sets of objects into equal parts, cutting fruit into equal shares, and dividing a dollar into fractions. Other titles you may want to consider are Full House: An Invitation to Fractions by Dayle Ann Dodds and Give Me Half by Stuart Murphy.



Teaching Tip
Pattern Blocks are great manipulatives for developing understanding of fraction concepts. Alternatively, if you do not have access to the blocks you can provide students with paper models of this tool using a pattern block template or have them explore using virtual pattern blocks. Give students either model then challenge them to find fractional parts of the whole.

Chick here for a treasure trove of online activities that teach fraction concepts.
Funny & Fabulous Fraction Storiesby Dan Greenberg and Jared Lee is a useful resource book for teachers.

Introducing Fraction Concepts

This week we will explore books that can be used to teach fraction concepts. First up Fraction Fun by David A. Adler teaches the basic concept that a fraction is a part of something. In Apple Fractions by Jerry Pallotta different varieties of apples are used to demonstrate halves, thirds, fourths etc. Whole-y Cow: Fractions Are Fun by Taryn Souders introduces fractions both as part of a whole and part of a group.

Teaching Tip
Use apples to replicate the demonstrations in Apple Fractions. Not only are apples a healthy treat, they can easily be halved, quartered and compared.

Click here to have students explore equivalent fractions using an Illuminations activity.

Memorial Day Math

For some, Memorial Day is simply a 3-Day weekend that marks the unofficial kick-off for summer. Actually, the first Memorial Day observance was in 1868 when flowers were placed on the graves of soldiers in Arlington National Cemetry. You can use this Memorial Day to teach students the true meaning which is to honor those who have given their lives in service for our nation.

I do not have suggestions for math concept books today, but you can click here for a list of books about Memorial Day that you may find helpful.


Teaching Tip
For a math tie in, students can use fractions and geometry skills to construct a patriotic patchwork quilt using red, white and blue construction paper.

So Square

Thoughts of summer have me longing for the beach. Since I can't sink my toes in the warm sand just now, I'll have to enjoy Sea Squares by Joy Hulme instead. On the surface, Sea Squares might be mistaken for a simple counting or pattern book. Actually the rhymes are a great introduction to squaring numbers from 1 to 10.

Teaching Tip
Distribute grid paper and have the students create an array to represent the various animals found on each two-page spread. For example, ``8 `octos' on the ocean floor/ Have scrambled legs, 64.'' can be represented with an 8 by 8 square drawn on the grid paper. Guide the students to also express the representation mathematically as 8 x 8 = 64.

Lemonade for Sale

Yesterday we talked about class projects to raise funds for a class field trip. Stuart Murphy's Lemonade for Sale is a perfect follow-up. The children in the story want to raise money to repair their clubhouse and keep track of sales from their lemonade stands

Teaching Tip
Students can also use bar graphs to analyze data collected in their own fundraising efforts.

Field Trip

Here in Washington D.C. you can't go to any of the museums or historical spots without being surrounded by the swarms of excited children in town for spring field trips. While not every school can send students to the nation's capitol, there are just as many, if not more, great field trip destinations that are local. Whether traveling near or far, there is still the question of where the class will get the funds needed for transportation and other expenses. Planning the trip and raising the cash can provide for just as much learning as the trip itself.

Such is the case in How the Second Grade Got $8205.50 to Visit the Statue of Liberty.
It makes a great read-aloud.

Teaching Tip
After reading it lead a discussion where children share their own ideas for raising money or their own experiences with ventures such as lemonade stands or doing chores to raise cash. Have the students re-read the book keeping track of the profits and expenses. If your school allows, you class could launch their own fundraiser to collect monies to donate to recent disaster relief funds.

Getting Ready for Summer Fun

Today I am going to list a few titles of books filled with math challenges that are good recommendations for parents asking for ways to keep their children engaged in mathematics throughout the summer break.

The Everything Kids' Math Puzzles Book: Brain Teasers, Games and Activities for Hours of Fun is filled with games and trivia to keep children ages 9-12 using their math skills to solve riddles and puzzles all summer long.



Math Games for Middle School:Challenges and Skill Builders for Students at Every Level begins with basic operations and moves into plane and solid geometry, graphing, probability and simultaneous linear equations.

In addition to paper and pencil type puzzles, children can use a lot of math skill playing card and dice games.

Two books by author Charles Lund, Math Games Played with Cards and Dice, Grades K-1 and Math Games Played with Cards and Dice, Grades 2 and 3 is filled with age and skill appropriate games that promote computation skills, logical thinking and mathematical reasoning.

More on Measurement

Regretfully, I do not have time to flesh out more teaching ideas today. I will give you links to three more books that are useful when teaching measurement. I invite you to add your own teaching tips.

How have you used these titles in your math classroom?

Early Measurement Concepts

A growing number of you are beginning to stop by my blog each day and I thank you. My goal is to build a robust resource that continues to meet your needs throughout the year. I hope that you will take a few minutes to leave a comment or send me an e-mail to let me know how I am doing or make a request.

I thought I'd mix up the format today and begin with a few teaching tips before discussing any specific book titles. Let me know what you think or if you have format preference.

Teaching Tips

A skill that both teachers and students wrestle with year after year is measurement. Teachers struggle with creating meaningful learning opportunities to effectively teach measurement concepts and it is a skill many students find difficult to master. In my opinion, the best solution from both perspectives is finding numerous opportunities to measure through the school year rather than a single one or two week unit that is rushed through near the end of the school year.

Beginning with the youngest students we start with measuring and comparing objects using non-standard units. Ask the children variety of questions that encourage them to ponder their results. There is no need to use store-bought manipulatives if they are not readily available. For example ask How many paper clips wide is your desktop? How many pencil lengths wide is your desktop? Why do you need more paperclips than pencils to measure your desktop? Ask them to predict how wide the desktop might be using a different object as the unit. The more children are able to explore measurement the better they will be able to develop their skills.

You do not have to limit their exploration to linear units. They can measure capacity by filling different size containers with rice or sand. Challenge them to predict then test how many scoops of a smaller container are needed to fill a larger container. Weight can be explored using a balance scale and experimenting how many of one object are needed to balance the scale when a different object is resting in one of the pans.

Carrie Measures's Up by Linda Abner and Inch by Inch by Leo Lionni and Super Sand Castle Saturday by Stuart J. Murphy are good choices for children as they explore measurement concepts.

"Measuring Experiences for Young Children" published in the February 2004 issue of Teaching Children Mathematics is filled with more ideas for creating measurement investigations using non-standard units.

"Rulers of Different Colors" from the August 2007 issue of TCM offers teaching ideas for transitioning students from non-standard to standard units.

Drop by again tomorrow for more on measurement.

Royal reading and problem posing

Now that all of the hub-bub over the royal wedding between Prince William and now Princess Katherine of Wales is over, do you or your students want just a bit more pomp and ceremony? Perhaps imagining the joyous journey Margaret Mahy shows us in 17 Kings and 42 Elephants or pondering the clever conundrum the bright princess poses in One riddle, one answer by Lauren Thompson will satiate a longing for palaces and pageantry. This list would not be complete without including The King's Commissioner's by Marilyn Burns, and I would be remiss if I did not mention the many math adventures by Cindy Neuschwander--but a mention is all that you get today, because I am saving Cindy for a future author spotlight. Stay tuned!

Teaching Tips
17 Kings and 42 Elephants can be used as a bridge into a lesson on place value and/or double-digit addition. A related lesson plan was created by Mary Elizabeth Hoffman. Children will also enjoy place value games.

Counting strategies come to the rescue in The King's Commissioners. Check out this lesson plan from Betty Psychogios.

Rusty Bresser wrote a great lesson plan to accompany One riddle, one answer. He uses the book as a catalyst for student to first solve Princess Aziza's riddle then begin to create their own riddles.

Even though this blog is about math, I thought those of you who are homeschoolers might be interested to know that MacMillan provides this review sheet for One riddle, one answer as well as other online resources.

What ten things can you always count on?....Your fingers!

Now that the month of May is finally here most teachers will begin to breathe with a sigh of relief because they have the final goal line in sight. It has been a long school year. You've done your best to create a rich mathematical learning environment. Now, with only a few weeks left, you want to keep your students motivated through the end of the school year. Why not bring out a collection of jokes, riddles and puns that will not only tickle their funny bones, but also keep students engaged until that end-of-year bell rings?

"Where do math teachers eat? On multiplication tables, of course!" says Joan Holub in Riddle-Iculous Math. It is filled with jokes, puns and riddles that will get your math-laugh-fest off to a great start. Another perfect choice is Arithme-Tickle: An Even Number of Odd Riddle-Rhymes by J. Patrick Lewis. The most recent addition to this genre, Math Jokes 4 Mathy Folks, by my NCTM colleague G. Patrick Vennebush is a must have for every math classroom. Don't miss Patrick's blog for more math puzzles, wit and humor. You can revisit my April 7 post for the titles from Greg Tang filled with riddles and fun.

Hard to find, but worth looking for in your local library:
See you later, Escalator!:Mall Math by Time-Life Books
How Many Feet? How Many Tails? by Marilyn Burns

Teaching Tip
Challenge students with some amusing riddles as part of the daily class routine. Include puns and knock-knock jokes on worksheets or quizzes. Have them write original riddles to display in the classroom or exchange.

The article Math Riddles:Helping Children Connect Words and Numbers by Carl M Sherrill provides suggestions and guidelines for student authored riddles.

Happy May Day

May is a traditional holiday in many cultures. It is similar to the Labor Day holiday celebrated here in the United States. As we celebrate the contributions workers make to all of our lives. let's also note that none of their work could be accomplished without math.

Two books that emphasize that math and numbers are all around us are Missing Math A Number Mystery by Loreen Leedy and Neil's Numberless World by Lucy Coats.

Teaching Tips
Have children work in groups to list all of the different ways they encounter numbers and math in their daily lives. Later have the students share and compare their lists. Then the children can write their own stories.

What time is it?

Telling time using both analog and digital clocks is an important skill that some students struggle with. Telling Time with Big Mama Cat by Dan Harper, The Clock Struck One by Trudy Harris What Time is it? A Book of Math Riddles by Sheila Keenan and Clockwise a Time Telling Tale by Sara Pinto are a small sampling of the trade-books that help children develop an understanding of the concept of time.

Teaching Tip
Make the observance of time a natural part of each day. As you go through the schedule, emphasize the time various events take place both verbally and by noting the position of the hands on a classroom clock.

The TeAchnology and Just in Time sites houses a broad selection of time related lesson plans

More on a million...

I thought we would close out the week with a final look at literature and activities to help children grasp the concept of large numbers. A Million Dots by Andrew Clements begins and ends with a single dot, and the 999,998 dots in between show what a million really is. How Big is a Million? by Anna Milbourne, illustrates a million as well as smaller place value concepts. Millions of Cats by Wanda Gag is a fun read-aloud.

This University of Missouri site links to a number of other sites with representations or hands-on activities that help children visualize one million.

Teaching Tip
Project this illustration of a million dots in your classroom.

This page about Geologic Time includes great questions such as How long would it take to count to a million?

Checkers, chessboards and rice

"Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state." ~Plato

Yesterday we talked about large numbers. Continuing along that same vein today I offer The King's Chessboard and One Grain of Rice, two takes on the classic doubling problem. Students will be amazed at how quickly simple grains of rice can accumulate. At the same rate as the wise man accumulates rice in the story can your students determine how long it would take before he had one million grains of rice?

Teaching Tip
If your students aren't quite ready to tackle exponential growth you may want to begin with the concept of doubling. A good place to begin is with this investigation Dr. Jennifer M. Suh developed around the book Two of Everything by Lily Toy Hong. Suh's article was published in the November 2007 issue of Teaching Children Mathematics. Mathwire.com offers a free template to be used with Two of Everything.

Here is a lesson plan using The King's Chessboard.

I want to be a billionaire so freakin' bad.....

You may hear your students humming or singing the popular hit Billionaire by Travie McCoy and Bruno Mars, but do they even understand the concept of a million? Books such as How Much is a Million and If you Made a Million by David M. Schwartz can help children begin to grasp the magnitude of such a large number.

Teaching Tip
Rather than give you my own teaching tips, today I want to point you to
The Magic of a Million Activity Book, by David M Schwartz and David J Whitin, that is available as a free download. It is chock full of activities and reproducibles that will have your students exploring the concept of a million in concrete ways.













[A word of caution: Please do not interpret my attempt to be current and witty as an endorsement for using the song Billionaire in the classroom. While the chorus is catchy, the other lyrics are explicit and inappropriate for classroom use.]

Odd or Even ?

In developing number concepts and number sense children learn to recognize numbers as odd or even. Two books that are helpful are Even Steven and Odd Todd by Kathryn Cristaldi and Bears Odd, Bears Even by Harriet Ziefert. Opportunities to develop an understanding of odd and even numbers are bountiful throughout the school day.

Teaching Tips
1. While counting any found objects or manipulatives have the students group the items in pairs. Emphasize that an item that does not have a partner, or any 'left over' item is odd.
2. Have students skip-count by 2's.
3. Give students a hundred's chart and two crayons. Have them shade the even numbers with one color and the odd numbers with a different color.

These sites have activities to help children understand odd and even numbers:
Teacher and Parent resources
Odd and Even exploration

0, 1, 1, 2, 3, 5, 8, 13, 21, 34...

This famous sequence was first observed in 1202 by Italian mathematician Leonardo of Pisa, perhaps better known today as Fibonacci. Found in nature, this growing pattern has intrigued mathematicians for centuries. Students can explore the Fibonacci sequence using various math concepts appropriate to their grade level. Books such as Rabbits, rabbits everywhere: A Fibonacci tale; Wild Fibonacci and Blockhead: The Life of Fibonacci are perfect entry points into the world of Fibonacci.

Teaching Tip
Pose the same problem that Fibonacci wrestled with:
Rabbits can mate at the age of one month so by the end of the second month, each female can produce another pair of rabbits. If the rabbits never die and each female produces one male and one female rabbit, how many pairs of rabbits will be produced by the end of a year?

You can find a detailed version of the rabbit problem investigation here.

Other teaching resources:
Grade 4 lesson plan
Discovery School lesson plan

More on estimation

Yesterday my mind (and heart) were on the gulf shore. In retrospect I realized that I could have shared more literature suggestions and teaching ideas about estimation, so we will revisit the topic today.

Stuart J. Murphy offers a nice overview of estimation with Betcha! Teachers can replicate activities such as estimating the number of jellybeans, or other objects, in a jar to give students the opportunity to hone their own estimation skills. Another Murphy title, Coyotes All Around, introduces the concept of rounding to estimate.

Teaching Tip
Discuss real life situations where estimation is appropriate compared to when an exact answer is necessary. The Counting is for the Birds problem, from the February 2010 issue of Teaching Children Mathematics presents an interesting estimation challenge and two estimation strategies.
Sample solutions were published in the February 2011 issue.

A Million Fish...More or Less

With my own family roots deep in the South Louisiana marshland, today I am compelled to mark the one-year anniversary of the Deep Water Horizon disaster and subsequent oil spill that continues to impact the Gulf of Mexico. Rather than bemoan the on-going devastation and unknown long-term impact, I want to pay tribute to the strength and bravery of the citizens. For generations the unique culture has taken hit after hit, but each time these resilient people pick themselves up, patch their lives back together then continue moving forward.

In A Million Fish…More or Less, Patricia C. McKissack aptly captures optimistic spirit found in those who live on the bayou. This yarn, set in the Louisiana swamp, takes exaggeration to a whole new level. McKissack ‘s fish tale can easily be incorporated into a lesson on place value, estimation, or even division of fractions. In my opinion, it provides a natural segue into a lesson on reasonable and unreasonable estimations.

Teaching Tip
I found two lesson plans for you. The first is from TI Education and the second is from Scholastic. Share your ideas for teaching with this book by adding your comments to this post.

Counting Books

My previous entry was for older students, so today I'll offer you ideas for the little ones. Early childhood is typically considered to be when the child is age 0 to 5 (or 6) depending upon which expert that you are listening to. While the exact age span may be in dispute, the fact that the human brain grows as a rapid rate during the early years is well-known. During this period parents anxiously watch for signs that their children are reaching certain developmental milestones. Long before a child can add or subtract they are forming ideas that serve as the foundation for learning math concepts. To support the development of numeracy parents and early grade teachers can expose children to counting books.

Teaching Tip
Young children need many opportunities to count. At home they can be involved in counting everyday objects such as the number of eggs in a carton, setting the dinner table with the correct number of plates, or while helping to straighten the house counting the number of cushions on the sofa. In day-care or pre-kindergarten classes children can count along as the adult distributes snacks or toys. With counting books, the children may not be able to read the text, but you can ask them to re-tell the story from the pictures counting as they revisit the pages.

Flatland...not so flat

As always, the NCTM Annual Conference was a grand opportunity to renew your passion for teaching mathematics, reconnect with fellow educators, and reinvigorate by learning new ideas and strategies. Opening session Keynote speaker, Jeffrey Travis--director of the IMAX-3D movie "Flatland"-- wowed the audience with video-clips from the movie based on the classic by Edwin Abbott, first published in 1884.

During the talk Travis reminded us that," Stories make math matter." A claim that those of us who regularly use storybooks in our classrooms heartily support. He elaborated, "math and creativity go hand-in-hand to make great things happen."

I share the quote in hopes of encouraging you to continue to meld mathematics, literacy and the arts as often as possible. You hold the key to unlocking a world for your students that is not 'flat', but multi-dimensional, rich and exciting.

Teaching Tip
Rather than give you one brief teaching tip, today I offer you links to several teaching resources. If you have additional ideas and links. please share them by adding your comments to this post.

Printable lesson plan as well as links to three additional teaching guides reviewed by teachers.

Printable reading guide from Pearson Education



Abbott's book has been reprinted numerous times over the years. The links here include illustrated editions as well as a recent annotated version. I've also included a link to the DVD. Students will enjoy seeing the polygon characters come to life on the screen.

Author Spotlight: Greg Tang

Today I want to introduce you to an incredible author, Greg Tang who was inspired to begin writing for children after tutoring math in his first grade daughter's class. His first book, The Grapes of Math, is a clever collection of puzzles and riddles that challenge students to look for patterns, combinations, and other strategies to solve math problems quickly and efficiently. Since then his series has expanded to a total of eight titles each of which is filled with clever verse and engaging puzzles and riddles.



Teaching Tip
Students will benefit from simply reading Tang's books and solving the riddles. You can extend the experience by having students write, illustrate and exchange their own puzzles and riddles. Post the student work in a school hallway for other students to enjoy.