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.

Cloudy with a Chance of Meatballs

Today the forecast in Northern Virginia calls for rain. In your classroom, what is the probability that it will be Cloudy With a Chance of Meatballs? Children will delight in the absurdity in the tiny town of Chewandswallow where the weather changes three times a day...breakfast, lunch and dinner.

Teaching Tip:
Keep track of the daily weather forecast on a classroom calendar. Have the students watch for patterns as data accumulates. Use the data to make predictions. Compare current weather with weather records for your area.For weather data check outsources such as: NOAA, Weatherbase or UNISYS Weather. If using Cloudy with a Chance of Meatballs as part of a unit on probability another book that might be helpful is Bad Luck Brad.

Pattern Books

Long before they enter school, parents can do a lot to help young children develop the ability to think mathematically. One type of book that can help is "pattern books." Children will enjoy the hearing the repetition as adults read the text. In wordless books children will be able to identity the repeated patterns in the pictures.

Teaching Tip:
Ask children to model the pattern in the book by representing it with blocks or some other type of manipulative. Unifix Cubes (snap cubes) work very well for this purpose. Children can snap together cubes of two alternating colors to represent a simple ABAB pattern. A third color cube can be used to represent more complex patterns such as AABAAC.

Math Curse

One of my all-time favorite pieces of literature that connects with math is Jon Scieszka's Math Curse. Jon's engaging text, accompanied by the eye-popping illustrations created by Lane Smith, draws readers into a day in the life of our main character, but it isn't any ordinary day--this day is 'cursed' from the moment he wakes up. Cursed because he sees math problems in everything he does. Students will enjoy solving the problems as well as coming up with their own.

Teaching Tip:
Have students write, illustrate and exchange math problems that are based on the math that they encounter in their own daily life. Combine the student authored problems into a class book.

100th Day of School

The 100th day of school does not mean much to upper elementary students--other than the fact that they are that much closer to summer break. Kindergarten and First Grade students however, anticipate the 100th day of their first school-year with growing excitement. A sampling of the many pieces of literature that can be used to help build that excitement is shown below.

Teaching Tip:
Plan a 100th day celebration. Have each children bring in small zip lock bag filled with a different collection of 100 items. One student might count out paperclips, another pieces of cereal, or pennies etc. They are limited only by their imagination, having 100 of the item and what will fit in the bag. During the day have students explore how many different way they can group their items and count to 100 (1's, 5's, 10's etc).