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.