Monthly Archives: May 2012

More Math MAYhem…
The test of a story is this: Can it be read over and over and still bring insight and entertainment to its audience?  If so, then it is good literature, no matter what the age or genre.  For parents, this means your child asks you to read it to you so many times that you about have it memorized!  For teachers, this means the kids love the picture book you used in your mini-lesson in September, and you see potential to re-read parts of the book to support other subjects throughout the year.  This can save time while providing meaningful connections and common prior knowledge to build upon.

With this in mind, I’d recommend this next book hot off the presses in 2012 for your personal or classroom collection.  Please refer to my “teachable moment” ideas below and adapt them to the classroom or home.

Zero the Hero

by Joan Holub Joanholub.com
Illustrated by Tom Lichtenheld
2012
Price new $16.99

Age Range
With adult interaction: 5-8 years old (grades Kindergarten-2^nd)
Independent reading:  8-10 years old (grades 3^rd -4^th)
Ideal for year-long teacher mini-lessons: 2^nd and 3^rd grades

Review
This entertaining book revolves around a comic book kind of hero with high-action illustrations and captions to accompany (and even add further humor) to the text of the story.  It is a great underdog story that shows the value of the individual (and teaches some GREAT math ideas).  The solution to this tale involves an unpredictable group of characters that march in with their own layer of humor and teachable moments.

Teachable Moments (Note: Text from actual story is in quotation marks.)

WRITING
Who are some of the heroes in your life: real and fiction?  What do you admire about them?  In what ways are you like them and in what ways are you different?  How can you be seen as someone else’s hero?  This could also tie in to Social Studies when you study community, leadership, Labor Day, Veteran’s Day, etc…

Synonyms: Search for all the words that mean the same as “zero” in this story: nothing,

Place value prompt: Zero’s spot in a number makes a big difference.  What would happen without him?  Brainstorm places that would crumble into disorder: banks, maps, street signs, grocery stores, books, etc…

READING
Making Connections:  What other story has a similar character? Problem? (Rudolph the Red-Nosed Reindeer is one that immediately came to my mind, but there are MANY that have this same underdog theme.)

Setting: Does this story have a setting (place, time)?  What would happen if these numbers lived in a big city?  Or out in the country?

Plot: What was the problem?  Solution?  Can you think of a different way to solve the problem and end the story?

Character feelings: How did Zero feel when _______ happened?  What clues (words, actions, body language) made you think he felt that way?

COMMUNITY CIRCLE (CLASS DISCUSSION)
Reflect on Our Choices: put downs or name-calling like “Zero”; bullies; including versus excluding.  Can you connect with how Zero felt?  Have you ever seen someone being treated this way?  You’re a kid…what can YOU do about it?  (Ask them to come play with you and walk away with them.  Tell an adult if it continues.)

I’ve done a great demonstration with an apple when discussing this topic of name-calling.

1. Take a red apple and tell students this apple has skin on the outside, just like us.  Review what name-calling is and how it feels.
2. Drop the apple on the floor once, saying something age-appropriate like “Someone just said my glasses looked dumb.”
3. Then drop it again  “Someone just told me they hated my haircut.”
4. Repeat about 10 times.
5. Have kids look at apple.  It should look pretty much the same as it did before the drops (in other words, don’t throw it to the ground with all your might).
6. Then cut it open and show the kids the brown and tell them that’s bruising.  You couldn’t see it from the outside, and sometimes we can’t see with our eyes how people really feel on the inside.

I also found a great website that ranges in simple topics to more complex topics like cliques, stress, excluding, getting out of bad relationships, etc… http://www.healthykidsmo.org/services_counseling/Self-esteem.pdf

MATH
Counting (or natural) numbers vs. whole numbers (The wholes are just the naturals with zero thrown in.): “left out of counting games” (compare to Rudolph story); can’t count a zero number of things; “In order to count, he had to stand in shadow of others more glamorous than he was.”

Place value: Zero’s spot in a number makes a big difference.  What would happen without him?  Brainstorm places that would crumble into disorder: banks, maps, street signs, grocery stores, books, etc…  In this story, sums need Zero because of place value: 5 + 2 + 3 = 1??  Also can’t round numbers without zero.

Odd and Even Numbers: How does the digit zero affect these types of numbers?  List a bunch of odd numbers.  Then take out the zero.  What do they turn into?  List a bunch of even numbers.  Then take out the zero.  What do they turn into?  “Odd numbers felt so ODD without zero.” Even numbers miss him too.

Properties of Addition (http://www.aaastudy.com/add74ax1.htm):
Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4 Zero tries to go first, but it doesn’t change anything.
Additive Identity Property: The sum of any number and zero is the original number. For example 5 + 0 = 5. How did this make him feel? “When it came to addition, he was virtually invisible.  Other numbers seemed to pass right through him.  Almost like magic. ‘This is getting embarrassing.’  ‘I got nothin.’”

Properties of Subtraction:
Identity: Same as Additive identity. 0+(-N) = -N , where N is positive.
“The same thing happened with subtraction.  In their frustration, some numbers were unkind.”

Properties of Division: http://www.mathatube.com/division-properties.html  Website has videos, too!
Divisive Identity: Any number divided by 1 will stay same. 14 ÷ 1 = 1
Zero property of division: The zero property of division have two rules. Rule1– If you divide zero by any number the answer will be zero. You have nothing to divide. Rule2– If any number is divided by zero, then the problem cannot be solved. You cannot divide by nothing.
“Turns out, Zero stunk even more at division.  So badly in fact that other numbers simply refused to be divided by him at all.”

Properties of Multiplication:
Commutative property:  You can multiply two numbers in any order and the product will be the same. Example 4 x 3 = 12 and 3 x 4  = 12
Property of zero: any number multiplied by zero will be zero. The number can be in any order. 12 x 0 = 0       6 x 0 = 0
“Still his belief in his wonderfulness persisted. Then one day, during multiplication, it was discovered that any number times Zero equals—you guessed it!-Zero. Fearing extinction, the others ran from him.  Who could blame them? A real superhero wouldn’t multiply his friends into nothingness.  That’s the kind of stuff only an evil villain would do.  Could it be that he wasn’t a hero at all? The thought gave Zero a hollow feeling inside.  He rolled away.”

Roman Numerals: The Roman soldiers take them to the Emperor.  X (ten) looks like x; V (five) = V
Discuss differences, advantages and disadvantages of each. “We could teach you math using the ones, tens, hundreds.”—say the digits. “We don’t do math.  We just count.”—say the Roman numerals.  Roman Numeral humor 8= VIII “So it takes four of you to do my job?”

Poems, riddles, and superheroes, oh my! Are we talking about math? May is here and I have several books to keep that child or student of yours engaged these last few weeks of school and into the summer.

The Problem with “Story Problems”
You remember those “story problems” we had to do as kids, don’t you? Most people I’ve talked to have not-so-fond memories of those from their textbooks. And we were especially thankful there were only 1 or 2 at the end of the lesson. Some of our teachers would even skip them altogether. Great, right? But as adults, how many of you find that most of life’s “real world math” is never presented in a one-step problem? And all the math problems I encountered today didn’t use the exact same strategy or algorithm that I just learned this morning. Our kids today deserve, in fact NEED, to embrace real-life problem solving, not shudder at the thought. Need proof? Compare Round Rock Independent School District’s (RRISD’s) expectations for Mathematical Problem Solving in the following grades. Compare/contrast the expectations for kindergarten, 2nd and 5th grades.  http://www.roundrockisd.org/index.aspx?page=1008

I’ve highlighted the few differences. Obviously the difficulty of problems increases each year, but the bottom line is the same: Your child needs to know how to confidently UNDERSTAND a problem, make a PLAN, and SOLVE it using an appropriate strategy that includes checking for reasonableness.

The Problem
Kindergartners love to count on their fingers, or count by ones to solve a problem. It’s necessary, and even cute, because they haven’t learned many other strategies yet. But when your 5^th grader, who HAS learned a variety of strategies, counts on her fingers (under the desk to remain unseen, of course), it’s more worrisome than cute. But the reality is this is actually quite common when we teach strategies, but don’t give kids PRACTICE, PRACTICE, PRACTICE in school and at home to get comfortable with these other ways of thinking. They’re just more comfortable with their trusty, tried-and-true fingers.

Fingers aren’t the only culprit, lest you thought you were off the hook. I’ve also seen kids grab onto other strategies like tally marks, for example. “Sue has 16 cupcakes. John has 10. How many cupcakes do they have altogether?” So a student draws out 26 tally marks and tries to count each one, maybe accidentally double-counting a tally, maybe not. But when they do this with the numbers 62 and 16, your mouth drops as a teacher. “Why didn’t he draw base ten blocks at least, or use a number sentence?” we think to ourselves, feeling a sense of defeat.

The Solution
Once kids learn a strategy that makes sense (counting on fingers, or maybe a step beyond that like tally marks) they try to apply THAT SAME strategy to fit any and every problem after that. And this simply won’t work. They must have a tool belt full of a variety of strategies, understand which kind of problem calls for which types of possible strategies, and then have the confidence to actually choose and use a reasonable one. If this all sounds a little overwhelming to you, don’t worry. Math is all around your child in everyday situations. As a parent, you can use these teachable moments with just a little help from a great author and mathematician. 

Child’s Natural Curiosity + Greg Tang =MATHEMAGIC  

I’ve broken down two of his books for you, so you can decide which book is best for your child. This is also a great gift idea for your child’s teacher because we are always looking for engaging ways to bring the real world of math into our classrooms.

The Grapes of Math	Math for All Seasons
by Greg Tang, Illustrated by Harry Briggs
Ages 5-10 (Problems have larger numbers)	Ages 5-8
Published 2001	Published 2002
Teaches problem solving through math poems and illustrations. Aims to transition kids from counting to arithmetic. Challenges them to think through problems and see multiple strategies. This critical thinking and ability to see a variety of strategies is expected in school as early as kindergarten.
Topics:Using math riddles, each page presents an everyday math situation that needs a solution. But mathematicians are often given a warning: “Please don’t count them, it’s too slow, this hot pie was made to go. ” or hint to guide them to see differently: “Instead of seeing groups of threes, count by fives and it’s a breeze.”Strategies taught:multiply and then subtract or add (multi step), find convenient sums, multiplication as fast addition by grouping, making tens, organize info by looking for patterns and symmetry. It also introduces great vocabulary for this age group. To find one answer, you much “look askew”. For many ages it’s tempting to count one-by-one. Don’t be so surprised to see your 5thgrader counting a group of objects this way. Sometimes they just lack the confidence to try a different way. My dad always said “Work smarter, not harder.” This book aims to get students comfortable with a variety of strategies that they’ve probably already been taught, but have little experience using in real world situations. As their confidence soars, they’ll learn how to apply these to other situations.	Topics:Using poems about annual events in the life a child, each page presents an everyday math situation that needs a solution. Within each poem, the author provides a challenge to see things differently. When presented with 3 rows of 3 chicken eggs, the question is “How many have hatched?” Left alone, a child will often choose to count one at a time, even when other strategies have been taught in school. This poem provides the scaffolding for the strategy “subtract to add” by saying “to quickly count this chirping batch, subtract the one that’s yet to hatch” (3,6,9, minus the 1 hatched egg = 8).Strategies taught:Smarter ways to group like making tens or skip counting, doubling, subtract to add, spot patterns and symmetries, think creatively. Answer key in back explains the smarter way to group versus just counting. With small amounts, kids would rather count. But as amounts get larger, this is a disaster. Learn smarter strategies using this book and they’ll be on their way to bigger and better things in no time! To the classroom teacher:I’d introduce one poem (problem) a month on chart paper and have students share their strategies with the class. My students gained the confidence to try a different strategy when they saw a classmate try it and heard them explain their thinking. The poems fit nicely with various holidays and special events each month such as spring and new life, rainy April, Easter, summer ice cream, spring butterflies metamorphosis, cutting grass, fireworks in July, maize/corn in field, acorns, Halloween, fall leaves change, snowflakes, snowmen, holiday presents and gingerbread, new year.

Next up… Zero the Hero.

Unlike most numbers, Zero believed himself to be a hero. He just needed a chance to prove it.  But Zero’s belief in himself didn’t count for much when it came to fitting in. 

Find out how this mathematical Rudolph-like story can hook your child and enhance his or her learning in my next post.