Wednesday, January 23, 2013

Math and Literature: Books and Suggestions/Links for How to Use Them


Focus on NUMBER--counting, addition and subtraction:





Complete grade K lesson with links to everything you need to enrich the story is here.

More resources online:



There are excellent ideas at the end of the book, following the story:

Double the Ducks (Doubling Numbers)
                After you've read the story together once, reread the story, using small objects such as buttons, marbles, or blocks. Ask the child or students to "double the number" of objects to match the storyline.
                Tell the child or students that you have thought of a number and then doubled it. Then say what the doubled number is and ask if they can figure out what the original number was. For example, if the doubled number is 10, the correct answer is 5. If the child has difficulty, use a group of small objects—buttons, paper clips, or pennies—that total your doubled number. Then have the child separate them into two groups.
                When making a simple treat, like instant pudding, help your child or students double the recipe.
                Have the children make “Doubles Books.” To prepare, take sheets of 8 1⁄2 x 11 inch paper, turn it so it’s horizontal (wide) and draw a line down the middle. On the left- hand side of each page, draw an object (for example, 1 person, 2 ducks, 3 balloons, 4 trees, and 5 flowers). Make enough photocopies so that each child gets a set of pages. Ask the children to draw double the number objects on the right-hand side of each page (for example, 2 people, 4 ducks, 6 balloons, 8 trees, and 10 flowers). Using a new sheet of paper, have the children draw a cover for their Doubles Books. Staple each book on the upper left hand corner. Your math whizzes are now authors!

I think the story lends itself to exploring more advanced concepts involving ratios and proportional reasoning, so I like the idea of sharing the book with older children as well.

Go BEYOND the numbers in the story with questions like:

If 5 more ducks joined the group, how many more _____ would be needed?

If 3 more friends showed up to help the boy in the story, how many ducks could they care for?

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Sixteen Cows


By
Lisa Wheeler


What If We Changed the Book? Problem-Posing with Sixteen Cows


Problem Posing with Sixteen Cows
OBSERVATIONS    “WHAT IF” EXTENSIONS
There are 16 cows. What if there were 20? 30? 100?
There are 2 fields. What if each owner had 2 fields? 4
                                            fields?
There are 2 owners. What if there were 3 owners each with
                                            8 cows? 4 owners?
Each owned the same What if each owned a
number of cows.         different number of cows 
                                    but the total was still 16?
All the cows escaped. What if only half the cows escaped?
All the cows were the What if some cows were brown and
 same (adult, female,   white? Calves? Bulls?
 black and white).

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A Counting Story in Reverse, (a Tale of Wickedness-- and Worse!)


From Utah State Office of Education, Academy Handbook Kindergarten:

Ten Sly Piranhas Practice Ideas
To reinforce the concepts introduced in the book and strengthen subtraction skills, here are some ideas you can try at home with your child:
• Count out 10 Goldfish crackers and have your child “gulp” down one at a time. Talk about how many crackers there were before and after the “gulp.”
• Have your child draw a picture of a river. Have them retell the story with Goldfish crackers.
• Using 10 small items from around your home (buttons, Legos, cars, cereal) to practice subtraction.
• After practicing subtraction with the items, repeat and write numbers along with subtraction.
• Using the crackers or small items, have your child tell you subtraction stories. These are simple tales that give meaning to the subtraction process. For example: “Five birds were in the nest. Two flew away. Three birds are still in the nest.”
• Have your child make a book retelling the story of the piranhas. Let them read it to you.
• Involve your child in everyday subtraction around your home. Talk about what you are doing with them and have them solve the problem. “We need five glasses for dinner. I have three on the table. How many more glasses do I need?”
Use your imagination and have fun with your child. Math is an important skill we use everyday.
Make it fun!
Thank you for your help!



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Focus on NUMBER--multiplication and division, factors and multiples:






From blog --- mathmarsha.blogspot.com

An excellent resource to use when creating your list of books to look for at the library is Math Patterns in Children's Literature. Before I read this book with my granddaughter, I found photos of a chocolate chip cookie and a plate from my everyday china pattern to make it realistic, and we acted out the story, sharing a dozen cookies among an increasing number of children. My granddaughter personalized the experience by using her stuffies to replace the humans in the story.

I can share the cookie and the plate:


                                               


Questions Parents Can Ask: *How many cookies for each person? How do you
know?
*What if the doorbell rang only one time in the story?
*What if there were twice as many cookies in the story?
*What patterns do you notice?

Challenge:
Try making up your own story about division and fractions.

From  Math Through Children's Literature: Making the NCTM Standards Come Alive  By Kathryn L. Braddon, Nancy J. Hall, Dale B. Taylor














(need your library card for access; for some reason Evanston didn’t work for me but Wilmette did!)






Review

Ma has made some cookies for her two children and is now trying to wash the kitchen floor. There are twelve cookies -- six apiece-- and the children think they look and smell as good as Grandma's, but "no one makes cookies like Grandma". That phrase is repeated throughout the book, as is "the doorbell rang" as more and more children enter to share the cookies (tracking up the floor as they come.) Eventually the children only have one cookie apiece and the doorbell rings yet again. However, this time it's Grandma with a big tray of cookies, which is perfect because no one makes cookies like Grandma.
This is one of those picture books that practically begs to be included in the math program. We've got pattern, problem solving, computation and data gathering for starters. The book is full of visual and verbal patterns. The children seem well conditioned to share their bounty so the computing of how many cookies apiece changes as the other children enter the picture and that, of course, involves problem solving. Since the number of cookies and the number of children is left to the reader, data gathering becomes necessary.
Much of the action in the illustrations goes beyond that mentioned in the text -- Ma's attempt to keep the floor clean, for instance. In fact, readers may notice that the increasing dismay on the faces of both Ma and her children is caused by two different factors: the cookies and the kitchen floor.

By: Conaway, Betty ; Midkiff, Ruby Bostick

The Doorbell Rang by Pat Hutchins (1986) can be used to extend the understanding of fractions… Although this book does not directly discuss fractional concepts, the story provides a real-life problem-solving situation using fractional portions of 12. After the students have listened to the teacher read the book and have discussed ways to divide twelve items, ask the students to divide twelve paper cookies, twelve real cookies, or twelve pieces of popcorn. Extend this discussion by writing similar problems using a different number of children and cookies. For example, these two bags contain twelve cookies each. How many cookies do we have? (24) We have twelve students in our group. How many cookies will each student receive? (2) What fractional part of the cookies is that? (2/12) Then, depending on the grade level of the students, explore the concept of simplifying or renaming.



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 100 Hungry Ants
Materials: counters for building arrays, copy of 100 Hungry Ants; Elinor J.Pinczes
__________________________________________________________________________
1.     After listening to the story, ‘One Hundred Hungry Ants’ choose one of the following numbers: 12, 24, or 36.
2.     Suppose that there were this number of ants going to the picnic.
How many different ways could the ants arrange themselves into equal rows?

3. Draw an array and write a number sentence for each solution that you find.
4. How do you know that you have found all the possible solutions for the number you chose? 


Utilizing children’s literature in teaching mathematics not only can enhance early childhood learners’ understanding of abstract concepts in concrete ways, it can also serve as a vehicle for addressing diverse learning abilities and styles. Children’s math-related books have been increasingly incorporated and shown to be effective in teaching mathematical concepts (Forrest, Schnabel, & Williams, 2006; Huber & Lenhoff, 2006; Whitin & Whitin, 2006). The following set of activities based on the children’s book, One Hundred Hungry Ants, written by Elinor J. Pinczes and illustrated by Bonnie MacKain (1999), demonstrates how teachers can incorporate this book to facilitate children’s understanding of mathematical concepts:

In the story, a hundred ants are marching to a picnic and want to get there as quickly as possible. Marching one by one takes a long time, so one of the ants suggests two by two, then four by four, and so on.

After listening to the story, young children can count aloud the number of ants that are illustrated on each page. The teacher models oral counting by twos on the page where the ants march in pairs. By doing this, she provides the opportunity to enhance learning for visual and auditory learners.
When the teacher asks the children to physically become the ants and march one by one and then two by two, she has created a situation that appeals to kinesthetic learners.

To further apply the mathematical concepts from the book and engage children in open-ended mathematical investigation, she could ask questions, such as:

What would happen if there were 24 ants on their way to the picnic?
How could you show different ways these 24 ants could march?
How could you use blocks to show the 24 ants?

When children share their pictorial representations of the situation and describe verbally how they chose to show the ants marching, they are translating the visual into oral language.

By demonstrating their selected arrangements with blocks, and then describing the actions they use to solve the problem, children are again provided with the opportunity to make connection between concrete experiences and abstract concepts.

The activities described above utilize children’s literature to enhance understanding of abstract mathematical concepts by:

providing opportunities for concrete experiences
presenting situations that maximize various learning modalities
teacher scaffolding through modeling
engaging children in open-ended mathematical inquiry and investigation
promoting both individual and social construction of knowledge.


Excellent ideas in this article: 




Additional ideas – look at amazon.com customer reviews!

Here are a few:
My kindergartener and I were talking about money, one day, and he volunteered that he'd learned that ten dimes make a dollar when his kindergarten teacher read "One Hundred Hungry Ants". This book has no discussion of money, but it teaches that 100 equals 2 times 50, 4 times 25, 5 times 20, and 10 times 10, just the right lesson for him at that time.

This book was sent home with 100 unifix cubes to use along with the book. We used the cubes as the ants. We started off with one line of 100 cubes (as the ants). Then, in the story, they split into 2 lines of 50, so we split our cubes, too. Then, 4 lines of 25, and so on.... Excellent book to use with the cubes to demonstrate different ways to make 100.

This book is fabulous and a staple in any good elementary classroom. I love teaching arrays with this book. I use color tiles and 1cm graph paper to create the different arrays and then cut them out and place them on display to understand multiplication, addition and area.

Yet another treatment of this very popular book appears in Math and Literature, Grades 2-3.   Here, children are asked some good “what if?” questions—e.g., “The littlest ant wants to know if he can put all one hundred ants into three rows with no leftovers. We have to tell if he can do that or not.” “Write a story similar to One Hundred Hungry Ants but using your own numbers, characters, and setting.”








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Best resource for this book:



Blackline master of ants for acting out the story:



Activity pages:





Lessons:








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Focus on ALGEBRAIC THINKING--Patterns:

and


Both of these books CAN be used simply as counting books—but that would be missing a great opportunity to investigate triangular numbers and tetrahedral numbers.

To start, just focus on the number of gifts received each day.

Day
Number of gifts my true love gave to me
1
1
2
2 + 1 = 3
3
3 + 2 + 1 = 6
4
4 + 3 + 2 + 1 = 10
5

6

7

8

9

10

11

12


Do you see a pattern?

How is the total related to the day number?

Can you write an expression for the number of gifts on day 12?
If the pattern continued, can you write an expression for the number of gifts on day 100? On day N?

The numbers 1, 3, 6, 10, … are called triangular numbers because each number of objects can be arranged in a triangular shape (think of 1 as a “degenerate triangle” – a mathematical term).



The notion that numbers have shapes is not unfamiliar to you—think about square numbers, obtained by multiplying a counting number by itself  (n)(n) = n2: 1, 4, 9, 16, …


There are many cool patterns to notice already.

For example, each square number can be separated (do this, using pennies) into two consecutive triangular numbers. That is, 4 = 1 + 3; 9 = 3 + 6; 16 = 6 + 10; etc.


Also--you obtain the next triangular number by adding consecutive counting numbers. For square numbers you add consecutive ODD numbers.
(This raises a nice “What if?” question – What if you work with EVEN numbers? Start with 2 and add consecutive even numbers? What shape are the resulting numbers?
2, 6, 12, 20, … are called oblong numbers.)

For the oblong numbers, it’s relatively easy to see that each number is the product of two consecutive counting numbers. That is:
1 x 2                        2 x 3                                    3 x 4                        4 x 5

So the formula for the kth  oblong number is k(k+1).

But then compare the oblong numbers with the triangular numbers. Each oblong number is twice the corresponding triangular number. So what is the formula for the kth  triangular number ?

k (k+1)
       2

But wait—there’s more!
We also want to find out about the TOTAL number of gifts received by the end of each day.


Day
TOTAL Number of gifts my true love has give me so far
1
1
2
3 + 1 = 4
3
6 + 3 + 1 = 10
4
10 + 6 + 3 + 1 = 20
5

6

7

8

9

10

11

12


This time we’re getting the SUM of the triangular numbers. This set is called tetrahedral numbers because they have the 3-dimensional shape of a tetrahedron (triangular pyramid). And this shape is also entirely familiar: You’ve seen cans or fruits arranged in a pyramid in the grocery store:


Finding the formula is beyond the scope of this workshop!  It is

So for n = 12:      2(13)(14)

The total number of gifts = The sum of the first 12 triangular numbers = 364.


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From the mathmarsha.blogspot.com discussion:


Recently my granddaughter and I were reading There's a Zoo in Room 22 by Judy Sierra.  (Preview here on Googlebooks.)

It is written in verse, so we discovered and labeled the rhyming PATTERNS.

This one is  ABAB CDCD:                                                This one is AABBCC:


                                                 

My granddaughter declared that "hexaflexagon is not a word."

Well!
I happen to HAVE hexaflexagons--in fact, all of the following:
trihexaflexagon
tetrahexaflexagon
pentahexaflexagon
hexahexaflexagon

So after finishing the book, we explored the flexagons.
For directions and patterns to make your own, go here.
And an exciting video here.
Another note about poetry and the mathematics of patterns:



Figure 2.3

Nursery Rhymes and Pattern Development



          Twinkle, twinkle, little star,                    ¨ ¨  ¨ ¨  ¨ ¨  l
          How I wonder what you are!                 ¨ ¨  ¨ ¨  ¨ ¨  l
          Up above the world so high,                  ¨ ¨  ¨ ¨  ¨ ¨  ¨
          Like a diamond in the sky.                     ¨ ¨  ¨ ¨  ¨ ¨  ¨
          Twinkle, twinkle, little star,                    ¨ ¨  ¨ ¨  ¨ ¨  l
          How I wonder what you are.                  ¨ ¨  ¨ ¨  ¨ ¨  l



          Jack be nimble.                                      ¨ ¨ ¨ ¨
          Jack be quick.                                        ¨ ¨ l
          Jack jump over                                      ¨ ¨ ¨ ¨
          The candle stick.                                    ¨ ¨ ¨ l



… students can use pattern blocks to build visual
correspondences to rhyming linguistic patterns.   Once students learn this technique, longer nursery rhymes can be constructed geometrically, thereby involving students in actively predicting, comparing, and checking both geometric and linguistic patterns.




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A Mathematical Folktale
By Demi

A Grain of Rice
Written and illustrated by Helena Clare Pittman

The King's Chessboard
By David Birch

From
One Grain of Rice: A Mathematical Folktale by Demi. New York: Scholastic, 1997. (ISBN 059093998X)
Middle – Using expressions, equations, and inequalities to represent situations and solve problems
Formulate algebraic equations that would predict the number of grains that would be given to the raja daily, etc.

From 








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Focus on HANDLING DATA:




From mathcats.com:        

Math Literature and Graphing Activities
> I will soon be a student teacher. In my method class for math I was instructed to create a book lesson intergrating math. I want to use Harriet's Halloween Candy by Nancy Carlson, since it will be Halloween when I present this to my class... I thought I would begin my lesson by reading the book, then demonstrate what they would be doing. I am going to tell everyone that they will all get a bag of candy, then when you get the candy, I want you to sort it out into different groups such as tootsie rolls, etc., then color in graph of the amount of candy you have. ( I am showing them as I am talking) How does that sound? 
Wendy, 10/25/00
Your thoughts are well thought out...
Other things might be: graph what they have sorted or create Venn diagrams of the candy -- those with wrappers, such as Toostie Rolls and those without wrappers, such as apples. 
KathyB/1st/IA, 10/26/00 on teachers.net math board
~~~~~~~~~~~~~~~~~
Best of luck when you present your lesson. I'd like to suggest some further ideas in a different format which you may or may not find helpful.
Integrating math with Harriet means not only sorting and graphing, which is good, but also how can you tie the feelings of selfishness and greediness into your lesson, which I believe is the lesson Nancy Carlson wants the reader to explore. Here's an idea:
Choose the attributes you want the students to work with (i.e. size, color, shape, etc.) and fill the bags with any and everything (not just candy) that can be sorted like this. (As candy is expensive, not very reusable, would probably take some of your young students off task just thinking about eating it, you might use different macaronis, shell beans, attribute or fraction blocks, some hard/soft candies with,w/out wrappers, paper clips, marbles, etc. -- the more creative the better!) Be careful that what you put in bags can easily be sorted into the attributes you work with in your lesson: you may only want to focus on size and color, for example, and fill as many bags as you have students. Put these bags into larger bags so that you end up with one huge bag!
Hand this bag to one person - what do others think? I'm sure you'll hear, "That's not fair;" talk about why and what would be fair. Also, tell that one person that s/he will have to do all of the work. Discuss briefly and then go on to give everyone their own bags.
Go on to sort, graph, diagram (using rope circles on the floor works well and working in groups helps).
Then read the book, drawing on students' experiences and how they felt when doing the math lesson and tie it with Harriet and her brother's feelings, summing up similarities/differences.



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Focus on MEASUREMENT AND GEOMETRY:




Ask why the bed created by the apprentice is not what the king expected.
Print a Making Beds activity sheet for your child.

Discuss your child’s responses to the tasks described on the Making Beds activity sheet. In particular, discuss responses to questions 5 and 6. Question 5 asks, "Why do you think the ruler was invented?" Question 6 asks students to consider, "The preface of the book says, 'To the wonderful metric system without whose absence in this country this book would not have been possible.' What do you think the author means by this statement?" Students might discuss how the Metric system is not used in our country. Students may discuss how much easier it is to use and convert in the Metric system because it is based on powers of ten.


Another excellent treatment of this book is in



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COUNTING ON FRANK


Clement, R. (1991)



From:













In this lesson, students read the book Counting on Frank. They use information in the book to make estimates involving volume. In particular, students explore the size of humpback whales.

Story Summary
The narrator likes to collect facts with the help of his dog, Frank.  Each two-page spread of this book includes a different fact involving such mathematical topics as counting, size comparison, and ratio along with delightful illustrations.
Structuring the Investigation
Ask students to brainstorm what they already know about humpback whales. If they do not know a great deal about this topic, discuss where this information can be found. Two internet resources include:
                Enchanted Learning
                PBS Nature
Ask your child to predict the size of a humpback whale, and explain her estimates.
Read the book, Counting on Frank, by Rod Clement aloud. Print a copy of the Getting The Facts activity sheet (reproduced below).
Ask your student to calculate how large a box is needed to hold the average humpback whale. Because the data will most likely include weight and length, your child will have to make inferences about several dimensions of the box. These decisions should be justified in questions 1 and 2 of the Getting The Facts activity sheet.
After estimating the size of the boy's house, encourage your child to describe the process she used to find the answer. Discuss the information needed to determine the number of whales that would fit inside the house. Have your child complete the activity sheet.




~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A Math Adventure











1.            Read page 3 and stop before the last sentence. Describe the mental picture that you see, such as many men on foot and knights in armor on horseback congregating on a hill overlooking the place where you are standing. Ask some students to describe the picture they see.
2.            Read the story stopping at page 8 and ask some students to describe their mental images. Have all students sketch or make a picture of the new table.
3.            Read through page 11 and again have students represent the newest table using the special rectangular papers.
4.            Read through page 14 and ask students to quickly sketch one of the flags.
5.            Read pages 16 and 17. Give students time to work with a partner to create the octagonal table from the parallelogram. Provide written or verbal clues from the diagram on page 17 if necessary.
6.            Read pages 18 through 25 and have the students sketch, create with string and pencil compass or select a circle.
7.            Read pages 26 through 31. Have students identify the diameter, radius and circumference of their circles at the appropriate point.

 See also

Sir Cumference and the Dragon of Pi
which explores how the number pi is calculated as the constant quotient of the circumference divided by the diameter of every circle.


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A Cloak for the Dreamer
By Aileen Friedman


Complete lesson and discussion, with black line master at


Activity centers around these shapes, on the BLM. Two approaches are presented.
The first teacher interrupted the story and had the children describe the problem and propose their own solutions. The next day they read the entire story, got tagboard printouts of the BLM below, and the directions that follow.





In the second approach, on page 13, Marilyn Burns read the whole story with the children in one sitting. Then:








Here is a video describing how to create a tessellation:

http://www.youtube.com/watch?v=_Lg19NvW_sU



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Grandfather Tang's Story 
by Ann Tompert

Three Pigs, One Wolf, and Seven Magic Shapes 
by Grace Maccarone

These books introduce your child to the Tangram Puzzle -- seven geometric shapes that can be used to explore a wealth of topics in geometry and measurement.









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Suggestions are provided in the margins of the text itself.  Cooking is one of the best real life situations in which your child naturally gains experience with fractions.

Available online resources:







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Book: Inch by Inch by Leo Lionni

First Reading of Inch by Inch
Prepare to read the book, Inch by Inch.
Show cover; give title, author and illustrator. (Explain that author is the person who writes the book and the illustrator is the person who draws the pictures.)
Ask children to look at the cover and predict what the story is about. Call attention to the inchworm and say, “This is an inchworm. Let’s read and find out what happens to the inchworm in the story.”
Read the story so all children can see the pictures in the book.
Follow up by showing pictures and inviting children to help you name the different
birds that the inchworm met and which parts of each bird’s body the inchworm
measured.
_______________________________________________________________________
Second Reading of Inch by Inch
Bring measuring tools to story time: ruler, metal measuring tape, cloth measuring tape, yard stick. Keep them out of sight of the children until you have read the story to them.
Prepare to read the book, Inch by Inch.
Show cover, give title, author and illustrator.
Ask children why they think the title of the book is Inch by Inch.
Ask children to show how big they think an inch is.
Read the story so all children can see the pictures in the book.
Follow up the second reading by showing the children the measuring tools. Allow
them to examine the tools.
Ask children to find the numeral 1 on their tool. Explain that this means one inch.
Help children find the numeral. Children may notice other numerals on the tools.
Explain that the 2 means two inches and so forth.
Place the book on the floor and turn to the page where the inchworm is at the top
of a plant looking at the nightingale. Use one of the measuring tools to measure
the inchworm and say, “This inchworm is one inch long.”
Invite children to suggest other objects in the room they might measure.
State that some of the measuring tools will be placed in learning centers for
children to use for measuring.
Place measuring tools in Block Center and in Discovery/Science Center, for
example.
_______________________________________________________________________
Third Reading of Inch by Inch
Prepare to read the book Inch by Inch.
Show cover and invite children to recall the title. Give name of author and
illustrator.
Involve children in discussing the objects in the room they measured. “How many
inches long was______?” (objects they measured)
Read the story so all children can see the pictures in the book.
Follow up the third reading by asking children why the inchworm could not measure the nightingale’s song. (Inchworm measures things, not songs) How did the inchworm keep the nightingale from eating him? (He inched out of sight of the nightingale).

Another lesson on estimation and measurement based on this book is included in Math and Literature, Grades 2-