2 X 2= Boo!- Loreen Leedy
Basic facts, demonstrating the understanding of multiplication - for the introduction of facts, younger students. Unrelated in the fact that they teach to different aspects of multiplication - Bunches and Bunches of Bunnies - squares of multiplication, Too Many Kangaroo Things to Do - ones up to four, 2 X 2 - zero to fives by fives.

Computation - Multiplication facts
Facts organized differently. Each chapter is a specific factor - ex. - zero , ones, twos, etc. up to fives. Shows arrays. Could be extension of addition. Have students move further on to the sixes, sevens, etc. Draw their own arrays.

The 329^th Friend - Marjorie Weinman Sharmat Emery Raccoon is feeling lonely. He thinks it is a good idea to invite some guests for lunch. He invites 328 guests in hopes of getting at least from that. He goes through elaborate plans, but when his guests come and eat, they totally ignore him. He's feeling very dejected, but in the end realizes his best friend is he, himself. Number Sense - Counting, Reading/Writing Numbers, Place Value
Counting and reading numbers - 301 - 329
Place Value charts - students write the number in the place value chart 50 SimpleThings You Can Do To Save the Earth- Earthworks Group 50 Simple Things You Can Do To Save the Earth - Book about many conservation ideas. The book explains many interesting things as well, such as, how much water is wasted when water is left running while teeth are being brushed or dishes are being washed. It's for the entire family. Good for interdisciplinary use - Science, Social Studies, Math

Data Analysis -
Interpreting data-The use of charts, graphs and tables to interpret information.
Graphing - Create circle graphs - Data they collect, record it in a circle graph to show results.
Measurement
How students can prove statements such as "brushing your teeth, you can save up to nine gallons of water if you just wet and rinse your brush instead of letting the water run the whole time." Have them experiment and collect data and record.
Computation
Estimate how much water you could conserve by turning off the tap while you brush your teeth. How could we figure out the answer to this problem more precisely?
Questions students if the calculations are correct. A leak that fills up a coffee cup in ten minutes will waste over 3,000 gallons of water in a year - pg. 42. ( 8 oz. /(cup) x 6 c./ hr x 24 hrs/day x 365 days/yr. = 420,480 oz/yr. Dividing by 128 oz in a gallon indeed equals 3,285 gal. a yr.
Make comparisons of energy-saving strategies. Example: Compare the cost of standard and rechargeable batteries for operating a portable tape recorder over the course of a year.
Problem solving. The use of charts, graphs and tables to interpret information.
Illustrating a mathematical statement.
How students can prove statements such as brushing your teeth, you can save up to nine gallons of water if you just wet and rinse your brush instead of let the water run the whole time. Have them experiment and collect data and record.

Alexander Who Used to Be Rich Last Sunday - Viorst

Computation

Recall how Alexander spent his money
Create your own spending story - $10.00
Questions:
Did Alexander spend his money wisely?, If you were given one dollar, what would you do with it? If you spent it, what would you buy?, If Alexander's grandparents give him money again, what do you think he will do with it?
Have students write up a worksheet representation of the transactions in this story. Emphasis on the placement of the decimal point when subtracting money.

Amanda Bean's Amazing Dream - Cindy Neuschwander
Understanding the concept of multiplication. Discusses why multiplication is important and how it relates to the world around us. It explains multiplication in different contexts. Anno's Mysterious Multiplying Jar - factorials, upper elem., multiple factors Number Sense Understanding of the concept of multiplication. Discuss with your students why multiplication is important and how it relates to the world around us. It explains multiplication in different contexts. Computation - Multiplication Have students create riddles to peers to solve. Ex. - Which has more wheels - 5 tricycles or 7 bicycles? Go over the pictures and arrays in the book of the many items. Extend that to having students create their own riddles. Use the book, Math By All Means - Multiplication - Grade 3, Marilyn Burns, Things That Come in Groups, and the 1-99 chart Anno's Mysterious Multiplying Jar - Amanda Bean's Amazing Dream - Understanding the concept of multiplication. Discusses why multiplication is important and how it relates to the world around us. It explains multiplication in different contexts. Anno's Mysterious Multiplying Jar - factorials, upper elem., multiple factors Number Sense Number of seating possibilities at a table or number of possible arrangements for 3 crayons. Creating factorials - definition - a number is multiplied by the next smaller number, then the next smaller number, and so on, all the way down to one. The symbol for this is an exclamation mark. It expresses the number of possibilities in which something can be arranged. Ex. - 4 students and four desks, 4! Would describe the number of different ways they could be combined.
Develops a stronger number sense by analyzing the distinctions between various problems and comparing different contexts for multiplication.

Algebra - Patterns

How many jars in all? 3,268,800 jars
Extension piece - Create your own factorial study or factorial problems
How long is a million seconds?
1 mm square on a sheet of graph paper
grains of rice cover one square meter
Indicators - multiply accurately / rounding off
Predict how many pages to show number of boxes and jars
Able to use this pattern to create a new story
Able to think of and use another number pattern to create a story

Computation - Factorials

Discuss the factorial numbers- To get to the total the calculation would be to multiply the first ten counting numbers together. They are represented by dots in the back of the book in arrays. 1 x 1 =1, 1 x 2 = 2, 1 x 2 x 3 =6, 1 x 2 x 3 x 4 = 24, 1 x 2 x 3 x 4 x 5 = 120. It helps the learner to visualize the abstract numerical pattern of factorials by illustrating numerical progressions through pictures, narrative, arrays and numbers.

BFG, The - Roald Dahl The Big Friendly Giant is seen by a little girl named Sophie. He snatches her from her bed and arrives in his home, a secret cave underneath a big stone. Sophie learns that he is friendly. She does meet the mean giants, however. They eat humans every night. Sophie does not like this and she and the BFG set out to get rid of the bad giants. The Queen of England helps out and they capture the bad giants.
 

Measurement - Proportion, Scale
Proportion - The BFG is 6 times as large as Sophie. If he is 24 feet tall, how tall is Sophie? The other giants were at least twice as big as the BFG. One of the giants was 54 feet tall. Use that to make up problems.
Chapter - "The Royal Breakfast" - Everyone was busy creating furniture that would fit the BFG. See how they determined the measurements. They used a base of a 6-foot tall man. What didn't they use Sophie's height? Use pg. 56, "So Big"
Use grid and scale to draw a larger picture from a small one. See pg. 57.
Feet size - What foot size would the BFG be if he is 6 times as tall as Sophie? Brainstorm the process of figuring it out. (Since the BFG is 6 times as large as Sophie, his feet would be also.) Find a student who is Sophie's height, 4 feet tall. Trace the foot pattern. Cut out the pattern, and arrange them in the shape of a foot so they are six wide and six long. Glue the feet together and draw the outline of a large foot around them. Cut out the "big foot" and mount it on the wall.
Extension: From inch tall to giant. Use Jim and the Beanstalk, Raymond Briggs. The giant can't see and needs glasses. Used a gold coin to measure for the lens. He also needed his teeth redone. Then, he needed a wig. Needed red hair and curly.

Bunches and Bunches of Bunnies - Louise Mathews
Basic facts, demonstrating the understanding of multiplication - for the introduction of facts, younger students. Unrelated in the fact that they teach to different aspects of multiplication - Bunches and Bunches of Bunnies - squares of multiplication, Too Many Kangaroo Things to Do - ones up to four, 2 X 2 - zero to fives by fives. Number Sense/Computation - Multiplication, Square numbers Facts of 1x1 up to 12 x 12 are explored. Which is easier to count the bunnies, in a large group or by twos, threes, or fours. Justify their reasoning. Have students predict the multiplication sentence for each set of bunnies. Write the sentence and have students model the multiplication sentence. Have them cut out the multiplication sentence, to have a sense of the shape of the sentence. Extend the activity by discussing the squares of numbers. Ask them if the product with create a square. Extend with an activity that deals with folding paper. Fold it in half and half it again. Can you fold it in half eight more times. Show the math involved. Create own problems - real world - a female rabbit can have four to eight litters per year with three to nine bunnies in each. If the rabbit has 6 bunnies in each litter and has 6 litters in a year, how many bunnies will she have in a year? One pound of pellets will feed approximately three bunnies each day. How many pounds of rabbit would be necessary to feed all 144 bunnies? Counting on Frank - Rod Clement

Computation
Boy's giant feet next to a very small Frank - problem - "We've got a tree in our yard. It grows about 6 feet every year. If I had grown at the same speed, I'd now be almost 50 feet tall". The boy says that he would be almost 50 feet tall if he had grown 6 feet every year. Question: How old is the boy? Talk with your group.
Does the narrator of counting on Frank have all the right answers, or is he just a strategy show-off, using estimated numbers in place of mathematical calculations? How could he find out how many humpback whales would fit in the house, or how tall he would be if he grew six feet a year?
Invent interesting problems similar to the ones in the book. Show the strategies
Recall a situation in the book. - Select the most outrageous event, and work together to find a strategy that would prove whether the narrator's estimation in right or wrong. Present solutions and strategies to the class. Ex. - "The bathtub is 6' x 3' x 2'. It took 10 minutes to fill it half full. Then it would take 20 minutes to fill it to the top."

Doorbell Rang - Hutchins (Division, also)

Computation
Concept of partitioning - important in division, fractions, and decimals - the dividing of discrete items or continuous quantities into groups of equal size. It might involve baseball cards (discrete) or a length of cloth (continuous). It might use the entire quantity or it could use a remainder in some special way.
Map out the series of events: - 12 cookies - 2 children, 4 children, 6 children, 12 children - 6 cookies, 3 cookies, 2 cookies, 1 cookie. - 1/2 of 12 = 6, 1/4 of 12 = 3, 1/6 of 12 = 2, 1/12 of 12 = 1
What would happen if Grandma didn't arrive with those extra cookies? How could eight kids share twelve cookies?
Have children use equations to tell the story in numbers
If each child in the story had one cup of milk with cookies, how many gallons of mild would they drink altogether?
Make chocolate chip cookies. Recipe says it makes 5 dozen. If that is true, have students determine how many cookies each one of them will get to eat. Make the cookies and see.

Each Orange had 8 Slices - Paul Giganti, Jr. Computation - Multiplication An intro to multiplying multiple factors. Write own problem. How would you solve the problem? Questioning piece very important - How do you know that? Write out some columns - ex. 3 waddling ducks; 4 baby ducks; Quack, Quack, Quack; questions (see book), number sentences = 3 x 4 x 3 = 36. Be your own author - what would you do? Ideas - ant farms, ornaments on a tree Fraction Action - Loreen Leedy

Computation
Have students group themselves in two halves. If there are leftovers, discuss that. Divide into thirds and fourths.
Create a class fraction book - Chapter for halves, thirds, fourths. Encourage to include fractional parts of groups as well as fractional parts of a whole.

Frog and Toad Are Friends, Chapter - "The Lost Button" Toad loses a button from his jacket. They try to find it. Toad had lost a white, four-holed, big, round, thick button. The buttons they find do not match.  He goes home angry because his friends can't find it. He finds it at home on the floor. Feeling bad, he decides to sew all the buttons that his friends find on his jacket. He gives the jacket as a gift to his good friend, Frog.
 

Number Sense - Attributes Sorting buttons - Use a felt board to allow students to manipulate the story. In groups, have children select a handful of buttons and sort them according to a specific attribute. They need to describe their attribute.
"Button Factory" - Tell the class you are a shirt designer and need buttons for your shirt. Hide a button in your hand and describe its attributes. Have children draw the button. Have the children continue the game in pairs.
One difference Train - Prepare one set of buttons for each pair of children. Use Activity sheet 20 on two colors of construction paper. One child is each group places a button on the construction paper. Another child finds a button that is different in only one way, then places it next to the first button. Partners continue, in turn, to form a one-difference train.
"Button Up" - Describe an attribute of a button such as color, size, shape, number of holes, … If the children are holding a button with that attribute they hold the button up.
Estimate the buttons in a jar - Ask the children to guess the amount of buttons that would fit in a jar. Do not show the children the jar or the collection. Indicate to the children that it is difficult to get an accurate prediction because they do not have enough information. Suggest that if they saw the jar they could get closer to the number of buttons. Have them verbalize their estimation. Ask them how they arrived at that estimation. Have them record their estimation according to tens and ones.

Gator Pie - Louise Mathews

Computation
The inverse relationship between the size of the piece and the number or pieces is illustrated
Discuss the mathematical concept of the equal partitionship of a whole.
Equivalent fractions - 50/100 = 1/2, n/n = 1
Write your own stories and share with class.
Explore the concept of equivalence through partitioning.
Challenging question: What would happen if you had already divided the candy bar in half and this third person came to join you. How could you divide the candy bar equally among these three people?
Use fractions to describe events in your own lives
When and why is it important to make pieces the same size? Is it ever appropriate to divide a set or an object in unequal pieces?

A Grain of Rice- Helena Clare Pittman
A Grain of Rice, King's Chessboard - dealing with factorials, exponents - Used for upper elementary, after the basic facts are mastered, delving into the application of multiplication.  This book also uses discrete materials (grains of rice) to demonstrate the doubling pattern

Number Sense
Exponents - What if Pong Lo had received one grain of rice the first day? How many grains of rice would he have received the second day, the third day, etc.? The numbers can be written in exponential form. 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2 ⁴ = 16
Algebra - Patterns
Extension - find patterns in Pong Lo's chart - see the diagonals, rows and columns
Data Analysis
Range, Mean, median, mode - Have the class arrange the estimates in order. How much rice in a pill bottle or some other container. What was the greatest estimate? The least? What was the middle value?
Problem Solving
How many grains of rice would be given in 100 days? Use calculator as 2 X = = = …push as many keys as the days to find out how many grains of rice.
Computation - Estimation, Exponents
Predict how much rice was given Pong Lo on the tenth day? When did he get his millionth grain of rice? 50 grains of rice weigh about one gram. Estimate the weight of Pong Lo's rice on the fortieth day.
Estimate the number of grains of rice in the plastic bag. What would ten rice grains look like? 100?
How can the rice be counted to verify the estimates. ? 1) Area estimation: spread rice out on 2-cm. Grid paper in a single layer, adjusting it to make a rectangle. Count the grains in one square and multiply. 2) Capacity -fill a small container such as a cap from a small bottle. Count how many grains fit in it and then how many capfuls fill the container. 3) Use weight: Count out 100 grains and weigh them. Weigh the total. 4) Use fractional parts. Divide the contents of the container in half, then in half again, and again, until the pile is easy to count.

How Many Feet in the Bed? -Diane Johnston Hamm Computation - Multiplication, Counting Counting by twos. Shows relationship between addition, subtraction and beginning multiplication - skip counting. Could extend to how many toes in the bed (one foot = 5 toes, 2 feet = 10 toes, etc.

How Much is a Million? - David Schwartz- Learnings: questioning numerical information, devising an appropriate mathematical experiment, exploring a variety of mathematical concepts, and sharing personal interpretations of "one million".

Computation
Estimate if that is really true that you can count to 1 million in 23 days. What will you use as your reference point?
Write the numbers of one million, one billion, one trillion. What do these numbers represent?
Would the population of the world be in the millions, billions, or trillions? How many starts are in the Milky Way? How big is the national debt?
See back of book for 4 activities. Have group work. Do you agree with this figure? Why or why not? Illustrate your conclusions with graphs, pictures, or posters. Prepare a brief presentation for the class explaining the author's strategy and their opinion of it.
Create a class book filled with questions and answers about a million. Have them find the answer. Example: "How long a line can be made with one million postage stamps laid end to end?" (1 1/2 " long)
How long would it take to count to one million? What if we wanted to make an estimate, an answer based on some experimentation and calculation?

If You Made a Million - David Schwartz

Computation
Imagine what you could do to earn a million dollars
How many different combinations of coins can be put together to equal 25 cents? Write on index cards and share findings by displaying on bulletin board
Challenge: Find the different coin combinations that add up to a dollar.
What happens to money in a savings account? Write the interest for one year at 5%. It says the dollar would earn $.64 in interest if the money is left in the bank for ten years. Ask students if this is the right answer. Talk about compound interest, using calculators. After the second year, interest would be paid on $1.05 and would equal $1.10, and the third, $1.16. If the interest and dollar are left in the bank, each year interest is paid on the dollar and in interest, not just the dollar.

In the Year of the Boar and Jackie Robinson- Bette Bao Lord In the Year of the Boar and Jackie Robinson - A Chinese girl, Shirley Temple Wong, comes to Brooklyn, New York. She has a hard time adjusting until she finds an interest, baseball, the Brooklyn Dodgers, and Jackie Robinson. Very culturally oriented. Discusses immigrants, countries, baseball and who was able to play the sport and how does it reflect on what is going on socially in the United States? Data Analysis Graphing - Have students chart the national origins of classmates or schoolmates. Interpret data on immigration statistics.
Statistics - Figuring baseball batting averages. Speak to Jackie Robinson's record or any player on the Rockies team, or students in the class. Computation Ratios - Experiment with taking shots at a wastebasket. Find out the ratio to hits and misses.
Averaging - Baseball statistics - batting averages, won/lost average, probabilities of a winning/losing team Extensions (Other resources) "Learn about Statistics - Math League Baseball - Arithmetic Teacher - Drafting, Scoring, gathering and evaluating data Jesse Bear, What Will You Wear? -  Nancy White Carlstrom

Combinations & Permutations

After reading the book, discuss the idea of deciding what to wear and how many combinations you can make.  (You can't make permutations since you can't wear pants on your head.)
When you have 31 flavors of ice cream, however, you can develop a variety of permutations, double scoop, triple scoop, which toppings, cone on top.  Begin with your three most favorite flavors.  How many different combinations can you make?  How many different permutations?  How many different combinations can be made when eating 2 scoops?  3 scoops?  4 scoops?  How many different permutations can be made when eating 2 scoops?  3 scoops?  4 scoops?

Jim and the Beanstalk - Raymond Briggs

Computation
Problems to pose - Could the giant's hands fit in this room? Your job is to estimate the length of the giant's hand. You'll have to decide what size book to use for comparison. Explain how you got your answer.

Julie of the Wolves - Jean Craighead George

Measurement - Time

Pg. 5 - "Lying on her stomach, she looked across a vast lawn of grass and moss and focused her attention on the wolves she had come upon two sleeps ago"
Pg. 6 - "Miyax was lost. She had been lost without food for many sleeps on the North Slope of Alaska."
Pg. 10 - "She had run away from him exactly seven sleeps ago, and because of this she had one more title …".  Why isn't time recorded as "days"? Or as "nights ago"?
Pg. 153 - " Time passed, fountains of the magnetic northern lights came and went, and the moon waxed and waned many times.
How is Julie determining the passage of time?
Pg. 61 - " One night she watched the dipping sun, trying to guess the date. It must be the second week of August, for the sun sat almost on the rim of the earth. The wolves had no doubt about the date; they were using a calendar set by the pups, and today was the second day of exploration."
What is the month and week? How does Miyax know? Explain the author's meaning. What day is it on the wolf pup's calendar.
Pg. 10 - "I am lost and the sun will not set for a month. There is no North Star to guide me."
What season is it?
Pg. 64 -65 - " "Autumn," she whispered and scraped faster. She saw several birds on the sedges. They were twisting and turning and pointing their beaks toward the sun as they took their readings and plotted their courses south. With a start, Miyax noticed the sun. It was halfway below the horizon. Shading her eyes, she watched it disappear completely. The sky turned navy blue, the clouds turned bright yellow, and twilight was upon the land. The sun had set. In a few weeks the land would be white with snow and in three months the long Arctic night that lasted for sixty-six days would darken the top of the world. About an hour later, the sun arose and marked the date for Miyax. It was August twenty-fourth, the day the North Star reached Barrow. Of this she was sure, for on that day the sun lingered below the horizon for about one hour. After that, the nights lengthened rapidly until November twenty-first, when the sun disappeared for the winter."
Miyax knows what season it is and the exact date. How does she know these things? How will Miyax know when it is November 21? What will the next 3 months be like?

King's Chessboard- David Birch
A Grain of Rice, King's Chessboard - dealing with factorials, exponents - Used for upper elementary, after the basic facts are mastered, delving into the application of multiplication.  This book uses discrete materials (grains of rice) to demonstrate doubling pattern. Rajah's Rice, an Indian folktale touches on the same concept.
King's Chessboard - Old folktale of a wise man who, in return for doing a favor for the king, asked for a grain of rice for the first square of a chessboard, two grains of rice for the second, four grains of rice for the third, and so on, doubling the number of grains of rice each time. May use a calculator to figure this out.

Number Sense
1,2,4,8,16 What's happening?( how many squares on the chessboard? 64) What happened on the 64^th day? Discuss with group. How did you figure it out?
On which square would enough arrive to feed everyone in class? Info. needed - 1) students in class, 2) how much each students eats (1/2 cup) 3) how many grains in 1/2 cup? Teaspoons? (24) Are there other ways to figure this out? What about cooked or uncooked rice? (expands 3 times) Make a convincing argument. See back of book - compare to real world stuff - 32^nd square - enough rice to fill 256 wheelbarrows. 64^th square - a stack of rice as large as Mt. Kilimanjaro - 19,340 ft ( 4^th tallest)
Algebra - Patterns
Computation - Doubling, Exponents
Extensions- Have students write their own doubling stories - ex. Teaspoon of water is doubled like rice on a chessboard, how long to fill a swimming pool? Story about doubling pennies to $1,000,000. Doubling an ounce of pepper until it fills a baseball stadium could bring on a giant sneeze.

King's Commissioners- Aileen Friedman Computation - Multiplication How many ways can you count 56 - by twos, fives, tens - reinforce the idea that there are different ways to think about the make sense of numbers. What are the advantages to grouping by 10's or other ways. This deals with number sense and understanding place value and counting as well. Make Way for Ducklings - Robert McCloskey Mr. and Mrs. Mallard have 8 ducklings. It shows the different adventures the family goes through, especially when crossing the street to the park with a pond. Number Sense - Computation Set up a scenario in connection with the story. "Mr. and Mrs. Mallard had 9 ducklings. Tell a story about what might happen if some of them wander away. Draw a picture and write a number sentence to go with your story." Student responses would be a great assessment tool. The student would demonstrate an understanding of subtraction and a number sentence that goes along with that.

Matilda - Roald Dahl

Story about a little girl, who would be considered a genius, uses these talents to trick people. Actually, it was mainly to trick her headmistress, who was very mean to children as well as to her teachers. She scares her enough to force her out of the town. Matilda ends up being adopted by her teacher, Miss Honey and they live happily every after. Matilda is a book that could teach honesty, and right and wrong, and how happiness could not be had.

Number Sense - Foreign Currency, Profit
British English written - use of pounds and pence. Research currency in England. Solve the problem that Mr. Wormwood had his son solve on pg. 34 - Chapter "Arithmetic"
Computation- Mental Math
Matilda was a whiz working problems in her head. Create problems where students could: figure two or more items in a store and they must figure out if they have enough money, how much of a certain ingredient to use when doubling a recipe, how much time they have left before they have to be home.
Data Analysis - Graphing
Heart Beats - Chapter, "A New Home". Heartbeat of a mouse ( 652 times a second). Compare that rate to that of a human. What about other animals' heartbeats? Does the size of the animal have a bearing on how fast the heart beats? Have students take their own heart beats. Have them run around a track outside and then take their heart beats once again. Why did that occur?

"One Inch Tall"- Shel Silverstein (Read the poem)
If you were only one inch tall, you'd ride a worm to school.
The teardrop of a crying ant would be your swimming pool.
A crumb of cake would be a feast.
A flea would be a frightening beast
If you were one inch tall.
If you were only one inch tall, you'd walk beneath the door.
And it would take about a month to get down to the store.
A bit of fluff would be your bed.
You'd swing upon a spider's thread,
And wear a thimble on your head
If you were one inch tall.
You'd surf across the kitchen sink upon a stick of gum.
You couldn't hug your mama, you'd just have to hug her thumb.
You'd run from people's feet in fright,
To move a pen would take all night,
(This poem took fourteen years to write --
'Cause I'm just one inch tall).

Measurement

Bring in a thimble, stick of gum, and pen
Show 1" tall
Show 4" tall
Pose problem - If the person was 4" tall how big would his hat ( thimble) be, surfboard (stick of gum), and writing tool (pen) be?
Have students make a 4" tall person. They would then plan and make a hat, surfboard, and writing tool for that person.
Have each group display their items in an interesting way.
Writing piece: respond in their journals how they determined and made the hat, surfboard, and writing tool for the 4" person.
Share with class.

Phantom Tollbooth - Norton Juster

• Discuss averages with the class. Write on the overhead: "Every 100 families would have 258 children" Display a grid with 100 squares to represent the families. Write a number in each square to represent the children in that family. The numbers in the squares must add up to 258.
• Survey questions: How many children are in your family?, How many pets does your family have?, How many cars (or TV sets) does your family have?, do you live in a house, a condominium, an apartment, or a townhouse?
• Ten questions: "I'm thinking of a decimal number between one and twenty. Can you guess my number?" You must answer the questions with "It's greater than… or it's less than…"

Measurement

Pg. 107 - 108 - "Of course not," replied Alec, sitting himself down on nothing. It's only mine, and you certainly can't always look at things from someone else's Point of View. For instance, from here that looks like a bucket of water," he said, pointing to a bucket of water; "but from an ant's point of view it's a vast ocean, from an elephant's just a cool drink, and to a fish, of course, it's home. So, you see, the way you see things depends a great deal on where you look at them from."
Pg. 110 - 114 - (see book)
How can this be?
How does this compare to Gulliver's Travels?
Have students create comparisons of different objects from different perspectives.
We develop number sense by comparison. Have students create statements using this form: ____ could not be the number of _____, but it could be the number of ____. Have them do this for small numbers, medium numbers, and large numbers. Do not specify which are small, medium, and large. You will be able to assess their number sense by their choices. Students can work in pairs and illustrate their statements on newsprint. These make colorful, interesting, and sometimes amusing wall displays.
Examples:

100 could not be the number of kids in this class, but it could be the number of keys on a piano.

5000 could not be the number of houses on a block, but it could be the number of shreds of cabbage in coleslaw.

1,000,000,000 could not be the number of books in our library, but it could be the number of people in China.

Number Sense Humbug wants to travel by miles because it's shorter, and Milo wants to travel by half inches because it's quicker.
Do their answers make sense? Where is their reasoning faulty?
Students can create similar equivalency charts for other measures and weights. Have them describe when using each measure is appropriate.
Examples:

• To remove a wart, a doctor might cut millimeters
• To remove an appendix, she might cut centimeters
• To perform an open-heart surgery, she might cut decimeters
Pg. 179 - "BY THE FOUR MILLION EIGHT HUNDRED AND TWENTY-SEVEN THOUSAND SIX HUNDRED AND FIFTY-NINE HAIRS ON MY HEAD, IT'S MINE, OF COURSE!"
Pg. 179-180 - " By the eight million two hundred and forty-seven thousand three hundred and twelve threads in my robe, I'll say there are."
Is this reasonable? How is this number written with numerals? What word is inserted incorrectly?

Fractions/Decimals

In chapter 16, Milo meets half a child. Milo is a little surprised by this child because he has never seen half a child before. The child responds, "It's .58 to be precise". He responds from the left side of his mouth (which happened to be the only side of his mouth). The conversation continues, "I beg your pardon? " said Milo. "It's .58," he repeated; "it's a little bit more than a half." (see book, pg. 196)

Number Sense - Infinity

(see pg. 189-191) The mathemagician tells him "add one to it. Now add one again. Now add one again. Now add one…" - the largest number.
The smallest number - "Now divide it in half. Now divide it in half again. Now divide it in half…" Again, the process can goon forever. This may be the first time students ever consider that smallness is also infinite. Initiate a discussion about what is infinite.

Sea Squares - Joy N. Hulme

Number Sense/Computation - Multiplication, Square numbers Different way to show squares - see Bunches and Bunches of Bunnies Three Pigs, One Wolf & Seven Magic Shapes - Grace Maccarone

Geometry/Shapes

Read the book to the students while using overhead tangrams to show pictures as they appear in the story.  After finishing the story, share a brief history of the tangram and have students locate its various pieces.  Students put their pieces together to make a square.  Have students try to recreate the pictures in the book.  Further challenge students by having them recreate other (non-outlined) tangram shapes.  Then have students create their own shapes.

Too Many Kangaroo Things to Do! - Stuart J. Murphy
Basic facts, demonstrating the understanding of multiplication - for the introduction of facts, younger students. Unrelated in the fact that they teach to different aspects of multiplication - Bunches and Bunches of Bunnies - squares of multiplication, Too Many Kangaroo Things to Do - ones up to four, 2 X 2 - zero to fives by fives.

Computation - Multiplication facts Building understanding of multiplication, one by one , find the total of the four times tables up to four. They are added up to 100 - counting by tens. This allows for the communication piece with students. Develop arrays using real objects, relate to real world . Develop the sense of items that come in twos, threes, fours - ex. Shoes, tricycle wheels, table legs. If we have four tables, how many table legs do we have? Have experiences in cooking - make arrays of cookies on sheets, nature - legs on animals, money - purchase food items, figure out how many of what and what do I owe?