Friday, April 30, 2010

Children's Math Book Reviews

With a sick student (or two) we've been doing a lot of reading. What incredible affirmation as to the power of math combined with literature! Little Student made connection after connection. So on our "no school" day, we learned a TON. (Or is that 2000 lbs?) Here are our top picks:

My opinion about The Wishing Club; a Story About Fractions by Donna Jo Napoli, totally changed. When I read it alone, I wasn't terribly excited. When I read it to my student, his enthusiasm was catching. In the book, siblings, ages 8, 8, (twins), 4, and 2, wish on a star. Over several nights they discover that their wishes are granted in fractions, determined by their ages: 8yos get 1/8, 4yo gets 1/4, 2yo gets 1/2. My student quickly understood the concept of fractions, exclaiming after the second page (which shows four 1/4ths make 1), "then one penny is 1/5th of a nickel!" In the story, the siblings put their wishes together to make one whole wish and get the wish that all of them want. [Concept: fractions]

My current student and I have not talked much about probability. The book, A Very Improbable Story, by Edward Einhorn, proved to be very effective when introducing the topic. Ethan, the main character, wakes up to find a cat, "Odds," attached to his head. An improbable event, indeed! He can only remove the cat if he is able to win in a game of probability. Several games are played and the odds of winning are thoroughly discussed in each scenario. By the end of the book, my student talked about the odds of Ethan winning or not winning the games. He also got a good laugh at the question at the book's end...what's the probability that you will open the book to a page with a picture? (Odds: 32 in 32 or 100% chance.) [Concept: probability]

In Equal Shmequal by Virginia Kroll, some animals witness children playing a game of tug-o-war and set out to play their own game. It quickly becomes obvious, however, that they have a problem making the sides "equal" with five animals competing. But even when the sides have equal numbers, the groups still aren't fair because the weights aren't equal. They set about figuring out how the animals' weight can be evenly distributed by balancing on a park teeter-totter. But when the bear is distracted by honey, they learn that equal effort is also important. Super cute. [Concept: equality]



The Candy Corn Contest by Patricia Reilly Giff is part of "The Kids of Polk Street School" series, chapter books for young readers. This book has a reading level (R.L.) of 1.9 (first grade, ninth month). I read it aloud to my sick 7yo. The story captivated him and he would read ahead over my shoulder and then hide his eyes because he was nervous about the events.

The main character, Richard, would like to guess the number of candy corns in the Thanksgiving class contest. Problem is, each guess is earned by reading a page in a book and Richard is not a good reader. Left alone with the candy jar, temptation becomes too much and he secretly eats several candies. Then what is he to do? He learns the teacher has written the number of candies on the bottom of the jar. Should he change the number? When the class ultimately shares the candies, the reader can think about division. [Concept: estimation, briefly division] Easy reader chapter book.

365 Penguins by Jean-Luc Fromental is an oversized picture book that provides many opportunities for problem solving. Each day, beginning January 1st, a single penguin is delivered to this family's home. After two months they have 31+28 penguins. Then they organize them into 4 groups of 15. But yikes! What about the food? They eat 2.5 lbs of fish/day at $3/lb. By the 100th penguin, it's getting expensive. They decide to arrange the penguins like eggs, in dozens. 12 boxes of 12 penguins. Later, they're stored in a cube shape = 6x6x6. By Dec. 31st, they have 365 guests. At last, Uncle Victor, the ecologist, arrives to transport the penguins. But, on January 1st, another BIG box arrives. Uh oh! [Concept: problem solving]

Thursday, April 29, 2010

The Art of Teaching Math (video worth watching!)

Sick kiddo = no school today. Learn from this video today... :)

Wednesday, April 28, 2010

Portfolder - Farm Unit

We wrapped up our farm unit today by making a Portfolder, characterized by the following:
  • made from poster board
  • show student thinking from beginning (What do I know about my subject? What do I want to know about my subject?) to end (What have I learned?) of any given unit of study
  • filled with students' comments and reflections about what they've learned
  • photos show children actively learning
  • include book/materials list of resources used during the unit
  • cover reflects original student artwork
  • charts, graphs, timelines and other graphic organizers are kid-generated
  • layout is determined by the child

Today, my student did the layout and paste-up for his farm portfolder. [Cover photo, left.] Since the portfolder is intended to show the learning process, he wrote in little dialogue bubbles, describing various activities and lessons from the unit. He also took time to reflect on learning: what was the most fun, what proved to be the greatest challenge, etc. This became an interesting point of conversation when the assignment that was the most fun was also the part that gave him the biggest challenge. (Little Red Hen book) It was great to be able to note that challenges can be quite fun!

When a Portfolder is finished, it's time to celebrate and share learning with others. Tonight he shared the contents with Dad and siblings. Tomorrow with grandparents. And, perhaps a celebratory lunch?

Here are several views of the finished Portfolder. It's impossible to show the fronts/backs of the numerous flaps, but you'll get the general idea.

Open to first section:


Open to second section:


Closed, back cover:

The beauty of a Portfolder? He'll return to look at his work again and again, reviewing and sharing with others in the process.

Tuesday, April 27, 2010

Math and Poetry ("Smart" by Shel Silverstein, money lessons)

Have you ever considered combining math and poetry? You might join a friend and read Math Talk: Mathematical Ideas in Poems for Two Voices. You could read "Shapes," by Shel Silverstein in his book, A Light in the Attic. Or you might consider using the hilarious poem, "Smart," (also by Silverstein in Where the Sidewalk Ends) and combine math (money), poetry, and drama.

(Note: you can purchase just the MP3 of "Smart" on Amazon, cheap. I own the audio recording of the books, available on CD: Where the Sidewalk Ends CD, A Light in the Attic CD.)

Today, Little Student and I read "Smart" aloud. We then used real money to demonstrate each of the exchanges that take place in the poem. As we made each exchange, my student (in the role of the son) told me how much money he lost in that step. He cut out coins and a dollar bill from printouts to represent the money used in the poem and glued them onto a 5-flap book. He read the poem again, pointing to each visual representation of the money as he went. Finally, he wrote number sentences to demonstrate what happened in each exchange; he wrote subtraction problems with blanks to fill in (see photo) to show how much money was lost each time.



He also played some money games on-line, selected from the following...

On-line Money Games:

Cash Out--Player becomes the cashier at a store and must give change. Varying levels of difficult.

Making Change--Pet store worker must make change with fewest possible coins.

Moneyville--fun, on-line role plays from the Moneyville touring exhibit. Become a neighborhood lemonade tycoon!

National Library of Virtual Manipulatives--(look under "money" by grade level)--Count the money and enter the correct amount.

Practice Counting Money--Player has to click and drag coins to equal the total amount shown.

Scottie Nickel-- Change money into the smallest number of coins possible.


Additional Teaching Resources on Money
Mathwire also has some fabulous lessons on money.

Additional Math Poetry Resources
Math Poems--from Math Mama's Poetry Challenge. Thanks, Sue, for the link!
A blog: Intersections--Poetry with Mathematics. Thanks, Maria, at Natural Math.

Next week, a group of my students will be dramatizing "Smart." Check back here for results. This is going to be FUN! :)

Saturday, April 24, 2010

Kids, Homeschool, & Schedules

Since I began homeschooling NINE (gasp!) years ago, I've tried any number of different schedules. For many years we didn't need a schedule. But I've found that sometimes we need one for various reasons... Young siblings on the sidelines. A particular personality who craves order. (Sometimes that's ME!)

The last time I used a schedule, I wrote it and everyone else followed. This time I'm doing it a little different...and loving the results!  Here's what I did...

Gather supplies:
  • pocket chart
  • old business cards or small pieces of cardstock in 3 colors
  • markers
As part of school I had my student make labels indicating every half-hour. On orange cards I listed the parts of the school day that are landmarks: breakfast, lunch, and (sometimes) nap. On blue cards he wrote down each of the things he does independently during the day. On green cards he posted things that he needs my help with during the day. Then, in the bottom right of each card we listed how much time (in 15 minute increments) each job takes.



He then placed all the time cards in the pocket chart, followed by the orange cards. It was then his job to make the schedule for our day, using the blue and green cards. I really didn't care what order he put them in (which gave him a lot of control!) as long as all the jobs made it on the chart. I did suggest that he put the "school" type cards before lunch as much as possible. I also explained that during the blue card (independent work) time that I would be doing household jobs.

As he finished each job, he turned the card over so I knew it was complete. This worked great! He does well on a schedule, but especially if it's a schedule that he has some control over. The fact that he has to think through what he must do each day and analyze just how much time it will take to get it done is an incredible life skill. He'll do this each morning so that the day's schedule is fresh in his mind.

See also: Kid Scheduled Workboxes!

Friday, April 23, 2010

The Little Red Hen (student authored pop-up book)

As part of our farm unit, Little Student, age 7, has been working on his own version of The Little Red Hen. After we read several versions of the story, he made a story map and then dictated his version to me as I typed. Although he often (physically) writes, in this case I wanted him to be able to concentrate on text without worrying about manually putting the words on paper. I think he produced a more fleshed-out story as a result. This is truly his work.

He chose to make a pop-up book; they are tremendously easy to make with great results. He is excited to "publish" his work here and eagerly awaits comments from his readers. ;)


Once upon a time there lived a hen, a rat, a dog, and a mouse. The hen wanted to make a pizza. The hen asked the rat, dog, and mouse to help her get the ingredients.




Who will help me go get the dough and the toppings?”


“I will,” said the dog.


“I will,” said the rat.


“I will,” said the mouse.


So they went to the store and got the dough and the toppings. The rat and the mouse argued over who would hold the cheese.





When they got home the hen asked, “Who will help me make the pizza?”


“I will,” said the dog.


“I will,” said the rat.


“I will,” said the mouse.


The dog put on the pepperoni. He took a nibble and stuck out his tongue. The rat and the mouse put on cheese. They took a little bite. When they were done, they made a disgusting face.





“Who will help me bake the pizza?”said the hen.


“I will,” said the dog.


“I will,” said the rat.


“I will,” said the mouse.


So they baked the pizza.





When the pizza was ready, the hen asked the dog, rat, and mouse to help her eat the pizza. “Will you help me eat the pizza?”


“I won’t,” said the dog.


“I won’t,” said the rat.


“I won’t,” said the mouse.





So the hen ate it by herself. The dog chewed on a bone. The rat and the mouse found seeds and ate them. The hen made a disgusting face.

The End.

Thursday, April 22, 2010

Geometry Class #4, Geometry with Quilts (ages 7-10)

Today we began by looking at homework (optional) from last week. I wished that my blog readers could see the homework (fun stuff!), then remembered that Bridges Home Connections are available, free, on the Math Learning Center Website. We've done several of them in the recent past. Go HERE and look under "Home Connections" for Home Connections 11-15 (pdf). They are:

#11: "Crossing the Pond" (game)
#12: "3-D Shape Hunt" (looking for geometric figures around you)
#13: "Last Shape in Wins" (game we've been playing during choice time) and
"What Can You Do With a Square and 2 Triangles?" (our homework this week)
#14: "Is it Symmetrical?" (exploration around home for symmetrical items)
#15 "Sorting Quadrilaterals"

Again this is all FREE! Comes with gameboards, paper patterns for manipulatives, etc.

We continued by reading aloud A Cloak for the Dreamer.** Excellent read! Reflecting on the book, we talked about what shapes could be pieced without holes or gaps and experimented with pattern blocks. [Refer to my post on Tessellations for more ideas.]

We made our own patchwork quilt blocks with paper. We explored the number of lines of symmetry in each block and graphed our class results. Next session, each child will select a favorite block to replicate for our own paper mini-quilts.

Toward the end of our class, students participated in choice time ("Work Places") utilizing activities from Geometry with Geoblocks (hands-on math for homeschoolers) and Bridges.

I ended the session by reading Sir Cumference and the Sword in the Cone.The kids were thrilled to have another Sir Cumference title...and were especially happy when they correctly guessed where the sword would be found.

 If I'd had a few more minutes, I would have read a book on quilts. I'd prepared several to  choose from:

The Keeping Quilt, Patricia Polacco
The Log Cabin Quilt, Ellen Howard
Oma's Quilt, Paulette Bourgeois
The Name Quilt, Phyllis Root
The Patchwork Quilt, Valerie Flournoy
The Promise Quilt, Candice Ransom
The Quiltmaker's Gift, Jeff Brumbeau
Quilts in the Attic, Robbin Fleisher
The Quilt Story, Tony Johnston
Selina and the Bear Paw Quilt, Barbara Smucker

This is only skimming the surface of the abundant children's book titles on quilts. It would be an excellent unit study in tandem with geometry. If your children are up to the challenge, consider having them make their own wall hangings. The photos capture examples that my students did several years ago during a study of the Oregon trail. The drawings are done using Pentel Fabricfun Pastel Dye Sticks. With these sticks, you can draw directly onto the fabric rather than having to transfer from paper with fabric crayons. As you can see, the colors are vibrant and the drawings are clear.

**Our lessons today come from The Math Learning Center's  Geometry with Geoblocks (hands-on math for homeschoolers) and Bridges. I noticed that they sell A Cloak for the Dreamer for less than I've found it elsewhere. But it's also available through Amazon.

Have fun! And if you do any of this, I'd love to know how it turns out! :)

Tuesday, April 20, 2010

Walking & Talking Math in Your Sleep

Remember how we love Mythmatical Battles? Well, I'd better love it a LOT because my 7yo student just discovered it and wants to play it ALL. THE. TIME.!!! How much does he love it? He's dreaming about it.

He is my sleepwalker. Last night, after playing a round of M.B. with Dad, I found him wandering down the hallway, fingers rubbing against his blankie as he murmured,

"Look how powerful our defense is!"

I cannot make these things up. If you want a chance to win a game and have children in your household sleepwalking and uttering things about "defense powers," join the Mythmatical Battles giveaway.


Disclaimer: I make no money off Mythmatical Battles (unless you buy a set off Amazon, in which case Grace and Hope gets a couple cents.) I just like them. Or I did until I was asked to play it 39,000 times a day. But 7yo student suddenly knows a bunch of multiplication. And we haven't even started studying that yet!

Monday, April 19, 2010

Exploring Area with Pattern Blocks


Last week I mentioned how we used pattern blocks to explore area during our geometry class. Today, my student continued the lesson as he explored area using pattern blocks with puzzles.

I own several different pattern block books: Pattern Block Problems for Primary People, Patternables and Magnetic Pattern Blocks. I used the first two as it was easy to find puzzles that did not use the tan parallelogram and orange  square (not used in this lesson.) I took all the pages out of both books, slipped each page into a plastic sleeve, and put them all into a 3-ring binder. This allows multiple children to use materials at once; I just pull out a page or two at a time. Today, little student, age 4, put pattern blocks onto some of the easiest puzzles while big student, age 7, calculated area. [Side note: the magnetic books are great for younger kids who may have trouble keeping the blocks in place as they work on a puzzle.]

I again explained that "just for today" a green triangle has an area of 1. With that in mind, I asked him to figure the area for 6 puzzles. He first had to solve the puzzle itself, trying different pattern blocks until he found the ones that fit correctly. After the puzzle was finished, he figured the area for each figure if a triangle = 1. I put a small post-it note next to each puzzle where he could write the answer. When he finished, he explained to me how he got his answer. He calculated so quickly that I sometimes had to ask him repeat himself because "Mommy can't add that fast!" I videotaped one example...it's the first time he's sharing this puzzle with me. See if you can keep up! ;) I wouldn't expect students new to pattern blocks to be able to add so fast, but he's obviously familiar with the shapes and how many triangles fit in each. (You'll want to investigate how many triangles fit in each pattern block shape with your own student before figuring larger puzzles.)

video

If you keep the puzzles in plastic sleeves, you could ask your student to trace each shape using a dry erase marker, then write the value inside each outline. [For example, a trapezoid would have a "3" written inside it, a triangle a "1", etc.]

Before bedtime, we'll read Spaghetti and Meatballs for All!, a book that considers area and perimeter as tables and chairs are readied for a family reunion.

P.S. Pattern blocks are widely available for purchase. Amazon and The Math Learning Center are two options. Disclaimer: I make a few cents on purchases if you click from here to Amazon. I do not make money on pattern blocks through The Math Learning Center, but they are an awesome non-profit and worth supporting. :)
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