Wednesday, March 31, 2010

My Little Farm-Day 5 & 6

The boys watched themselves on video this morning. Over and over and over. Then they wanted to perform. Again and again and again. No shortage on activity for a rainy morning around here. ;)

We're continuing with lessons in My Little Farm, buying sheep and goats to add to the pasture. My student calculated how much the animals, land, and fencing would cost him. He's beginning to explore perimeter as he figures how much fencing he needs for each animal pasture. The lesson comes with a fact sheet of cards you cut out naming characteristics of sheep and goats. He sorted them, pleased that he knew which facts go with which animals; we decided that he will quiz Daddy on them later tonight.

Tomorrow we'll head to the library to pick up a few more books on farm life. Which brings to mind a few favorite books with animals in starring roles...

My 4-year-old student is new to English. We've read a lot to him since he came home about 10 months ago. He loves most books. But he has two favorite series worth mentioning: Elephant/Piggie books by Mo Willems and the boy/dog/frog books by Mercer Mayer.

The Elephant/Piggie books (such as I Am Going, which the 4-year-old now recites) are easy readers with hilarious text/photos. It's not often I find myself laughing aloud at an early reader, but I do with these!

The boy/dog/frog books (such as One Frog Too Many) are wordless picture books with captivating story lines. Wordless picture books help children to become readers as they first understand the concept of a story (front to back, beginning/middle/end) and then build vocabulary and comprehension as they tell the story in their own words. The readers in my family enjoy these books just as much as the non-readers. Wordless picture books can also be used with older kids as a basis for creative writing.

Tuesday, March 30, 2010

Puppet Shows & Public Speaking

In conjunction with our farm unit we decided to do a puppet show of The Three Billy Goats Gruff. My student drew one goat which we photocopied and reduced by 75% and 50% to make the two smaller goats. He also drew a troll. Little helper, just turned 4-years-old and only 10 months into learning English, assisted in the performance, repeatedly begging, "Do it again! Do it again!"

"Speaking" of which...

When I first started homeschooling, I had a few concerns. "Socialization" was near the top of the list. (I soon came to realize this was a joke. We socialized so much the first year that we hardly had time left for school. We cut waaaayyyy back and eventually came to a happy medium.) Related to socialization was the idea of public speaking/presentations. Since my children were not in large classes, I felt that speaking opportunities must be deliberate, frequent, and purposeful. At young ages we acted out stories or made puppet shows, performing for anyone who would listen...usually Daddy, siblings, and grandparents. We joined book clubs and co-ops where students regularly presented. Later came Lego Robotics and Shakespeare productions. It's paid off. My daughter, now a freshman in a large public high school, has excelled in speech competitions. Last year, two of my kids competed in Lego Robotics on a national level, where their performance depended heavily on their speaking/presenting skills.

All that to say that this is where they began...

The older kids did their own version of The Three Billy Goats Gruff when they were young. We all start somewhere. :)

When kids are young, I start by repeatedly reading a story. When they have the story line down, I like to do the puppet show with them, modeling how to use the puppets in the context of the story. As soon as they're ready to take over, I happily bow out and let them continue without me. Today I heard many, many different versions of the story as they considered what they wanted to say. (A lot of whispering went on "backstage.") It's fascinating to watch them internalize the story, getting louder and more clear as they become more comfortable with the performance aspect. The request to "do it again, do it again!!" didn't stop today.

Love of learning. What more can we ask?

Monday, March 29, 2010

Tessellations: Lessons & Fun Manipulative

Love tessellations. They're like a puzzle. Artsy. Challenging to make. And, yes, math-y. Love the patterns.

Tessellation Posters, Individual

I've often done tessellations with second through sixth grade students--both at home and at school--with pretty cool results. I usually have kids use this method. Here's another set of step-by-step instructions. Basically, start with a square and draw a line (curved or several straight) from the top left to the top right corner. Cut this out, slide straight down across the figure, and tape onto the bottom edge of the square, straight edges together. (This must line up exactly.) Then make another line (again, curved or several straight) from the top left corner to the bottom left corner. Cut. Slide to right side. Tape, straight edges together. After you've got your pattern piece, trace repeatedly on a larger paper.

Here are a few student examples of tessellation posters:

Go to bottom of this entry for some fabulous tessellation links.

Tessellation Poster, Group
Last year every child contributed one "fish" to our large tessellation poster. I used an index card to made a fish that would tessellate. I traced the fish onto individual index cards so that each child had one. I brought in my junk art supply box and they used fabric, glitter, sequins, pompoms, yarn, crayons and colored pens to decorate their fish. They cut them out, very carefully. We then mounted them on a blue piece of posterboard, leaving a "blank fish" space in between each one. I used fish from two different classes to create the poster. Each group was pleased to see what the other group had constructed.

Bargain Bin Manipulatives
But why am I posting this under "Monday Manipulatives?"

I rarely shop. (Food is an exception. I do eat.) Even rarer that I buy much. I'm quite frugal. Quite. :) But on a spring break trip to the mall, I found something in the bargain section that I just had to buy. For math, you know.

They are called "Puzzellations" and are basically magnetic puzzles that tessellate. You can get snowflakes, undersea adventures, garden shapes, and more. When I taught the lessons above, I would have loved to have had these to illustrate the concept on the white board, also magnetic.

We opened the dinosaur kit last night and my 7yo son, my 15yo daughter, and I played around with it a bit. My 7yo had trouble fitting the pieces together at first. So did I. Then we realized that you have to be very precise about placement...which was also the case when I did tessellation lessons with it made sense. My 7yo could do some simple patterns with a lot of effort, the greatest difficulty being with fitting pieces together smoothly. My daughter and I enjoyed experimenting. The box says "ages 8 and up." [See photos below. We tried a variety of things--tessellations as well as other patterns.]

It comes with magnetic pieces, a magnet board, and a booklet. In addition to pattern ideas and tessellation info, the booklet also contains math (involved in making the dinosaur pieces, symmetry--rotational, translational, glide reflection), art (coloring, drawing your own), and tessellations in nature. Pretty involved for a booklet.

Related Children's Book
If you decide to do a tessellation lesson, consider reading A Cloak for the Dreamer as you begin.

Tessellation Links

Here's another great how-to site.

Here's a way to make even fancier designs.

And a wonderful award-winning website of kid-safe Escher-style tessellation art and teachers' tutorials
button for

A step-by-step YouTube video:

Happy Tessellating!

Sunday, March 28, 2010

Investigating Growing Patterns

Investigating Growing Patterns is the featured topic in MathWire: April 2010. Tons of great stuff! Many pdf files to print for student use. Also,

"...samples of growing pattern problems created by ED 556 students at Monmouth University in West Long Branch, NJ during the Fall 2004 session. In each case, students should draw and/or describe the next couple of stages in the pattern and create an input/output table to describe the relationship between the stage and the number of blocks used. Students should be challenged to write a rule in words and more capable students should be challenged to write a general mathematical rule that would calculate the number of blocks needed for any given stage."

Links are listed for on-line practice with function machines. They also recommend several children's books to introduce functions as growing patterns: Two of Everything, One Grain of Rice, The King's Chessboard. (Also see pdf files and lesson plans available for the books.)

Thursday, March 25, 2010

My Little Farm-Day 4, Part II

Today we reviewed coordinates and learned map skills as we mapped our farms**.

We also enjoyed reading The Three Billy Goats Gruff and drawing a picture to accompany the field trip report. The picture is as cute as the real thing! :)

P.S. When my older kids did this unit, they drew figures to mount on sticks for a Three Billy Goats Gruff puppet show. I was just thinking that I could photocopy my student's drawing from today and reduce it to make three sizes of figures for another puppet show. (He's not ready to draw all the figures himself.)

**Farm mapping exercise comes from My Little Farm.

Image Hosting

Wednesday, March 24, 2010

My Little Farm-Day 4, Part I

Day 4 of My Little Farm is taking several days because we're having so much fun going down rabbit trails...or should I say "goat trails?" We first read about goats and documented what we'd learned in a chart. After learning that a friend's goat gave birth to triplets, today we set off on a mini field trip to see the babies, less than a week old. We learned some things we didn't those little babies are very LOUD!

We discussed our visit and began writing. My industrious little pupil decided to add a attempt to add one of his new vocabulary words to his paper. He's been reading Charlotte's Web and recording each new word he notices, along with a definition and a brief sentence. Each night at the dinner table he captivates his older siblings by using words that they don't always know. (He's rather pleased about this!) So on his goat paragraph he wrote, "We went to Mary's house to look at goats. We went to see the triplet goat babies. The baby goats BAAAD unremitting for five seconds. They were running and jumping 30 minutes after they were born. The goats were cute." Any guesses as to what his new vocabulary word is? [Smile.] We'll map out our farm tomorrow.

Tuesday, March 23, 2010

Tuesday Titles! (The Librarian Who Measured the Earth)

This summer I feel lucky to be teaching a class on "Linking Mathematics and Literature." It's a natural outgrowth of my children's books. Through "Tuesday's Titles" I hope to present some of my favorite math-related books, both for children and educators.

Kathryn Lasky's picture book, The Librarian Who Measured the Earth, tells the story of Eratosthenes, a Greek astronomer and geographer who measured the circumference of the earth in around 200 B.C. with incredible accuracy. Lasky writes, "He calculated the circumference of the earth to be 252,000 stades, or 24,662 miles. When the earth was remeasured in this century, there was only a two-hundred-mile difference between the modern-day figure and the one that Eratosthenes had calculated over two thousand years ago!"

I'm a bit perplexed by Amazon's age range for the book, 4-8 years. Last year I shared the story with a class of gifted and talented children in grades 2-6. They, like me, were captivated by this amazing story. Tonight I read it to my bright 7-year-old, who enjoyed it and asked a lot of relevant questions, but clearly didn't comprehend a lot of the mathematics involved. My 4-year-old ignored it and paged through his own book. I'd say it's best for about 7 or 8 years and up...waaayyyy up! ;)

Also see the Measure the Earth Project where students around the world participate:

Your student/class can participate in The Noon Day Project that replicates Eratosthenes's measuring techniques. The spring project runs until April 11 and starts up again in the fall.
The Goal of the Noon Day Project is to have students measure the circumference of the earth using a method that was first used by Eratosthenes over 2000 years ago. Students at various sites around the world will measure shadows cast by a meter stick and compare their results. From this data students will be able to calculate the circumference of the earth.

Possible curricular ties: biographies of mathematicians, circumference, measurement, Ancient Greece

Monday, March 22, 2010

Monday Manipulatives: Averaging with Unifix Cubes

When asked, "Do you own math manipulatives?" many people confidently nod.

But when the conversation continues with, "How do you use math manipulatives?" the reply often ranges from "Ummm, they mostly sit on the shelf," to "The kids play with them. Sometimes."

A new feature, "Monday Manipulatives," is dedicated to dusting off those manipulatives and considering fresh, new ways to teach math.

Please join me this week in "Averaging with Unifix Cubes."** I hope you find your own unifix cubes and try it with the kids!

Note: Due to video time limitations I could not show multiple ways to level the towers. When you work with children, however, I encourage you to help kids understand the idea of averaging by giving them 2 stacks, and then 3 stacks of cubes, and asking them to devise methods to level the towers.

Part 1:

Part 2:

**This averaging model is introduced and explored in more depth in "Measurement with Marbles" by the Math Learning Center.
Check out what Risa did with the lessons on Averaging with Unifix Cubes. Awesome! :)

Thank you, Risa, for alerting me to your blog! If anyone else is applying a lesson, I'd love to see your work. :)

Thursday, March 18, 2010

Mega Marble Rolls!

Over the last five weeks, my class conducted several experiments** with household cardboard tubes, marbles of various masses, and wooden blocks, to see what might produce the desired effects in their culminating project, the "Mega Marble Roll." Today they put their ideas to the test. Each team selected a problem, then designed and built a marble roll to solve it. They would like to share what they learned with you. (And would love it if you would leave them an encouraging comment or two! YOU are their audience!)

**Lessons are taken from "Measurement with Marbles" by the Math Learning Center.

Group #1 Problem: include two uphill and two downhill ramps

Group #2 Problem: include two jumps in your marble course

Groups pose with their finished products:

And a quick demonstration on averaging for the families...

Thank you for visiting our class. Please come again soon! (And the class thanks you for your comments!)

Wednesday, March 17, 2010

My Little Farm-Day 3

Today we added the barn, silo, and tractor. We were careful to follow "Land-Use Planning Codes."

Of course, like every responsible farmer, we must pay for our goods...

Tuesday, March 16, 2010

My Little Farm-Days 1 & 2

We just started a new unit based on My Little Farm (Bridges Breakout).

Description: "Life on a small family farm provides the context for exploring place value, money, area and perimeter, mapping, and computation. In this 4-week unit, students create a paper model of a farm and learn about farm life and farm animals."

Yesterday we created a web of things we might find on a farm. "Farm bucks" were distributed and cut. Farm mapping began this morning; you can see the house/land and road...paid in cash today! Each day we'll be continuing to add to our farm layout.

We are creating a portfolder of our work, adding to it as we go... I'm using Draw Write Now, Book 1: On the Farm-Kids and Critters-Storybook Characters for assistance with drawing farm critters. The drawings shown on the portfolder cover were independently done by a 7yo, following directions from the book.

New vocabulary words, found in Charlotte's Web, are recorded on notecards with definitions and sentences. It's sticking! The word "glutton" was giggled over at dinner last night. :)

7yo student quote: "It's kinda like Farmtown on Facebook." (BTW, I do NOT play Farmtown!)

Measurement with Marbles!

Class: Measurement with Marbles!
(lessons/kit available from Math Learning Center)
Dates: February/March 2010
Course Description: Measurement with Marbles gives children an opportunity to use mathematics in the context of scientific research. In this unit, students make ramps with household cardboard tubes to investigate some of the factors that cause marbles to roll farther and faster. They measure the distances their marbles roll (and learn to average) as they change the ramp heights, the ramp lengths, and marble masses. Finally, they apply the understandings they've gained as they design mega-marble rolls -- pathways designed to get the marbles to do a series of specified tasks. (Great for co-ops, btw!)

Do the math...

toilet paper tubes
paper towel tubes
wrapping paper tubes
marbles (of many masses)
wooden blocks
unifix cubes
lots and lots of masking tape

= lots and lots and lots of fun, making meaning in MATH!

Quote from one 7yo student: "We've been putting blocks on top of each other to see how far the marble goes. You have to make the unifix cubes so they're even (averaging.) It's really fun!"

Photos from our last class coming soon...MEGA MARBLE ROLLS! ;)

Welcome & Disclosure

Welcome to our school! Through this blog we hope to share bits and pieces of our days, loving learning! Often, entries will highlight community classes. Occasionally, we'll share excerpts from our personal school days. Grab a cup 'o tea and join us... LOVING LEARNING! :)

Edited to add "Disclosure Statement"...  This policy is valid from 28 November 2010.

Since the FTC rules that all bloggers need to disclose, here it is...  Hope you enjoy reading it as much as I enjoyed writing it. Heheh.

This blog is a personal blog written and edited by me. (No kidding!)

This blog accepts forms of cash advertising, sponsorship, paid insertions or other forms of compensation as stated in the "Note" below... (it's not what it sounds like, believe me!...)

Note: as of the policy date, the only compensation received is from:

1) Amazon links. (I tried to set up an affiliate account with Barnes & Noble, but it doesn't appear to be working correctly, so I took my $1.61 and ran.) As of 11/2010, all Amazon commissions are donated to Grace and Hope who helped to sponsor my son's foster care in China, giving him a wonderful start.

2) Google ads. If someone pushes on 'em. Which they rarely do. ;)

The community classes that I offer, locally, are my own; I receive no compensation through this blog for them.

This blog abides by word of mouth marketing standards. We believe in honesty of relationship, opinion and identity. The owner(s) of this blog is not compensated to provide opinion on products, services, websites and various other topics. The views and opinions expressed on this blog are purely the blog owners. If we claim or appear to be experts on a certain topic or product or service area, we will only endorse products or services that we believe, based on our expertise, are worthy of such endorsement. Any product claim, statistic, quote or other representation about a product or service should be verified with the manufacturer or provider. Clear as mush?

The owner(s) of this blog would like to disclose the following existing relationships. These are companies, organizations or individuals that may have a significant impact on the content of this blog. I consult with The Math Learning Center in ways unrelated to this blog. As of 7/10, I am also managing the MLC blog,...again, unrelated to this website. We have a financial interest in the following that are relevant to our blogging: small percentage on Amazon items if purchased through this site will be donated to Grace and Hope. If I don't like a book, I generally won't post a review; I don't like to be the bearer of bad news, but I get pretty excited about stuff that works...particularly when it comes to books/curricula.

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