Pumpkin Math

One of my favorite books, How Many Seeds in a Pumpkin?, is perfect for this time of year. Children estimate how many pumpkin seeds are in pumpkins of varying sizes. In order to find the number of seeds, children count by 2s, 5s, and 10s, and learn that the smallest pumpkin actually has the most.

Maybe you'll want to read it and do some of the "Pumpkin Problem Solving" or "Fall Math Activities" over at Mathwire...one of my FAVORITE math idea sites! ;)

Snowflake Symmetry (Geometry Class #2 Part 2, Fall 2010)

This week's math class continued with symmetry...

We read Snowflake Bentley, a Caldecott winning book, that tells the true story of Wilson Bentley, who first captured individual snowflakes on film. We noted that Willie was homeschooled until age 14. Some speculate that Bentley may have been autistic.

Bentley said, "I found that snowflakes were masterpieces of design. No one design was ever repeated. When a snowflake melted...just that much beauty was gone, without leaving any record behind."

Two years ago my husband and I were in Vermont. Driving through Jericho, I noticed a snowflake sign on the "Old Red Mill." We inadvertently discovered the Snowflake Bentley Exhibit with a tiny museum housing Bentley's cameras as well as some of his photos. If you're ever in Jericho, Vermont, be sure to visit! (pictured, left)

Using Bridges materials, my students made their own snowflakes using paper pattern blocks.

After thinking about the meaning of "line of symmetry," we sorted our snowflakes. It took a lot of work to figure out how many lines of symmetry in each! We held a ruler in front of each image so we could imagine where the line(s) might be. One snowflake had rotational symmetry; we will explore that in more depth next week.

As a last, optional, activity, students could make a symmetrical mask. I saw this posted on Mathwire and wanted to use it as an extension of our lesson on "line of symmetry."

If you'd like, try some symmetry activities on-line:

Symmetry Game

Learn About Symmetry

Symmetry Pattern

Cyberchase Symmetry

Symmetry Shape Games

Finish the Symmetry Picture

List of Kids' Symmetry Links

Also, check out this snowflake set. What a fun way to explore tessellations!

Polygon Play (Geometry Class #2 Part I, Fall 2010)

Math class today. We did so many things that I'm going to break it into a series of posts. :)

Started with a brief review of tangrams by reading Grandfather Tang's Story. I provided tangrams so the kids could construct the animals as the story went along, but the story became too captivating...they slowly abandoned the pieces to fully concentrate on what was happening. Great book!

We continued with a review of polygons. Last week we discussed the characteristics of a polygon. I drew a variety of figures on the board and they told me which were polygons and which were not. Since we'd read The Greedy Triangle last week, we quickly flipped through the book to see the polygons used there.

We then made a flapbook...the word "polygon" on the outside of the flap and the characteristics listed inside. (This is not pictured.)

And now...to make a quiz for their parents...to see if they know about polygons. They LOVED that idea! We made a series of 6 flaps (see right photo...one flap is open.) I had them cut off the top flap to make a "title" area..."Is this a polygon?" They then drew 5 figures of their choice on top of the 5 remaining flaps. Under each, they wrote "yes" or "no" to indicate whether the figure is a polygon. They used rulers to make sure the straight lines were actually straight.

In the process of assessing their parents, this became a quick assessment to see if they had a solid understanding of polygons. With fun in the process!

Nice addition to polygon lessons:


Geometric Stick Lessons

Math Poems

Someone posted on the Sonlight Forum to say that her sister/nieces had written some math poetry. I wrote to the author, Belinda, and got permission to share them.  I think they're fantastic!!! ;)

Rectangle got butted by a ram

And now he's a parallelogram

Headless triangle gets annoyed

When everyone calls him trapezoid

A square that gets caught in a wind gust

Directly turns into a rhombus

Rectangular prism gets the blues

When people use him as a box for shoes

Aren't they awesome?!!!! Try making up some of your own. Illustrate them! And explore more MATH POETRY ideas.

Probability Pouch Play!

This week, I told my son that I had a mystery for him to solve. I put 20 game tokens into our "Probability Pouch" and it was his job to try to figure out how many of each color was in the pouch. I didn't tell him what colors I'd used...only that 20 tokens were in the pouch.

Materials Needed:

• Probability Pouch (if you don't have one, either use a paper bag or find a large sock and fit a small yogurt container tightly into the bottom of it...this works great to draw from)

• game tokens (or look at game markers)

• felt markers

• paper

I asked him to draw four tokens. He drew 3 red and 1 blue. I encouraged him to think of a way to keep track of his draws. He chose to make tallies in a pen color corresponding to each game marker.

We talked about how important it was to shake the bag and to put the game markers back in the bag after each draw. Once, he ended up with 3 markers on the table. I asked what would happen if he kept doing that. He grinned and agreed that we'd know what was in the bag based on what was on the table. He took away the data for those 3 draws, put the markers back in the bag, and redrew.

After about every 10th draw, I asked him to stop, look at the data he'd collected so far, and predict what he might get over the next ten draws. Which colors would he draw least? Which most? How many of each did he think he'd get?

He quickly recognized that he was consistently drawing the most red, the least yellow, and blue somewhere in the middle. As he considered what he might draw in the next 10, he made predictions like: 5 red, 4 blue, 1 yellow, and later, 6 red, 3 blue, 1 yellow. He kept a running total of what he'd drawn so far. After 40 draws, he'd gotten 25 red, 12 blue, and 3 yellow.

I asked him if it was possible that there was another color in the bag. He said yes, that there could be one green that he just hadn't drawn yet.

I asked, "What do you think the bag contains? Why?" Initially, he guessed the numbers based solely on the fact that he "drew the most red then blue then yellow." (He had the most red, followed by blue, then by yellow, BUT he didn't have any particular reason for the number of each color he selected as long as they were in that particular order.) I asked him to look at his data again (25 red, 12 blue, and 3 yellow) to see if there was any pattern to it. For instance, about how many more red did he have than blue? His eyes lit up. I gave him the option to change his prediction if he wanted to. (I did not push this.)

He altered his response to 12 red, 6 blue, 2 yellow. When I asked, "Why did you pick these numbers?" he responded, "I got lots of red and half blue and I got a 1/4 of yellow than blue."

Last question..."If we made more draws would it help you decide what is in the bag?" He said yes. Although he didn't use this vocabulary, he seemed to understand the concept of theoretical probability vs. experimental probability.

I asked if he wanted to know what was in the bag. Um, YES! He dumped it out, quickly counted and GLOWED. His response? "I got it EXACTLY!" (See answer pictured below.) While an exact answer was not my goal, it was fun to see his excitement. ;)

I love teaching probability. I'm sure it stems from the fact that lessons* are high interest, creating incredible "AH HA" moments in kids.

[*Note: The lesson that I did with my son taps from Bridges. I modified it to fit our needs.]

Kids LOVE probability!  Funny thing is...I don't remember EVER doing a lesson on probability when I was a student. Do you?

I asked one group of students to brainstorm a list of all the ways that probability is used in daily life. Their list was huge. Probability has so many implications for daily life. Perhaps you'll consider generating your own list with your kiddos and submitting it as a comment?

Resources to check out:

• Probability Paper Bags

• ProTeacher Collection (several ideas here)

• Tootsie Pop Pull (might need a bigger bag!)

• Bridges Breakout: Math With a Sock--Probability and Fractions 
  (or see economy version)...also love the tie dye probability containers

• If you need help coming up with color combinations, here is a page of probability clipart that might give you some ideas on what to put in the bag.

• And here is a nice introduction to probability.

•  Children's Books on Probability, Data Analysis, Graphs: 

• Do You Wanna Bet? Your Chance to Find Out About Probability, Jean Cushman (chapter bk) 
• Pigs at Odds, Amy Axelrod
• Probably Pistachio, Stuart J. Murphy
• Socrates and the Three Little Pigs, Mitsumasa Anno
• A Very Improbable Story, Edward Einhorn

What is the probability that your family will have fun with a lesson like this? :)

P.S. Don't forget to enter to win your own "Probability Pouch!"

Our Science Lesson for Today

Can you identify what the boys found in our backyard?

Tangrams (Geometry Class #1, Fall 2010)

[Note: Most of what we did today comes from Bridges materials.]

We began by reading a Marilyn Burns book, The Greedy Triangle, in which a shape takes on one additional side after another, transforming from a triangle to a quadrilateral to a pentagon, etc.  I then asked the kids to consider what they already knew about geometry. They recorded their thoughts (words and/or pictures) in a 2-flap book. (We made our own flap books--photo left--but you can see a template under "Flip Flap with 2 flaps.") They wrote what they knew under the left flap and questions or things they wonder about under the right flap.

We then compiled our information on a class chart.  It was exciting to see lightbulbs begin to go on; several kids had little to nothing on their individual flaps as they thought "geometry" was something totally new. As they heard ideas from other kids, our list became longer and longer as they began to make connections.

We began thinking about Tangrams by reading Three Pigs, One Wolf, and Seven Magic Shapes. After the book, I slowly took them through the process of cutting their own Tangrams from 6x6" pieces of wallpaper. Here are instructions if you'd like to make your own. As they worked, we used a lot of mathematical vocabulary in context. Two words we especially highlighted: congruent and similar. A debate arose as to whether all triangles are "right triangles" or not. Some children were certain that they are; others were positive that there are exceptions. I told them to think about that for a time.

When the Tangrams were complete, we used them to create a variety of shapes using just 2 pieces: square, rectangle, parallelogram, trapezoid, etc. They were then challenged to create the same shapes with 3 pieces. They have homework (optional) in which they'll try to construct shapes out of 4 or 5 pieces.

Another challenge? To put the seven pieces back into their original square. This will be made easier by the fact that we used wallpaper with a pattern on one side. We finished with a reading of Agatha's Feather Bed.

During the week, students may try Tangram puzzles on an iPad/Touch/Phone or select from the following:

Tangram Puzzles

Cyberchase Tangram Game

Sagwa Tangrams

NCTM Tangram Puzzles

NCTM Illuminations Tangram Lesson

Tangram Puzzles to Print

Online Tangram Puzzles

We also have several tangram puzzle kits and a game called Classic Tangoes. Manipulating the puzzles by hand definitely uses a different set of skills than doing them on the computer. If you'd like to read some more books with Tangrams, pick up Grandfather Tang's Story or The Tangram Magician.

What an enjoyable class you are! See you next week! :)

P.S. We talked quite a bit about the properties of a trapezoid. Please have them look at this site.  It allows you to manipulate a figure so that it remains a trapezoid but allows you to see the wide range of possible figures.

Make Your Own Probability Pouch

You've been awake nights, waiting to know what this crazy fabric is for, right? I used it to make a "Probability Pouch" ...aka...something to hold my probability game tokens**. (I used to use paper bags, but by the time the experiment was over, kids would inadvertently learn what was in the bag...as the pieces started falling out the holes!) Want to make your own? Here's how...

 Find a really ugly piece of fabric that you cannot see through. If it has dice and playing cards on it, all the better. :) Cut a piece of fabric approximately 12" (width) by 10" (length). This isn't an exact science, so approximates are fine!

Turn over the top 1/4", twice, and stitch to finish the top edge. The left photo shows the back side (wrong side) of the fabric with the top edge finished.

About 2" from the top edge, you will stitch a piece of 1/4" elastic. If you've worked with elastic before, this is easy. If not, there's always time to learn...and this is a great learning project.

I anchor the elastic on the left seam, looking at the wrong side of the fabric. I backstitch several time to anchor. Then I turn the stitch to a slight zigzag and pull the elastic as tight as I can get it while the fabric itself remains smooth and flat. As you sew, the elastic starts to gather the material.

 When the elastic has been sewn all the way across the material, you have a piece of fabric that looks like the one at left.

 Turn the fabric so that the right sides are together, raw edges at right. Stitch the raw edge down the right side and across the bottom.

When you're done, it will look like the photo at left. If you want to make sure the fabric doesn't unravel, use a pinking shears to cut along the raw edge, being careful not to cut into your seam.
















You now have a "Probability Pouch" or cute little bag in which to put your probability game tokens. **Soon I'll show you how to put the bag to good use! ;) You can enter to win one, too!

Fabric...Freaky or Fabulous??? (While on a Whoopie Pie High...)

Amazed, aren't you? Jealous, perhaps? Don't you wish you had a bolt of this fabric to make into a gorgeous new skirt? Perhaps a shawl for poker night?

Hmmm?

Or are you just flabbergasted that anyone was dumb enough to spend money on it?

I picked up 2 yards. 2 bucks. Later this week, I'll show you what I made. For math. (You'll be able to make one, too!)

(You might be even more amused to learn that I purchased this disgusting, amazing, lurid fabric at a Mennonite Auction for world relief. I think I was the only Mennonite who picked it up. I figured if anyone asked, I could tell them the sugar from the Whoopie Pies was getting to me.)

Square Numbers

I LOVE this lesson at Childplay about square numbers. What fun! It's on my to-do list. When we do the lesson, I'll add the book, Sea Squares, in which "Rhyming text and illustrations of such sea animals as whales, gulls, clown fish, and seals provide opportunities to practice counting and squaring numbers from one to ten." (from book summary)

What lessons have you done with square numbers? Post your link! ;)

Schoolroom Organization

You'll recall that I asked for advice on schoolroom furniture/organization. We emptied the room to install hardwood floor and I've been very reluctant to bring back the huge mishmash of storage (bookshelves of all shapes and sizes, crates, bins, etc) that we've used in the past. This weekend, my sis-in-law was visiting and had a wonderful idea. She suggested we empty the coat closet adjacent to the room, move the coat storage to the garage, and use the closet for school supplies...particularly the jumble of stuff that's really an eyesore.

We saved shelving from a past remodel, so this is our no-cost result:

It's such a relief to finally have all that stuff nearby and in ONE location!

Feel free to post comments linking to photos of your schoolroom! I'd love to "visit."

New Class: Two and Three Dimensional Geometry

Class: Two and Three Dimensional Geometry

Age/Grade: appropriate for grades 3-6, ages 8-11(approximately).

Course Description: Students will "develop more precise ways to describe, classify, and make generalizations about 2- and 3-dimensional shapes. They'll identify properties of shapes and then link those properties to specialized geometric vocabulary like angles, sides, faces, edges, and so on. They will construct and sketch shapes, compare and discuss their attributes, classify them, and develop definitions for these new ideas.

Students will communicate their geometric conjectures and arguments in the context of problem solving. They'll fold and cut a square piece of paper to make a set of tangrams and then use spatial reasoning to investigate the relationships among the tangram shapes, using combinations of pieces to create familiar polygons.

[As time allows] students will use also use geoboards, geoblocks, and polygons formed with toothpicks to build understanding of congruence, similarity, and symmetry." (The curriculum and course description are taken from Bridges in Mathematics.)

Here are class examples from last year. (This is not the same content as the geometry class I taught last year.)

When:
5 sessions, 2 hrs. each
October 18, 25, November 1, 8, 15
10am - noon
Oregon's Willamette Valley area

If you have interest in participating, please drop me an email for more information. :)
love 2 teach 2 day @ gmail dot com

Minimalist Math Musings...

During our lessons on base 5, we talked quite a bit about "minimal collection." Apparently, the concept has stuck...

Yesterday, my 8yo ds walks up to me and says, "In Sleeping Queens, the minimal collection to get 50 is two 15s and one 20."

In the game you have to get 50 points and can get it by collecting various groups of cards. And, yes indeedy, the least number of cards you need to get 50 points is by the set of cards he mentioned. :)

I'm amused. Not minimally. ;)

Frigits Marble Roll (Gift Idea #3)

We bought the Frigits Deluxe marble roll last Christmas. It's been a hit at our house with ages 3* and up...way up. (*This assumes the 3yo does NOT put things in his/her mouth. That would NOT be true of the child I caught in my son's preschool class this morning. I asked him what the lump was in his mouth and he guiltily spit out a marble. True story.)

I bought the marble roll thinking it would be a good exploratory learning tool prior to beginning our math lessons on "measurement with marbles." While it was great for that, it's also been used by numerous visitors (ages 3-adult), my teens, and...heheh...yes, even myself!

The set is magnetized and designed to stick to a refrigerator. My biggest worry prior to purchase was that the magnets wouldn't be strong enough to really stick well on the fridge. It's been a non-issue...the magnets are VERY strong and no part has ever fallen off. Some parts are more "little kid" (preschool) user friendly than others; to use the entire kit really takes some thought or cause/effect construction skills. My 8yo can use all the parts effectively but it takes some effort...effort he is willing to put in because the result is quite fun. We did not buy the Frigits Extension - Launcher or the Frigits Extension - Corners, but my son says "we should buy a bigger fridge so we can get them."

In order to keep the play interesting, I get this out for up to a month at a time and then take it down for a while. It continues to be a sought-after toy!

See more math "Gift and Game" ideas here.

Disclaimer: I bought my own set. Love it. Make nothing from my review unless you purchase one through Amazon, in which case a few cents commissions (at no cost to you) goes to Grace and Hope to provide foster care in China (see link in banner at top).

P.S. This would make a great math/science workbox activity! :)