Geometry Class #3

The irony. To think that one of my most dreaded high school classes is now one of my favorite classes to teach. How things change. Especially how we teach math. Here's what we did today...

Each morning I welcome children by inviting them to select from a basket of "math" books. I like this opener as it makes for some relaxing conversation as we wait for children to arrive. I've found that books with short segments are ideal; kids can pick up a book and exclaim over some fact or be amazed at a few photographs without having to read an entire story in what might be a very short sitting. Several books my students are currently enjoying:

A Closer Look--This book shows an object at close proximity, gradually showing it at a greater and greater distance, allowing students to try to guess what they are seeing.

The Amazing Book of Shapes--all kinds of shapes and patterns are shown in full-color photographs with ideas for constructing.

Incredible Comparisons--The boys reach for this one every week! It compares biggest, smallest, fastest, slowest, etc. for countless things around the world. Jam-packed with facts.

When all students arrive, I like to open with a book. Today's selection, Mummy Math: An Adventure in Geometry.

We continued with several lessons taken from The Math Learning Center's Bridges in Mathematics. Many general ideas could be replicated at home.

Area with Pattern Blocks
We began with a lesson using pattern blocks. I told the children, "Just for this lesson, a triangle has an area of 1." I took out a blue rhombus. "If a triangle has an area of 1, what is the area of a rhombus?" [TWO!...they then "proved it" with pattern blocks.] "What about a trapezoid? A hexagon?" In each case, they had to prove their answer, sometimes proving themselves wrong in the process; but as we know, we often learn more from our mistakes than from our successes! Children then determined the area of several larger shapes on a handout. Some could immediately "see" the answer in their minds and then drew lines on the paper to prove it. Others needed to lay down pattern blocks and trace around them to determine area.

Home extension for students: If you have pattern block puzzle books and pattern blocks at home, you can continue the lesson this week by asking students to find the area of various puzzle block pictures. "If the area of a triangle is 1, what is the total area of the picture?" If you don't already own materials, you can find a pattern block template here and some pattern block puzzles here under "pattern block pictures." (Look for puzzles that use these shapes: triangle, rhombus, trapezoid, hexagon. The square and the parallelogram will have to wait for another activity.)

Area with Geoboards
We moved on to another "area" lesson from Bridges, "If the 4-Peg Square is Worth 1," which uses geoboards. Most of my students were unfamiliar with geoboards, so we first took time to explore the new manipulative.

Then I put a rubberband around 1, 4-peg square, and told them that just for today, this square has an area of 1. Next I put a rubberband around several squares and asked them to find the area. They used geoboards and  geoboard paper to help. We shared our findings with one another on the overhead (see photo for a later example.)

For our last group activity, we pulled out the geoblocks for a lesson from Hands-On Math: Geometry with Geoblocks, "How Can You Build It?" In this lesson, students try to figure out multiple ways to "build" a block using other combinations of blocks. I LOVE this lesson and have frequently used it with parent groups because it demonstrates the wide range of learning that can be done with one activity. Very simple combinations can be made: 2S=B or S+S=B. But it can get more and more complicated...  If S+S=B and B+B=R,  then how many S's make R? Students of ALL ages and ability levels can produce wonderful equations.

Students spent the last portion of class choosing from a list of "Work Place" games and activities. They worked hard, as always.

[Last part mentions God.] In the last few minutes we looked through an old book, Isador A. Inchworm's Magic Math Glasses, at  photographs of geometry in nature. Since all of the children in my group come from Christian families, we talked about how God is at work in geometry. In nature. They all left feeling the "fixed point" on top of their heads. ("...the place where your hair radiates, or starts, from." p. 22)

Thanks for a great morning! We missed you, K! See you all next week.

Teaching Math: A Video Library

Want to improve your teaching skills? If you're looking for on-line videos that demonstrate great math teaching in action, these are for you! In most cases, you can observe the lesson and then replicate it for your own kids. Really worthwhile stuff!

Teaching Math: A Video Library, K-4
From the site: "See how the National Council of Teachers of Mathematics standards are used in elementary classrooms across America. Elementary teachers tap the excitement and energy of children from kindergarten through grade 4 as they solve problems, learn to make connections between concepts, and communicate and reason mathematically. Teaching Math K-4 documents effective teaching and learning in many schools: small, large, rural, suburban, and inner-city." Support materials for lessons are found here.

Teaching Math: A Video Library, 5-8
From the site: "See real middle school teachers incorporating the National Council of Teachers of Mathematics standards into their lessons, while learning as much about teaching as their students do about math. The programs demonstrate how teachers guide and assess student understanding, and offer strategies for keeping students motivated and engaged at this critical age." Support materials for lessons here.

Teaching Math: A Video Library, 9-12
From the site: "See how high school teachers use the National Council of Teachers of Mathematics standards and group learning to reach a broad range of students. In this library, teachers demonstrate the fine art of guiding students through reasoning and problem solving. Students comment on the new way of learning, often expressing frustration as well as the sense of accomplishment they feel when working through problems with peers." Support materials here.

Organizing Children's Math Books

Warning: If you relate to this post there is a very good chance that you are:

A. A math nerd.
B. A children's bookaholic.
C. A homeschooler.
D. A teacher.
E. Broke.
F. Any assortment of A-E.

You know you need to organize your collection of children's math books when:

A. You've purchased three or more copies of the same title by accident.
B. You find the PERFECT book to go with a math unit...on the shelf...two months AFTER finishing the unit.
C. You either have to get rid of (or organize) books or you have to get rid of some kids.

As I've mentioned, I'm excitedly preparing to teach a class on children's literature and math. In preparation, I'm creating bibliographies, checking books out from the library, and buying, buying, buying. In the meantime, I'm teaching and trying to find the best book to go with each lesson. It's been a tad frustrating. It was either add onto the house or organize.

My husband went with "organize."

While I did have dedicated math shelves, I still couldn't easily find things. So, I took everything down and started categorizing... Here's the start...

Categorizing was a bit frustrating. A lot of books fit more than one mathematical strand...or they are in a class by themselves and fit none. But I managed to put them into categories that I thought I could sustain.

Then, I recycled some cardstock to make labeled dividers. So far, I'm happy. It's making it much easier to create the massive bibliography (which I will post soon.) :) Once the bibliography is complete, I will highlight the books that I own and carry a copy in my purse to make book hunting a bit easier.

Then, perhaps I'll be able to keep the kids. And the husband.

Assuming you are also a book nerd, I'd love to see your organization ideas! Post thoughts and links to blogs (hopefully with photos!) in the comments section.

Living Math

Homeschool Carnival of Blogs

I'm participating! Visit Our Curious Home to see what homeschool bloggers are doing this week.

Farmin', Farmin'...

Our little farm is growing. Today, little student bought horses to add to the farm, again investigating area with land squares and perimeter with fence squares. He also updated his farm map (as seen in the photo.) Just a few crops left to go...

Meanwhile, we're seeing some interesting creatures on our own "farm." Can you spot him?

Mythmatical Battles

To this day, when you ask my 13-year-old son how he knows what 7 x 8 is, he'll grin and say, "It's the attack power for The Red Dragon."

You know the card games that kids are really into...the ones that have an "attack power" and a "defense power?" Well, the smart folks at Mythmatical Battles came up with a card game that integrates this style of play with multiplication and mythology. (You can get a deck of Celtic/Greek or Norse/Egyptian cards.) At the ages of about 8 to 11, my son LOVED this game. From the Mythmatical Battles website: 

Each player uses his own Mythmatical Battles Deck, with 55 cards featuring gods, heroes, and monsters from Greek, Celtic, Norse, or Egyptian mythology. Every card has one multiplication equation for its attack strength and one equation for its defense strength. A single deck contains all the multiplication equations from 1x1 to 9x9.

The players take turns drawing cards from their decks, placing them face-up to the "Field" (known to grown-ups as the table, desk, or floor), and challenging their opponent's cards.  The card with the highest product wins.  But look out --Magic and Weapon cards can change card strengths, and weaker cards can team up to conquer a powerful card.

It's a small company. Nice folks. If you send them an email message, you get a personal reply from "the minions." They've also come out with a book, Walk Past the Wolf: A Mythmatical Battles Adventure, which I hope to review soon.

You can view information for educators by scrolling down the menu on the Mythmatical Battles website.

If your kids are into this type of card game, they're gonna love this!

P.S. Today I asked my son about this again (I had to edit which card was his actual favorite.) At almost 14, he said, "We need to play this game again. I own it, this game. Zeus is high, too. He's either 8 x 9 or 9 x 9. But I never personally liked Zeus." [He grins.] He continues, "You know what our favorite thing was? Any time we got you to say we didn't have to do math if we played this game." [Chuckles.]

Geometry Class #2

We flew through geometry this morning. Who knew that math could be so fun?!!! :) (We did!)

I started by reading aloud a book I don't particularly like. Why? I've been reading New Visions for Linking Mathematics and Literature in preparation for my summer teacher workshop. The authors give criteria for determining a book's mathematical integrity, the first being "the mathematical components of the book are accurate." They specifically mention appropriate use of mathematical vocabulary. In my read aloud, The Silly Story of Goldie Locks and the Three Squares, Goldie encounters a variety of shapes. The text reads,

"Goldie Locks tried the beds. One was shaped like a circle. Goldie Locks hated it. Another bed was shaped like a triangle. She hated that one, too. The last bed was shaped like a rectangle. It was just right and Goldie Locks fell asleep." 

Upon hearing this and seeing the illustrations, the kids hopped up and down on the rug.

"That's not a triangle! It's a triangular prism!"
"That's not a circle! It's a cylinder!!!!"
"And that's not a rectangle! It's a rectangular prism!!!"

Frankly, I think the whole class was slightly horrified. So, in retrospect, I take back what I said. I LOVE that book because it gives kids a chance to challenge the use of incorrect mathematical terms. :)


I introduced several new activities today. With "Caterpillar Fill and Add" (taken from Bridges Curriculum, Math Learning Center), they had to race to fill up caterpillar game boards using pattern blocks. They also tried to see how few pattern blocks could be used to make a variety of shapes in "Build 4 Less."

The remaining activity, a favorite, is taken from Hands-On Math: Geometry with Geoblocks Kit for homeschoolers. We've been working with geoblocks, 26 uniquely shaped wood blocks, each labeled with a letter of the alphabet. Today, kids were enchanted by "Faces of Mystery," in which they had to try to figure out which the "mystery block" was. I revealed one of the mystery block's faces at a time. They searched through the 26 blocks to see which blocks fit the first face. Upon seeing the mystery block's second face, they continued to narrow down their options. When only a block or two remained, they described what the third face would look like if was one of the remaining blocks. Students repeatedly brought blocks up to test against the set of face clues. They were thrilled to discover the mystery block's true identity! :)


During "Work Place" time, students made choices about which of the activities they wished to visit. They loved setting their own schedules!

I ended with a couple of additional read alouds. While I'm not personally excited about the story of Captain Invincible and the Space Shapes, I chose it so students  could listen for integrity in the mathematical vocabulary used, comparing it to the text in our earlier book. Surprisingly, they loved the book, also expressing approval at the author's use of terms. (Deserved. :) ) We ended with a favorite of mine, Sir Cumference and the First Round Table. Several kids grinned to learn that the terms "diameter, radius, and circumference," are named after book characters. I'll have to confess that I've never been confused about those terms since reading the book. Every time I hear "diameter" I picture "Lady Di of Ameter."

Class...See you all next week! Thanks for your hard work today!

Readers...Have stories about your students, children's literature, and math? Love to hear from you!

Lesson Pathways - Free, See it to Believe it!

Are you a homeschooler? A teacher? Have you seen Lesson Pathways? Wow.

You join the website for free. Upon joining, you have access to "pathways" in every subject (science, history, reading/phonics, language arts, math), grades K-5. Let's say you are looking for a curricular pathway for first grade history. You go to that pathway and then access 36 weeks worth of lesson plans and links. Tons of hands-on projects, links to readings, games, and videos... Here's a summary from the site:

    A Guided Journey is a 36 week learning plan in one of the core subject areas, for a specific year or grade level (ie. Year 1 Science).  A Guided Journey is made of individual Pathways. You may follow our recommended Guided Journeys or mix and match Pathways to create your own 36 week course.
    A Pathway is a single unit on a given topic. (ie. Animal Life Cycles)  Each Pathway contains content for one week of instruction, depending on how often you teach a given subject.  Each Pathway is made of multiple Stepping Stones.
    A Stepping Stone is a single resource.  This may be a lesson, video, worksheet, hands-on project, ebook, online game, or other activity.  (ie. Create a Spider Life Cycle Poster). Multiple Stepping Stones make up a Pathway.

They are doing this for free with the hopes that revenue will come from ad related links. I am very impressed with the navigation/layout and am amazed that this is all available for free. The site allows you to customize the pathways using a planner that's also free on the site. You can add multiple students with individual planners for each. Totally flexible. Lots of hands-on, "living" material. Seriously, check this out. You have to see it to believe it!

The Little Red Hen (on My Little Farm)

We're continuing to add animals to our farm. Today, with the addition of chickens, we're doing a side trip with the Little Red Hen.

In the last few decades, the children's book market has been inundated with "fractured" versions of traditional folktales and fairytales. When examined together, this provides an incredible opportunity for doing some comparison/contrast. We collected several versions of The Little Red Hen. Possibilities include:

The Little Red Hen Makes a Pizza
The Little Red Hen; A Tale About Cooperation
The Little Red Hen and the Ear of Wheat
The Little Red Hen and the Passover Matzah
The Little Red Hen

After reading the books, we talked about the similarities and differences. My student noticed a difference in the setting, characters, item being made/problem and the conclusion. We made a chart to directly compare the three books.

And I couldn't say "no" to a request to make a pizza together after reading The Little Red Hen Makes a Pizza. Who will help me make the pizza?  "I will!" say two little students.

After pizza lunch we printed a story map to plan out my student's own version of The Little Red Hen which he'll begin writing tomorrow.

Class Begins: Geometry, Not Just for Big Kids Anymore!

What was your high school geometry experience like? Mine was LOUSY. When I entered my first "geometry" class as a tenth grader, it was like someone plopped me on Mars with no oxygen mask. I didn't speak the language. I had absolutely no idea what a "proof" was or why anyone would ever use one. Up until that year, I don't think I'd ever been exposed to much geometry in math class, save perhaps a lesson on triangles in first grade.

Thankfully, things have changed. Thanks to a theory proposed by two Dutch high school math teachers, we now recognize that most students pass through a number of levels of learning in geometry. Five. Unfortunately, many high school students enter classes at a level of zero or one while high school geometry texts are usually geared toward a level three. Doesn't take much to figure out that math!

I entered my high school geometry class at a geometric thinking level of 0-1.

 +  High school texts are geared toward level 3. 

Equals...stress, anxiety and abject confusion!

But things truly have changed. Students today are learning those lower levels of geometric thinking long before they enter high school classrooms. My ninth grade daughter, currently taking geometry, was exposed to geometric terms and concepts regularly from kindergarten through her school career. And what a surprise...high school geometry is a breeze.

Which takes me to my new class..."Geometry: Not Just for Big Kids Anymore!" Today, I began working with children ages 7-10 to introduce geometry in fun, meaningful ways. Here's a little peek into our morning...

I asked the class, "What do you know about GEOMETRY?" While the entire class had heard of the term, very few had ideas to contribute. I compiled a short list from volunteers: shapes (squares, triangles, circles) and geoblocks (which some of the kids had used before and I'll explain shortly.) I told them that we're going to be thinking about geometry for several week and that I wanted to share a book with them that included some--but not near all--ideas about geometry. I read The Greedy Triangle by Marilyn Burns in which a triangle is changed into different polygons with increasing numbers of sides. Students enjoyed predicting what each subsequent shape would be called...triangle, quadrilateral, pentagon, hexagon, etc.

We then spent time exploring geoblocks. Quite a few of the lessons I'm using with my class come from Hands on Math: Geometry with Geoblocks by The Math Learning Center.

Product Description: Designed for use at home. Contains six exercises that provide many opportunities to introduce and use geometric terms using geoblocks. Adapted from Bridges in Mathematics, this kit comes with teaching instructions that encourage play, observation and geoblock manipulation. Includes 26 uniquely shaped wood geoblocks.

We talked about the properties they noticed and began using some terms: triangular prism, rectangular prism, cube, pyramid.

We explored the number of faces, edges, and corners on a variety of geoblocks. Students quickly noticed that all the triangular prisms had the same number of faces, edges, corners. Likewise, the cubes and the rectangular prisms had the same number. Interesting... :)

Students then got into groups to sort their blocks into as many different categories as they could...by shape, by size, by height and width, etc.

We then played a game, "Last Shape in Wins" to see who could be the last person to put a pattern block into our grid. To end our session, we discussed a variety of 3-dimensional shapes and read Tana Hoban's book, Cubes, Cones, Cylinders, & Spheres. Wow! Now THAT'S a lot of GEOMETRY for one day! :) Can't wait til next week!

Lessons with Mrs. Piggle Wiggle

I know I must have read it before now. I even saw a dramatic presentation a few years ago. But I can't remember ever enjoying Mrs. Piggle Wiggle like I did this time. My little student and I laughed and laughed, sometimes until tears rolled down my face. Perhaps it's because I "know" some of the children in the book?

Using a Graphic Organizer
In the book, parents seek help from Mrs. Piggle-Wiggle, a woman of immense knowledge when it comes to curing childhood problems. She is able to fix anything from selfishness to messiness to slow eating. Each chapter is dedicated to one child, his/her problem, and the cure to that problem. The book's structure makes it perfect for using a graphic organizer such as a chart.

We chose to set up the top/horizontal with some of the characteristics we wished to compare:

1. Who has a problem?
2. What is the problem?
3. How is the problem solved?
4. What is the result of fixing the problem?

On the left/vertical side, the student recorded chapter titles:
*Won't-Pick-Up-Toys Cure
*Answer Backer Cure
Etc...

[The photos do not show the complete chart.]

After reading and discussing each chapter, the student completed the chart. Sometimes this alerted me to elements of the story he hadn't completely comprehended and we could discuss it before he continued.

Vocabulary
The book is rich in vocabulary. If I had it to do again I would have started the vocabulary cards (mentioned here) during this book. We had a great time learning the word "impudent" and discussing ways we could use it in day-to-day life.

Problem Solving, Manipulatives
I plan to talk more about this in future posts, but I like to keep my eyes open for problem solving opportunities as we read. A great one presents itself in the chapter titled, "The Selfishness Cure."

Dick is a selfish boy. His mother asks him to divide a box of candy amongst his friends and reminds him not to forget to save some for the neighbor lady who loves candy. Dick proceeds to clout another child on the hand with a baseball bat when she tries to take some. Dicks mother then tells Mary O'Toole "to divide it up among all the children, even the little ones, and to take one or two sticks over to old Mrs. Burry because she [is] so fond of peppermint.

There [are] fifteen children, not counting Dick, and fifty sticks of candy so..."p. 53 (the book goes on to tell how much each child and Mrs. Burry receive...I stopped reading before the answer was revealed.)

After hearing the problem, my student used base 10 pieces to represent pieces of candy. (You could use any manipulative, although base 10 pieces allow students to use 10s and 1s if they would like.) He chose to use the remainder differently than the text. (Mrs. Burry was more fortunate in the story!)

If you find opportunities for problem solving within your reading, I'd love to hear about it!

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.

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?