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! :)

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.

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!

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!