Thursday, April 15, 2010

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.


  1. Great post. I ordered Mummy Math for our Geometry 'class'. Thank you for your inspiration.

  2. Hi I'm new to your blog-found you via Living Maths (new there too!) We're a South African family with 2 young children (3b & 5g). I haven't followed any curriculum yet-haven't felt a need yet-but I'm starting to feel a little edgy about maths. I was a grade 1 teacher before becoming a mommy, but school maths is so different to home maths.(I'm really not sure if it's necessary anymore to do all those "readiness" activities-if the kid understands-why take them back?) I want our learning to be fun and natural-got any ideas on your blog for 5 year olds? I'm not one to "do" maths just for the sake of having done it. I want it to be REAL! So difficult to put into words how I feel..... hope you get the idea! Thanks Nikki

  3. Thanks to you both for commenting!

    Nikki, when my kids were 5, I didn't do much except have fun. ;) I think at 5, the most important thing you can do is read to them (a lot!) and play! At 5, my kids lived in an educationally-rich environment, but we didn't do much of anything formal. My youngest, 4, now "plays" with math manipulatives as his brother does "homework" but it's really just play...learning through play! You can do things like sort buttons (lots of different ways), talk about measurements and numbers, and ask questions about the world around you. But it can all be done so informally, so naturally. If it makes you feel any better, my son was in public school kindergarten last year (at age 6) and they rarely even had time for "math." At least for my kids, a lot of the readiness activities came as a natural part of living. And, if they don't, there is always time to do those activities when they are a bit older. I say read, play, and enjoy the outdoors as much as possible! :) Based on what you've said, I have little doubt that you are giving them a rich learning environment! Enjoy!

  4. What a great blog! Thanks so much for sharing your hands on ideas. I'm looking forward to learning from you.

  5. My 9 year old likes geoboards but the rest didn't. For some strange reason they liked 1/2 inch block graph paper instead. We would take turns building areas on the graph paper and the other person would figure out the area. It is a game that they sometimes play themselves just for fun...they think they are just playing a game, but we know better, right? (wink)


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