Showing posts with label Geometry. Show all posts
Showing posts with label Geometry. Show all posts

Tuesday, April 26, 2011

Magnet Board Math: Pattern Block Puzzles

I'm beginning to doubt my intelligence.

For years I have put pattern blocks in front of my kids only to have them slide all over the place on the block puzzle sheets. I had a DUH moment and finally gave them a magnet board (this could be a cookie sheet) to STICK the puzzle on while they used MAGNETIC pattern blocks to complete the puzzle.

My son explored symmetry in the process. One page asked him to complete patterns "so that the dotted line becomes a Line of Symmetry." You'll see (right) that he made a lovely pattern WITH symmetry, but didn't pay attention to the dotted line/line of symmetry. We had a good discussion about "line of symmetry" and used a ruler to help (below.) This was a nice extension to our symmetry lessons with Magic Mirrors that I'll show you later this week.



Note on materials: I own several different pattern block books: Pattern Block Problems for Primary People, Patternables and Magnetic Pattern Blocks. (That last one should have given me a clue!) I took all the pages out of the first two books, slipped each page into a plastic sleeve, and put them all into a 3-ring binder. This allows multiple children to use materials at once; I just pull out a page or two at a time.




Monday, February 14, 2011

I Spy Shapes in Art (Math + Art = Fun!)


I recently picked up a delightful book, I Spy Shapes in Art. Each left page says, "I spy with my little eye" and names a particular shape: a square, a circle, a rectangle, a triangle, etc. Toward the end of the book, shapes are 3-D: cylinder, cube, cone, etc. Each right page then shows a major work of art (think Matisse, O'Keeffe, Warhol, Escher, etc) in which the named shape can be found. Some are rather obvious, while others need a little searching. Interestingly enough, sometimes my 4yo found the shapes before my 8yo.

We used the book to begin an art/math lesson. As the boys located each shape, I asked my 8yo to identify properties of that particular shape. "Why is that a rectangle?" (sides are parallel, angles are 90 degrees, etc.) For my 8yo, this was review. For my 4yo, some of the concepts were new for the first time. He was delighted to tell me that a shape was a triangle because it "has three sides." My 8yo first said that the sides of a triangle had to be equal, then changed his response, as he remembered that sides could be of different lengths.

We then modified an activity from another helpful resource, Using Color in Your Art!: Choosing Colors for Impact and Pizzazz. The original activity (p. 17) calls for children to create primary color abstract paintings using tools. This is what we did instead:

1. The children collected 3-4 shapes from around the room that they could trace onto their paper. They traced lids to make circles, boxes for rectangles, and they drew their own triangles by connecting three dots with a ruler. My 4yo even found an oval shaped garmet tag to use. When they were finished, they'd successfully drawn 3-4 shapes on their papers; it was fine to overlap.

2. Next, they drew two lines across their paper, left to right. These lines could be anywhere, as long as they went left to right, off the paper.

3. They drew three lines from top to bottom of their paper. Again, anywhere as long as it reached top to bottom.

4. Now the tricky part...coloring. We talked about primary colors and I explained how it might be easiest to start with yellow since lighter-colored mistakes could be more easily covered. I also explained how they needed to avoid having the same color share a line; the same color can share a corner/angle/vertice, but not a line. My 8yo caught onto this easily and started with yellow on his picture, working from one corner to the next diagonal corner. Since I knew this wasn't developmentally appropriate for my 4yo (who still wanted to do it exactly like his brother!) I told him which places to color. He liked this method. After they finished with yellow, they used both red and blue, making sure that the same color never shared a line.

5. We took a coloring break and read Little Blue and Little Yellow, a book my son suggested when he noticed that sometimes green was being formed where blue and yellow touched.

6. When we finished, I posted the pictures on the wall so the boys could do their own "I Spy Shapes."

Note: The top left picture is mine, done the night before with tempera paint. I wanted to see how difficult it was to paint. After trying it, I had my boys use crayons. It was nice to have my sample, however, because we did "I Spy Shapes" with my pictures before the boys got started on their own. My 4yo's picture is on the bottom left, my 8yo's on the right.

P.S. Almost Unschoolers wrote about another experience with art/math last week, also using the book I Spy Shapes in Art. I'd planned my lesson before seeing her blog entry, so it might be interesting for you to see two different approaches using the same book.

P.P.S. Here is an on-line preschool activity for finding shapes in pictures:

Storyplace Shapes Online Activity

Link up or see other ideas at A Mommy's Adventures.

Friday, December 31, 2010

Children's Math Book Review: Hamster Champs

Before I *finally* return this book to the shelf, I want to mention it. During our recent geometry classes, I read Hamster Champs to the class after spending some time talking about degrees and doing a little exploration* with angles and protractors. In the story, three hamsters attempt a daring series of stunts, measuring degrees on a car ramp that sends them flying through the air. The cat promises not to chase them as long as he doesn't get bored. They taunt him with larger and larger angles until they eventually reach 180 degrees and speed away from him.

My geometry class, ages 8-11, loved the book...for two primary reasons, I think. First, they loved the taunting exchanges between the hamsters and the cat. Second, after having talked about angles in class, they understood some basics and could apply their knowledge to another "real" situation.

*Hmmm. I can't find notes about this on my blog. Hate it when I forget to write something from a lesson. I had the kids hold up two popsicle sticks and make acute, obtuse, straight, and right angles. We also looked at the vocabulary in Sir Cumference and the Great Knight of Angleland... the "'cute" steeply angled rooftops (acute angles) and the Mountains of Obtuse (obtuse angles.)

Workbox activity: after learning about acute, obtuse, straight, and right angles, have children form them with popsicle sticks and draw models in their math journals. Read the two books mentioned here.

Monday, December 27, 2010

Citibloc Fun

On the recommendation of friends, our two youngest boys received Citiblocs for Christmas. Looking around on Christmas morning, however, you would have had a hard time figuring out who actually owned the blocks. My 20 and 16 yo daughters were the first to take the plunge. Here are some of the many creations from the past couple days...





Wednesday, December 22, 2010

ThinkFun: Block by Block (Holiday Deal!)

I'm still watching for last-minute Christmas deals. Here's one that I just noticed...again, the cheapest I've ever seen it. My 8yo son got ThinkFun: Block by Block for his birthday. It's a 3-D puzzle with small groups of cubes stuck together in a variety of shapes. You receive a deck of cards with puzzles to make using the cube formations. It's a challenging activity to work on spatial relationships. My 8yo found it too difficult. We've set it aside for the time being, but I am looking forward to using it in a couple years when it will be a good next step up from geoblocks and some of the other geometric puzzles we own. With it's own little carrying bag for the pieces and the deck of card puzzles, it would make an excellent math workbox for older kids...say 10- or 12- and up...or younger kids who are spatially gifted. One Amazon reviewer noted that it's also a good activity to try to solve as a group.

P.S. I also just noticed that Zeus on the Loose is really cheap today. We play that game with my 8yo a lot...good for simple addition/subtraction practice.

Disclaimer: to date, I have no affiliation with anything listed on this page. If you order from Amazon, all commissions go toward foster care through Grace and Hope at no additional cost to you. THANK YOU!

Tuesday, December 7, 2010

More Snowflake Symmetry (3D paper!)

You'll recall that we did some snowflake symmetry earlier this fall. If you want to extend the lessons a bit, consider making a 3D paper snowflake. Does your snowflake have rotational symmetry? Line symmetry?

And before you leave the topic of snow, read Robert Frost's Stopping By Woods on a Snowy Evening. My older kids memorized this poem when they were little. Now I'm working on it with my younger two. The book itself is gorgeous and one that we pull out and read several times each winter.

Monday, November 22, 2010

Lego Symmetry

After studying line of symmetry and rotational symmetry I thought it'd be fun to do a little hands-on practice. With LEGOS!

Challenge:

1. Create a Lego masterpiece with line symmetry.
  • Basic level: build a Lego creation with at least one line of symmetry. When you're done, show the lines of symmetry.
  • Advanced: decide on how many lines of symmetry the creation will have. One? Two? More? Build a structure to those specifications.
Give kids a building plate and tell them to begin with a relatively flat structure...more picture-like than building-like.

[Teacher note: visit this site for more information on reflective symmetry.]

2. Create a Lego masterpiece with rotational symmetry.
  • Basic: build a Lego creation with rotational symmetry. You choose the order of rotation.
  • Advanced: decide on an order of rotation and build a project to match. 
[Teacher note: learn more about rotational symmetry and order of rotation. It's probably worth mentioning that while I don't remember being taught this in elementary school it's now a standard part of elementary math. I'm thrilled that my son will enter high school geometry at a higher level of understanding than I did! I knew squat.]
    See the video for our examples. I had my 8yo demonstrate the position of his lines of symmetry with yarn. As you'll see, it's difficult to keep the yarn straight to perfectly identify the lines, but it works. It'd be best to use some sort of frame to make it easier for kids to see the order of rotation. I'll work on that for my next rendition. ;)

    I didn't see this idea anywhere else and can't find it on the internet. Perhaps an original idea strikes once a decade. If so, I'm happy to share mine with you!!



    Please visit our other lessons on symmetry. Also, check out these art lessons using symmetry.

    And take a little peek at this "Symmetry Song." Love the way she filmed it in a mirror!




    Doing workboxes? Pop a handful of Legos in the box and challenge your kiddos!

    Thursday, November 11, 2010

    More Polygon Play! (Geometry Class #4, Fall 2010)

    Time for some more polygon play...wanna play along?

    I made a pdf (print it, free!) to review the terms for the number of sides of various polygons.

    1. Print the sheet on white cardstock, one per person.


    2. Have each child take a red crayon or colored pencil. As you say (or draw) the number of sides, they lightly color the rectangle with that term. Example: "Color in the word that means a 4 sided polygon." [Color in "quadrilateral."] After you've gotten through the first 8 terms on the sheet...
    3. Now do the same thing in reverse. Have each child take a blue crayon or colored pencil. As you say one of the terms from the top of the page (already colored in red), they color in the card with that number of sides using blue. Example: "Color in the number of sides on an octagon." [Color in "8 sides."] Now everything should be colored in except the last two terms.

    4. Do students know what "regular" vs. "irregular" polygons are? Review. If they don't, look here. Color the regular/irregular cards green.

    5. Cut out cards.

    6. Mix up cards. Match corresponding red and blue cards.

    Greedy Triangle (Scholastic Bookshelf)As you read the book, The Greedy Triangle, ask students to lay out the red and blue cards that match the polygon on each page.

    Give children some popsicle sticks. Tell them to lay out the "triangle"  and "regular" cards. Ask them to make a polygon with those criteria. What do students notice about their polygons? Are they alike? Different?

     Ask them to lay out the "quadrilateral" and "irregular" cards. Make a polygon. Are their figures the same?

    Ask students to set aside all cards except the following: triangle, quadrilateral, pentagon, hexagon, regular and irregular. Each child should select one card of each color (red and green) and lay it out in front of him. (Use the blue cards as needed if kids need reinforcement to recall how many sides are on each polygon.)
    This is one awesome irregular pentagon. Dude!



    Now, have kids switch places and build a polygon based on the cards at his new spot. Rotate around the table, placing cards, building, and checking polygons.

    See our first Polygon Play session here
    Look, Ma! Another irregular pentagon!

    Captain, we are ready for irregular triangle takeoff!
    Whoa. Irregular quadrilaterals are too cool for words.
    P.S. The content in this post has been heavily influenced by Bridges lessons. Love them! :)

    Tuesday, November 9, 2010

    Review: Monkey Pod Tangrams


    Last week, I received a wooden tangram set from Monkey Pod Games. The tangram set and a set of puzzle cards come in a hinged, wooden box, approx. 8.5"x5"x1". My husband happened to be there when I opened the package. He took the game from me, ran his hand over the wooden box, opened and closed the lid, and exclaimed, "That's a NICE box." While this may mean nothing to you, I'm here to say that my husband is picky discerning. He likes good quality stuff. (Picked me, didn't he? :) For him to take the time to comment on the BOX means a lot.

    This is a really nice set!

    The box contains a set of wooden tangrams, cut 1/2" thick so as to make them easy to manipulate. The 50 puzzle cards feel really durable (perhaps they have a light plastic coating?) A silhouette of each shape--animal, people, or abstract--is shown on the front, with the puzzle answer revealed on the back.

    While it makes a durable set for homeschool (my 4yo and 8yo have been playing with it!), I wouldn't hesitate to leave it available on the coffee table for guests to play. Such a high quality set would also make a great gift for a wide variety of ages.

    Later today I'll be back to post a Giveaway for one of these beautiful sets!

    Disclaimer: I received a review set. I tend to avoid reviewing items that I don't like. I really like this one. I get no monetary compensation from the company. If you order from Amazon, all commissions go toward foster care through Grace and Hope at no additional cost to you. THANK YOU!


    Saturday, November 6, 2010

    Math App Saturday (#15 Sound Drop)

    Each Saturday, I link a free game to download on your iTouch/iPad/iPhone. I try to select games that provide fun practice with math skills and concepts. Soon after I started reviewing math apps, a reader suggested I try Sound Drop. It's really quite incredible and I'm surprised that it continues to be free.

    The app combines music with geometry, physics, friction, gravity and more. Balls drop and create sound as they strike against the lines you create. Sound varies depending on angle and velocity. On the one hand, it's quite simple; all you have to do is draw lines. But with practice you can turn the app into a sophisticated, modern instrument.

    This app is incredibly unique. Go grab the freebie and try it for yourself. It's fun!

    P.S. If you're doing Workboxes, this would be a fabulous 10-15 minutes activity.



    Tuesday, November 2, 2010

    Reflective & Rotational Symmetry & More (Geometry Class #3, Fall 2010)

    Another busy day with geometry! Here's what we did:

    *read "A Square Puzzle" from Mathemagic. (This book, published in 1978, as part of the Childcraft series, has many interesting stories, puzzles, and activities. You can often find it cheap!)

    *added to our "What Do You Know About Geometry?" flap books.

    *shared symmetrical masks from last week, reviewed our understanding of "line of symmetry," and wrote definitions in a flap book.

    *checked to see how many letters in our names are symmetrical.

    *continued with lessons from Bridges, using an index card to investigate both reflective and rotational symmetry. We then explored symmetry with a variety of pattern blocks. I put a magnetic pattern block on the magnetic board, traced it, rotated, and asked the kids to stop me each time the block fit into the frame. They became very good at identifying the order of rotation and the number of lines of symmetry!

    *read A Cloak for the Dreamer.

    *used more Bridges lessons, building regular and irregular pentagons with toothpicks. Students followed up by drawing the shapes they made; this wasn't easy. (You try trying a regular pentagon!) We also built and drew regular and irregular hexagons.

      *finished by building toothpick polygons. We'll use these next week.

      Another great day! Thanks so much for all your hard work! :) If you'd like to do some "homework," check out the links below.







      Great Resources for Further Study: