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!

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.

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! :)

Milk Cap Math: Preschool Activities

I hate throwing things away. I'm less a hoarder than a I-don't-want-my-stuff-to-take-up-space-in-the-landfill kinda gal.

So, whenever possible, I try to recycle. Or, better yet, reuse.

We go through a lot of milk. A. LOT. My youngest came home from China drinking nothing but milk. LOVES milk. And with six people living here, we constantly buy milk.

I either recycle (on the good months that the local recycling center will take most plastics) or throw away 3-4 milk jug caps a week. Ever stop to look at a milk cap? They're actually sorta cool in a "I'm just a lowly milk cap" sorta way.

I decided to make use of 'em.

MILK CAP MATH!!!

I've come up with several games and activities. Here's the first few simple ones, designed for preschoolers.

Preparations:

1. Gather milk caps. Alternately, other caps would work great: juices, water, soda, etc. If they have writing on them, sometimes you can get that off with a little sandpaper. If not, stick to blank ones.
2. Have a variety of colors? Figure out a pattern. (Or, better yet, have the kids figure one out.) The pattern can be part of the math activities.
3. Lay out the caps in the pattern and number them. I first made one set of 1-12. I'm working on two sets for game playing. I put a line under 6 and 9 so as to distinguish between the two.

PreK-Grade 1 Activities:

Numbers/Patterning:

• Put the caps in numerical order.
• Do you see a pattern to the colors?

Sorting:

• Sort the caps by color. 
• Which color has the least caps?
• Which color has the most?
• How many more yellow are there than green? (various color combination questions)

Counting:

• Using tile or another manipulative, have the child place the correct number of tile below each number. If available, use the same color tile as cap.
• What do you notice about the lines of tile?

As soon as I save up a few more milk caps, I'll post another game for bigger kids. In the meantime, save caps. :)

P.S. I did NOT see this idea on any other blog. I thought I had an original idea. (A rare and exciting phenomena.) However, I thought I'd better do a search before I posted. Good thing. I discovered "nothing is new under the sun." Google search gave 120,000 results. Here are some ideas from folks who thought of this before I did:

Milk Cap Numbers and Animal Counting Worksheets--cool templates!

Milk Cap Letters--templates for words/letters

Bottle Caps Math Game--for middle schoolers

This would be a great Work Box activity!


Link up your math ideas at Joyful Learner! ;)

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:

• Video on line symmetry 
• Investigating Symmetry in our Alphabet 
• Which capital letters have line symmetry?
• Symmetry Artist

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! ;)

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

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! ;)

Place Value Structures, Class #4

Few things are more thrilling that seeing a child with an "ah ha" moment. Times that by several children and you've made my day!

Today was our last class on place value structures using material from Bridges. For the last three weeks we've been considering place value in base five, looking at units (1), strips (5), mats (25), and stripmats (125). Today I asked students to imagine what the pieces might look like if we were working in base four. They began by building the pieces with tile. They debated over whether the mat should have 16 pieces or 24 pieces. (I think that a few jumped from the logic that if base 5 had 25 pieces, then base 4 should have 24 pieces.) We looked at the base five chart we'd made. Students recalled that with base five, each place value was x5, so decided that with base four, each would be x4 with a total of 16 for a mat. No easy task.

They cut a unit, strip and mat from graph paper. I then asked them to cut out a strip mat. When they couldn't agree on the area, I asked them to build mats with tile. Ah-ha! Then they remembered how to follow the place value pattern and had no trouble building a stripmat of 64.

Since the base five building didn't come easy, I wondered how the next question (and one of my big goals for the whole class!) would go...  "Close your eyes. Picture base ten. What would a unit look like? A strip? A mat?" The quietest child in the class couldn't hold back..."100!" They all immediately told me that base ten would have a unit of 1, a strip of 10, and a mat of 100!!!  I gave them base ten pieces and asked them to create a strip mat. With shining eyes and wide grins they asked me for TEN MATS and told me that a strip mat would have 1000 units. They built a strip mat and then proceeded to tell me what the next piece would look like and that it would have 10,000 units. "And then 100,000 and then 1,000,000...!!!!!!!!!!!!!" They helped me to complete a venn diagram comparing base five and base ten.

We read Sir Cumference and All the King's Tens and talked about place value in base ten. I also read The 329th Friend and asked them to build 329 (and a few additional numbers) with the base ten pieces.

It isn't unusual for teachers to ask, "Why do we teach other bases to children?" It's elementary, my dear! When we teach other bases, we give children an opportunity to develop conceptual understanding of place value. That deep understanding transfers to work in "our base," base ten. The lightbulbs in my classroom were going off so fast today that the electric meter must have been smokin'! Base ten place value means something new and exciting.

It's elementary. :)

You've been a wonderful class! Can't wait to see you again!

100 Day Countdown to 2011 (#2, more math ideas!)

If you'd like to join us in our 100 Day Countdown to 2011, here are several fun activities designed for different ages:

1. We made 100 paper links and will take one down each day. Every 10th link is black. My 8yo stapled the links after I figured out he could do it independently with a mini stapler. I worked on the chain as well, asking my 4yo to hand me the correct color of paper, following the pattern. (Blue/orange/blue/orange until we'd get to the 10th link.) I used 12" construction paper and cut 1" strips. Had I been more thoughtful, I would have asked my 8yo to figure out how many pieces of each color paper we'd need to get enough links of each color.

As we constructed our paper chain, we counted by tens. After we had the paper piled on the floor, I asked the boys how long they thought our chain would be when we stretched it out. You can see it below, tacked across a wall...

2. Each boy has a hundreds chart. My 8yo is counting down from 100, my 4yo is counting up from one. Each day, they cross off one number.

3. We posted a hundreds pocket chart so we could add a penny each day, making conversions (to nickels, dimes, quarters, etc) as we go. I'm basically following Joyful Learner's suggestion.

4. My 8yo writes five number sentences each day for the day we're on. He can use any operations, making the sentences as long or as short as he likes as long as the total equals the day. So, for example, for day 100 (counting down), he wrote:

Share your "100 day" ideas in the comments below! ;)

Note: The student math journal page (as shown in #4) is from the Math Learning Center. Undoubtedly, some of these ideas are similar to things I've done with MLC materials, but I cannot give credit because I'm not sure where some of the ideas floating around in my head came from. Anyone else have that problem???

100 Day Countdown to 2011

The tradition of "100 Days of School" is a little difficult for us to pull off. We do school ALL. THE. TIME. Sure, we have days off--"it's a gorgeous day so we're playing outside" or "it's snowing so we're on vacation"--but when public school started here, we were already on week #9 of schoolish stuff. So it's hard to come up with "100 Days of School" to count. (I actually think the concept of "100 Days of School" could really confuse my youngest since our stop/start days are so vague.)

Instead, we are doing "100 Days to the New Year." Today, I begin by asking my ds:

1. How many days do you think it is until 2011? (estimate...I may have him show me on a number line how many days--how far--he thinks it is)
2. How could you figure out how many days until 2011?
3. Figure out how many days.

We'll be doing some activities with 100 over the coming months. It'd be great if others want to join us.* You can start by having your kiddos do the activities above. You can google "Countdown 2011" and find sites like this one that are counting down in days, hours, minutes, seconds.


*If you are doing "100 Days of School" it wouldn't be hard to join us since most 100 school days will come soon after the New Year.

P.S. I'm thinking about making the 2011 Children's Calendar a surprise gift for the 100th day! ;)

Who Sank the Boat?

Yesterday, my 4yo ds received a book at church; this was his reward for reading for 10 hours this summer. (Well, I actually did the reading. That could be a whole 'nother blog entry. Do you know how many hours my older son read on his own compared to how many hours I read to his younger brother? Shameful, I tell you! About 2.5:1 ratio!)

The book, Who Sank the Boat?, is one that I've wanted to buy.

Summary: The reader is invited to guess who causes the boat to sink when five animals of varying sizes decide to go for a row.

Spoiler Alert (as if you can't see this coming!): four huge animals (cow, donkey, sheep, pig) get in, but it's the final passenger, the mouse, that causes the boat to sink.

We did some math and science activities based on the story.

First, collect a variety of objects from around the house. Set out two objects at a time and ask child to predict which is heavier. For some comparisons, I use large, light objects (fluffy pillow) vs. small, heavy objects (rock). Place one object in each of the child's hands and ask him which one is heavier. If you have a balance scale, you can do a little informal work there as well.

We did some float/sink lessons. (pdfs available--I used the picture drawing one for the 4yo, the writing one for my 8yo) The site also links a BBC interactive video where kids get to predict whether various items will sink or float.

Although this lesson is primarily for my 4yo, my 8yo enjoyed participating in the sink/float scientific inquiry. Challenge question...find an object around the house that will trick mom...one that I think will float when it will actually sink or vice versa. (My son did it with Playmobile animals.)

Check out more Math Monday links at Joyful Learner or click on the Math Box below to find more math activities suitable for Workboxes.