Sand Dollars
We held it in our hands and felt the tiny hairs on the underside of it's body tickle our skin ans the animal tried to get away from us and wiggle it's way back down into the sand. We turned it over and watched it's mouth moving in the center of it's flat body.We set it down in the sand and watched it filter sand and water through it's body and out the five holes that radiate out from the center.
Then we started to feel just under the surface of the sand as the tide washes the waves back and forth and began to find more sand dollars. At first we found one or two. Then we found them by the tens. We soon realized that there were hundreds, thousands and possibly millions of sand dollars right there on that beach.
Talk about a teaching moment!
We spent the rest of the day observing, drawing, measuring and counting sand dollars. This lens is about the math that can be learned at the beach while observing sand dollarsl
Sand Dollar Table of Contents
- Finding Math at the Beach
- Math Day with the Sand Dollars
- The 5's of the Sand Dollar
- Counting Sand Dollars
- How Old is your Sand Dollar?
- Anatomy of Sand Dollars
- Sand Dollar Symmetry
- Symmetry in Sand Dollars
- Sand Dollar Worksheets
- Sand Dollar Number Line
- Watching the movements of a Sand Dollar
- Sand Dollars found at the Beach
- Sand Dollar Habitat
- How to Preserve and Harden a Sand Dollar
- Sand Dollar Cookies
- Dividing the Sand Dollar Cookies
- Cookie Recipe for Sand Dollar Cookies
- Playdough Sand Dollars
- Look Who's Twittering about Sand Dollars
- Sand Dollar Beach Day Discussion
- About the Author of this Sand Dollar Math Lens:
Finding Math at the Beach
Photo Credit: Creeping Sand Dollar
on Flickr, Creative Commons.
Many people think that math can only be found in textbooks, that learning only takes place in a classroom and that math is a boring but necessary evil.
The day we found the sand dollars was filled with fun and exciting activities that helped us describe our observations of the sand dollars while working on basic math skills. We spent the day observing, drawing, measuring and counting sand dollars.
Since then I have added many more activities to this unit study and found that children love to learn math when it involves the chance to learn in an exciting environment such as the beach and about a live animal living in that environment that they may never have seen before, such as the sand dollar.
This lens is about the math that can be learned at the beach while observing sand dollarsl
Math Day with the Sand Dollars
What do you need for your day at the Beach?
A Day at the Beach
Art Print
Kieffer, Christa
Buy at AllPosters.com
Be sure to take along plenty of sunscreen and water to drink. An underwater clipboard certainly comes in handy. A waterproof digital camera would be ideal. I also bring along a guidebook to the seashore that I keep in a Ziploc bag.
You also might like a stop watch to see how fast the sand dollars can bury themselves back under the sand, a compass to see if they always go into the sand in the same direction and a tape measure to measure the diameter of the sand dollars.
I keep these things in a bag in the back of my car so that we are always prepared for unexpected math adventures at the beach.
Underwater Write & Wipe Fun Tablet (Write & Wipe Fun Tablets)
Amazon Price: $5.99 (as of 11/12/2009) 
INTOVA INWD-IC600 6.0 Megapixel Digital Camera with Waterproof Housing -180FT
Amazon Price: (as of 11/12/2009)
Fisherbrand Traceable Waterproof/Shockproof Stopwatches; 2 1/8L x 2 3/8W x 1/2 in.H
Amazon Price: $17.36 (as of 11/12/2009)
Dritz(R) Lifetime Tape Measure - 5/8''x60'' White
Amazon Price: $2.29 (as of 11/12/2009)
A Field Guide to the Atlantic Seashore: From the Bay of Fundy to Cape Hatteras (Peterson Field Guide Series)
Amazon Price: $14.28 (as of 11/12/2009)
The 5's of the Sand Dollar
The sand Dollar is shaped like a Pentegon
A sand dollar is shaped like a pentagon with five sides. It has five holes that let water pass through. You can look through the five hole of the test or shell that washes up on the beach after the animal has died.
Pick up a sand dollar and observe it closely. Can you see other patterns or parts of the body arranged in fives?
- Cool Facts about Sand Dollars
- The sand dollar's mouth has a jaw with five teethlike sections to grind up tiny plants and animals. Sometimes a sand dollar chews" its food for fifteen minutes before swallowing. It can take two days for the food to digest.
-Monterrey Bay Aquarium
Counting Sand Dollars
How many sand dollars did you find?
Sand Dollars
As you walk along the beach you will find many beautiful shells, pieces of seaweed and sand dollar tests, "sand dollar shells". It can be fun to collect them and then use them in counting games.
For very young children that might mean just count to 3 or 5. For older children you might arrange them into groups of 10 and then count by tens to see how many you have collected.
You probably won't find 100's of sand dollars but if you find say, five sand dollar tests, each with five holes you can multiply to see how many holes there are all together.
What if you wanted to pretend to feed a pile of 20 small shells to the sand dollars. How could you divide those shells evenly amongst the sand dollars?
How Old is your Sand Dollar?
Calculating the Age of a Sand Dollar
Look for the hard white sand dollars along the tideline amongst the seaweed and shells. These are the exoskeletons or the dead remains of sand dollars. Look for growth rings along the edges of these plates.
Separate your sand dollar tests (the dead "shell" of the sand dollar) by age. What is the average at which your sand dollars died?
You can use your underwater tablet to make a graph representing the average lifespan of the sand dollars you found on the beach.
- Sand Dollar Printout
- You can often find the dead "shell" of a sand dollar (called a "test") washed up on sandy beaches. If you break open a test, there are many hard, loose, white pieces; these were the teeth of the Sand Dollar.
- Enchanted Learning Software - Intertidal invertebrates of California
- Scientists can age a sand dollar by counting the growth rings on the plates of the exoskeleton. Sand dollars usually live six to 10 years.
- Google Book Search
Anatomy of Sand Dollars
Background Information on Sand Dollars
Sand dollars (order Clypeasteroida) are flat, round marine animals related to sea urchins, sea stars, and other echinoderms. The most common sand dollar, Echinarachnius parma, is widespread in circumpolar ocean waters of the Northern Hemisphere, from the intertidal zone to considerable depths.
A sand dollar has a rigid skeleton known as a test. When sand dollars are living, they have a skin of motile spines covering the test. Movement is accomplished by the coordinated action of the spines. Like sea urchins, sand dollars have five paired rows of pores. In sand dollars they are arranged in a petal-like pattern. These pores are perforations in the endoskeleton through which the podia, used in gas exchange, project from the body.
Sand Dollar Symmetry
Symmetry at the Beach
- Sand Dollar Symmetry
- Like other echinoderms, sand dollars have fivefold radial symmetry (pentamerism). Unlike sea urchins, the sand dollar has secondary bilateral symmetry, with a front and back as well as a top and bottom. The anus is toward the rear rather than on the top.
Pentamerism
This variant of radial symmetry (also called pentaradial and pentagonal symmetry) arranges roughly equal parts around a central axis at orientations of 72° apart. - Poem of Dand Dollar Symmetry
- Such Touchstones
His stoop borrows the memory of a child
hunkered over jewels on the tide line,
as if he's been lifting seaweed from mother of pearl,
discovering sand dollar symmetry,
or poking the bubblegum globe
of a Portuguese man-o-war,
watching its varicose tendrils firing their last
electric volleys in receding waves.
Switched on by his finds, how he would beguile.
But though the lucid days are few
and in between the seven ages blur,
such touchstones, if infrequent, still occur.
He points to a sandpiper and to a secret cue
digs me in the ribs, goes shy, and smiles.
Paul Maddern
Symmetry in Sand Dollars
Understanding Symmetry and how it applies to Sand Dollars
Studies in Symmetry VI
Art Print
Knorr, George...
Buy at AllPosters.com
These books will help you and the kids understand symmetry at various different levels . Often as a homeschooling family there are children of various different ages but it is ideal to be studying the same subject.
For school teachers I suggest these books as a way to help children of various different academic levels to understand the concepts of symmetry and apply them to your discoveries of Sand Dollars.
Let's Fly a Kite (MathStart 2)
Grade 1-3. Bob and Hannah argue lean about cooperation and symmetry at the beach finding a solution to each problem using the concept of symmetry.
Amazon Price: $5.99 (as of 11/12/2009)
Symmetry: A Journey into the Patterns of Nature
Symmetry is all around us. Our eyes and minds are drawn to symmetrical objects, from the pyramid to the pentagon.
Of fundamental significance to the way we interpret the world, this unique, pervasive phenomenon indicates a dynamic relationship between objects. In chemistry and physics, the concept of symmetry explains the structure of crystals or the theory of fundamental particles; in evolutionary biology, the natural world exploits symmetry in the fight for survival; and symmetry-and the breaking of it-is central to ideas in art, architecture, and music.
Amazon Price: $19.72 (as of 11/12/2009)
Kaleidoscopes, Hubcaps, & Mirrors: Symmetry & Transformations, Geometry (Connected Mathematics Series)
Activities and hands-on projects to understand the concepts of symmetry and transformations.
Can be used at many levels of understanding Pre-K to adult.
Amazon Price: (as of 11/12/2009)
Sand Dollar Worksheets
Sand Dollar Worksheets
For the older children, challenge them to make more Sand Dollar Twins.
Sand Dollar Number Line
Counting by 5's with Sand Dollars
When you get back home you can start a number line using sand dollar mini accents for the multiples of 5. We used blank squares for the numbers 1-4, a sand dollar paper for 5 and then again blank squares for 6-9.
We also used the sand dollar mini accents for writing the numbers 1-5 next to each of the holes in the sand dollar and then writing a large 5 in the middle. One of my children really enjoyed this activity and continued on up to 100.
Later on we used these to remember the numbers that come right before the multiples of 5 when subtracting. We played a game like a spelling bee and used the cards when asking questions like what number is 3 less than 10.
CLASSIC ACCENTS SAND DOLLAR MINI
Amazon Price: $2.43 (as of 11/12/2009)
Watching the movements of a Sand Dollar
Measuring the Speed of a Sand Dollar
Using a tape measure and a stop watch you can determine the speed of a sand dollar. How many inches per minute can a sand dollar travel? How long would it take the sand dollar to travel a yard or a meter? a mile?
Does the sand dollar always head toward it's shadow? What happens if you block the sun? Can blocking the sun confuse the sand dollar's sense of direction? If you measure the length of the sand dollar's shadow and it's height can you determine the angle of the sun?
curated content from YouTube
"A beach in Costa Rica is the perfect classroom for homeschooling."
Sand Dollars found at the Beach
Finding Sand Dollars on the Beach
Sand Dollars, Parker River Nwr, USA
Verderber, Gustav
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Sand dollars can be found on the beach just under the sand at low tide in the tidal zone. Run your hands through the water saturated sand to feel for them. The are not harmful and do not bite. When you hold them in your hands they tickle as their hairs quickly move trying to get back down under the sand.
Sand dollars need to stay moist so don't keep them out of the water very long.
Photo Credit: Math at the Beach
on Flickr, Creative Commons.
Look for the tests of sand dollars that wash up with the seaweed at the tide line. These are the white remains of dead sand dollars that some call the shells. Compare the tests with the live sand dollars. Try to find ones of similar size and compare them. How much space does the live sand dollar take up in comparison to it's test?
Sand Dollar Habitat
Where can you find Sand Dollars
These sand dollar pictures have a Creative Commons License.
These sand dollars are at the bottom of the ocean about 30 feet below the surface in a spot where the water is calm.
30 feet is much deeper than the height of a human. How deep is that? Take your tape measure and measure thirty feet in the sand. Now have your dad lie down at the starting point of where you measured. Is he 30 feet tall? Now add another member of your family with their feet touching your dad's head. How many family members will it take to measure 30 feet.
An exercise like this will help everyone to understand just how deep the sand dollars are.
- Sand Dollars Alive
- What are sand dollars? Children who find them buried in beach sand often think that they may be mermaids' money washed up from the ocean.
Sand dollars live on top of or just beneath the sandy surface or muddy areas of the sea floor at thirty to forty-foot depths.
Sand dollars are abundant on the sandy bottom of deeper waters around the world
Sand dollars sometimes congregate in groups of thousands. In quiet waters they are tilted up on their edge waiting for floating food items. In rough waters they lay flat or burrow in. To fight fast-moving currents, the adults grow heavier skeletons while the young sand dollars swallow heavy grains of sand to weight themselves down.
Read more: Sand Dollars Alive - Habitat, Predators: Mermaids' Money and Doves are Nicknames for Sand Dollars - http://marine-life.suite101.com/article.cfm/sand_dollars#ixzz0CEvSp0VA
How to Preserve and Harden a Sand Dollar
- Cape Cod Sand Dollar, currency of the sea!
- In order to achieve a white and clean looking specimen it is important to soak your sand dollar in fresh water first. Follow the steps below to preserve your live sand dollar.
1. As soon as possible after discovering your sand dollar soak it in fresh water. The water will discolor and begin to give off a foul oder so change it frequently until it stays fairly clear.
2. Soak your sand dollar in a solution of bleach and fresh water for 5-10 minutes
3. Remove from solution, rinse in freshwater and let dry.
4. Repeat steps 2 and 3 if needed, but remember each soaking in bleach weakens the sand dollar. Time in the sun will also whiten your sand dollar.
To harden sand dollars, mix together equal parts white glue and water and apply to both sides using a sponge brush.
Sand Dollar Cookies
Sand Dollar Fractions
Once the cookies come out of the oven it's time to divide them equally between.
If there is no time to make the cookies you can't do better than to order some from Plum Island Cookie Company. Figure out the cost including tax, handling and shipping. How much would that be if you order two boxes?
How many cookies will there be for each person in your family if you divide them equally? How about if you invite your grandparents?
- Etsy :: Dmari :: Plum Island Cookie Company Sand Dollar Cookies
Plum Island Cookie Company is a small specialty bakery offering delicious Gourmet French Butter cookies hand-designed into exquisite Sand Dollars and other buttery sweets! The delicate vanilla-scented butter cookies come boxed with fou...- Cape Cod Sand Dollar, currency of the sea!
- Sand Dollar Cookie Ingredients:
* 3/4 C butter
* 1 cup sugar
* 2 eggs
* 1/2 Teas. vanilla
* 2 1/2 C flour
* 1 Teas. baking powder
* 1 Teas. salt
Procedure:
1. Mix the butter, sugar, eggs, and vanilla thoroughly.
2. Add flour, baking powder and salt.
3. Mix and chill the dough for one hour.
4. Roll out the dough on a floured surface to 1/8"-1/4" thick.
5. Cut out cookies using a 3" cutter or water glass.
6. Place cookies on ungreased cookie sheet.
7. Draw a star in the center of each cookie with a dull knife.
8. Bake at 400 degrees for 7 mins.
Dividing the Sand Dollar Cookies
Sand Dollar Division
Bringing Math Home: A Parent's Guide to Elementary School Math: Games, Activities, Projects
Includes a recipe for sugar cookies and relates it to fractions.
Amazon Price: $15.56 (as of 11/12/2009)
The Science Chef: 100 Fun Food Experiments and Recipes for Kids
Includes recipes for 4 different kinds of cookies using different kinds of sugar.
Amazon Price: $10.10 (as of 11/12/2009)
Cookie Recipe for Sand Dollar Cookies
Cookies and Math
-
Lumberjack Cookies
-
One summer I had the privilege of living with my Grandmother, an incredible cook, who taught me how to bake Lumberjack Cookies. She was famous for her skills at baking and often won the Vermont State Grange baking contest. This is the recipe that she...
Playdough Sand Dollars
Make your own Sand Dollars
Mix up some Playdough and add some sand. Make your own playdough sand dollars. Use the test of real sand dollars to press the details of the sand dollars into the ones you are making.
Once you have a pile of Sand Dollars you can use them as math manipulatives, adding and subtracting them from a beach in the sensory table.
How else could you use your playdough Sand Dollars?
Home Made Playdough
1 cup flour
1 cup of water
1/2 cup of salt
2 tablespoons Cream of Tarter
1 tablespoon of Oil
Cook this ingredients until it forms an item in the pan. Pour it out onto a Tupperware lid. Cover with damp cloth. Add food coloring if you like. Store new playdough in the fridge in an airtight container. This is non-eatable playdough.
Sand Play Dough
1/2 cup sand
1/2 cup cornstarch
1/2 cup boiling water
Mix ingredients together and knead.
Look Who's Twittering about Sand Dollars
-
- imakilu
- pooped after a long day: sand dollars, geodudes, dinosaurs, mini-golf, go-carts, and $8 hot dogs :D
-
- RJFlamingo
- RT @ednascafe: http://twitpic.com/p47dx Making the beachy stuff with fondant's been kinda fun! <-- Nicely done! Love the sand dollars!
-
- scrappyauctions
- http://bit.ly/1H5k5f MINI SAND DOLLARS - More at www.scrappyauctions.com
-
- racheljane80
- just finished assembling a brown silk boxed invitation with silver sand dollars
-
- fkobuszewski
- Did you know the beaches of Nevis (St Kitts sis island) are full of Sand Dollars? When they are furry on each side, they r alive!
Sand Dollar Beach Day Discussion
What math have you learned at the beach?
Children on the Beach
Cassatt, Mary
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Beaddoodler wrote...
What a great, indepth article on sand dollars. You are a fantastic teacher-and I'm not a child. Well maybe I'm in my second childhood.
Posted September 03, 2009
Frankster wrote...
Wonderful lens. I've always loved sand dollars but didn't know anything about them live. I have a collection of some. The smallest is only about 1 in across. It's pretty cool. Bear hugs, Frankie
Posted August 29, 2009
About the Author of this Sand Dollar Math Lens:
Find out what I'm up to when I'm not Measuring Sand Dollars
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Evelyn Saenz: Lensography of a Teacher
-
My passion is teaching and finding ways to teach children in fun, hands-on, creative ways. The unit studies I make on Squidoo reflect my view that learning should be integrated and no skills should be taught in isolation. I believe that each topic s...
