Sand Dollars and Math on the Beach
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Sand Dollars
One day at the beach in Costa Rica my daughter and I were digging in the sand making sandcastles when we ran across a live sand dollar. Finding a dead exoskeleton would have been exciting but finding a live sand dollar was unbelievable!
We held it in our hands and felt the tiny hairs on the underside of it's body tickle our skin as 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 dollars.
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
Kieffer, Christa
Available 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.
The 5's of the Sand Dollar
The sand Dollar is shaped like a Pentegon
Photo Credit: Sand Dollars
on Flickr, Creative Commons.
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
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 Sand 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

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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.
Sand Dollar Worksheets
Sand Dollar Worksheets
For the older children, challenge them to make more Sand Dollar Twins.
- Sand Dollar Activity Page - Find The Twins

- What Are Echinoderms?
- In this science printable about invertebrates, students will evaluate true/false statements about echinoderms and use reference materials to identify drawings of a sea cucumber, a starfish, a sand dollar, and a sea urchin.
- Marine Biology Game
- I Am a Marine Invertebrate.
Here are the names of the animals found in this quiz.
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.
“A beach in Costa Rica is the perfect classroom for homeschooling.”
Sand Dollars found at the Beach
Finding Sand Dollars on the Beach

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Sand Dollars, Parker River Nwr, USA
Verderber, Gustav
Buy at AllPosters.com
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 by legrave1
View other Sand dollar Posters
- 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

La Mer IV
Alan Blaustein
Buy This at Allposters.com
Now that you are back from the beach it's time to whip up a batch of Sand Dollar Cookies. Use fractions to measure the ingredients. The more the merrier so use your knowledge to multiple fractions as you double or triple the recipe.
Once the cookies come out of the oven it's time to divide them equally.
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


Searching for Sand Dollars
Read the story of the children trying to divide the cookies evenly as more and more friends show up at the door in the story The Doorbell Rang. Then make some sand dollar cookies and practice some division and of course, subtraction.
Cookie Recipe for Sand Dollar Cookies
Cookies and Math
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.
Marine Biologists study sand dollars.
Would you like to become a Marine Biologist and study sand dollars?
Sand Dollar development
From Fertilization of the Sand Dollar Egg to Zygote
Sand Dollar Eggs
Fertilization of Sand Dollar Eggs
How to extract and observe the fertilization of sand dollar eggs through the use of a microscope.0 points
Sand dollars (Clypeasteroida) on the Shores of Singapore
Fact sheet with photos on flora and fauna of Singapore's intertidal shores...Sand dollars have separate genders and are usually either male or female. They practice external fertilisation, releasing eggs and sperm simultaneously into the water.0 points
Look Who's Twittering about Sand Dollars
-
- moanteith
- RT @bonniewrightt: youstina'a la la ugh is insured for ten though sand dollars
-
- LawrencelyJen
- sobbing what RT @bonniewrightt youstina'a la la ugh is insured for ten though sand dollars
-
- bonniewrightt
- youstina'a la la ugh is insured for ten though sand dollars
-
- MuthaFuckaJ0ne5
- @ade_lyy @JoCeCoolPerson I don't think a person that will eat sand for ten dollars can be mean... hahaha
-
- couponSeven
- Marriott: Caribbean & Latin America: FREE night + $50 resort credit sand dollars http://t.co/QHwszrUK
Sand Dollar Beach Day Discussion
What math have you learned at the beach?

Children on the Beach
Cassatt, Mary
Buy at AllPosters.com
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jsr54
Jan 31, 2012 @ 6:19 pm | delete
- I found some live sand dollars in the Aegean Sea off the coast of Turkey. Had to go to 8 feet deep to scoop them up in very salty water, not east to do, but worth the prize. I took one out, snapped a picture, and returned it to the sea where it belonged. Very interesting lens.
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TransplantedSoul
Dec 31, 2011 @ 1:57 pm | delete
- These are such beutiful animals. This lense makes me want to be on the beach right now!
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liberia88
Sep 29, 2011 @ 3:43 pm | delete
- It was fun exploring this page. There is a lot of great information. I would love to see live sand dollars too!! I will have to look for them when I go snorkeling on the Pacific coasts of Guanacaste, Costa Rica.
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mommy2deb
Sep 25, 2011 @ 1:15 pm | delete
- Interesting lens.
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BigGirlBlue
Jun 13, 2011 @ 11:35 pm | delete
- We never learned math at the beach but I think it is a good activity to incorporate.
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snakesmom
May 19, 2011 @ 1:16 pm | delete
- Beautiful lens! I love the sand dollars, they are so cool!
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akumar46
May 19, 2011 @ 12:33 pm | delete
- What a cool Sand Dollar math lessons!Thanks.
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CreativeArtist May 19, 2011 @ 9:21 am | delete
- What an amazing find, and such a wonderful teaching moment.
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Shar
Apr 15, 2011 @ 12:47 pm | delete
- wonderful lens! Shar
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jmsp206
Jan 5, 2011 @ 8:34 pm | delete
- Arn't they lovely.I love shells.We used to find counters on the beach as kids.
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ViolinStudent Jan 5, 2011 @ 1:20 pm | delete
- Great page (as usual). Thanks!
Art Haule
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ChrisDay
Dec 31, 2010 @ 10:01 am | delete
- Great lens - home education is THE thing!
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Brick_House_Fabrics
Dec 21, 2010 @ 11:12 am | delete
- Wonderful lens about something that has always intrigued me!
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sorana
Dec 11, 2010 @ 4:12 pm | delete
- Evelyn your lenses are so creative and inspiring. Yet another wonderful one. Thanks
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Irenemaria
Dec 10, 2010 @ 7:41 am | delete
- Sand dollar is exotic to me. But what I really loved about this is, how you and your children were standing there feeling, watching and learning about this little guy. This is exactly the way my children were raised too.
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raphaelo
Dec 10, 2010 @ 7:27 am | delete
- Wonderful lense of Sand Dollars! Love to be here. Thanks for creating this natural lense :)
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CruiseReady
Oct 5, 2010 @ 7:58 pm | delete
- What a fabulous lens!
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LensbyLisa
Sep 16, 2010 @ 12:06 pm | delete
- I truly loved this lens! Wonderful imagery and descriptions. I didn't know how to tell the age of a sand dollar until now. Great lens! Thanks for sharing your memory.
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theraggededge
Apr 25, 2010 @ 10:01 am | delete
- Popped back here to bless this fabulous lens :-)
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Evelyn_Saenz Apr 25, 2010 @ 4:37 pm | delete
- Thank you so much and Congratulations on becoming a SquidAngel :)
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About the Author of this Sand Dollar Math Lens:
Find out what I'm up to when I'm not Measuring Sand Dollars
by Evelyn_Saenz
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... more »
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