Diversity Exists in Nature To Teach Us a Lesson: Counting, Pattern Finding, and More!

I could not resist in getting our home a bunch of beautiful red Tulips.  If you have read the other posts about looking at flowers in Nature to look for patterns, well this one is not any different.  Tulips taught me a lesson about diversity.

Fascinated about the black and yellow six-pointed star, I counted the points on the Stigma of the flower.  Three points on the Stigma, then six Stamen, then six red petals on the Tulip.

In Nature, there are flowers demonstrating these patterns of either doubling the original number from the Stigma, or simply repeating the original number from the Stigma.  However, this second Tulip (pictured below) surprised me because this Tulip demonstrated the same doubling pattern, but a different original number.

Looking at this particular Tulip, the Stigma has four points, not three points.  Then that quantity of four is doubled to eight Stamen and eight petals!  Wow!  I love Nature!!!! Yes, I realize that these Tulips were not cultivated in the wild, but this one grew to be much different then the other red Tulips.  So this hit me with a great example of showing kids and ourselves as to how Nature and Mathematics shows us that Diversity still exists even when we think we are all the same.

These two Tulips have the same color pattern, have the same green stem, and are both called Tulips.  However, both are still different and unique from each other, which is beautiful!

So how is this important with Mathematics?  Well, just by understanding how to count, how to compare and contrast, and how to find patterns, that can simply take you to a lesson of learning and appreciating Diversity.  Yes, Nature has an abundance of beautiful flowers of different shapes, sizes, and colors!  Each of them have their own purpose of making the world function and be beautiful! How exciting it is to further see that even when we think a bunch of flowers look the same, Diversity still exists!

This is why Mathematics is so very important and near and dear to my heart.  Mathematics is not just solely about numbers, but extends to our very own life and life lessons that we might encounter from day to day.  What a wonderful way to introduce this particular lesson to your child about how Nature can beautifully teach us about the importance of Diversity and celebrating the Diversity!  🙂

The world of Mathematics is in your home and outside, so go explore what new lessons are out there!  Always remember that it does not matter who crosses the finish line first, it is actually getting there that is more important!

If you would like to see the article describing number patterns on flowers, go to

https://learningmathwithmom.wordpress.com/2016/07/01/theres-math-in-them-there-mountains-spending-time-outside-exploring-math-and-building-vocabulary/

When Temperatures Rise, It is Time to Make Sugar Water for the Hummingbirds: Measuring with the Help of Little Hands!

This is not a new concept, but it is new for my child and that is what counts!  We love seeing our Hummingbird friends and they do remind us that the sugar-water is getting low.  For this activity, it takes just a smidge of time with your child and it is just right for the little hands to measure.

Materials:

1. A pot to hold at least 4 cups of water
2. Distilled, or Spring Water
3. 1 cup of raw sugar
4. A measuring cup, be it a 1/2 cup, whole cup, or 1/3 cup
5. Humming bird feeder

With those little hands, count out 1 cup of sugar and pour into the pot. If you are using a 1 cup measuring cup, then counting is easy.  If you are using a 1/2 cup, then you are counting to two.  If you are using a 1/3 cup, then you are counting to 3.  This would be a great time to show your child how two half cups of sugar equal into 1 cup and how three 1/3 cups of sugar equal 1 cup too!

Now count out 4 cups of water and pour it into the pot as well.  If you are using a 1 cup measuring cup, then count to 4.  Using a 1/2 cup will have you counting to 8 and using a 1/3 cup will have them counting to 12.  Then get a spoon to stir it up before putting this on the stove.

This is also a great time to tell your kids about the rules of the house with a stove.  To make sure my little one can still pour and scoop, the pot is first placed on the table and then transferred over to the stove.  Turn on the stove and let the mixture boil.  Once it is boiling, turn it off right away and let cool.

For us, we make this in the mid-morning and it cools off completely after lunch to be able to pour into the humming-bird feeder.

Now you can enjoy the Hummingbird friends coming over to your yard and take notice of the sounds they make when they call each other, fight over the feeder, or the different colors and sizes of the Hummingbirds.

Purchasing sugar-water at the store can be expensive over time and it also contains a lot of additives that the Hummingbirds should not consume in the first place.  This activity is much about being responsible to our animal visitors, as well as a mathematics lesson.  Planting flowering plants in your yard, that do not contain any pesticides, are also a wonderful addition to your yard.  There is plenty of measuring in that activity too!

Do not be surprised if you see a Woodpecker enjoying the sugar-water as well.  It is really fascinating to see them hang on to it to drink the water 🙂  If you also encounter a lot of Bees drinking the Sugar Water, do not be surprised either.  If this is a problem for you, then wait until the sun sets, or gets dark to remove the feeder, as Bees always go back to the hive at night.

The most important thought to keep with you, after reading this, is that you had a great time with your child that included mathematics and nature!  Enjoy!

Pi Day is Today!!!! Let’s Celebrate Another Year of Pi

Today is Pi Day again!  This post you will see each year because it is just that important 🙂  To learn more for yourself about Pi, or for your older children, try http://www.piday.org

What about for our younger children?  We can:

1. Begin experimenting with measuring different circles with a piece of string and then taking that against a ruler to figure out length, which leads to,

2.  Talking about circumference (which is really finding the perimeter of the circle, or length

3. Looking at diameter (the length or distance across the circle),

4. Looking at Radius, which is half the length of a diameter of a circle, and

5. Compare! Get the circumference of any circle you are measuring and divide that by the measurement of its diameter. What number do you get? Get another circle and take its circumference and diameter and compare. What number do you get? How does that compare with the other circle?

6. This item can be either you number one choice to do before choices 1-5, or you can save this best for last. Read story books about Pi! This one is really fun and doesn’t take a whole lot of planning.

Where is this in the schedule of Activities of 3-5?

1. Monday- Reading a Math Story

2. Tuesday- Math under Numbers

http://www.learningmathwithmom.com/sites/default/files/CALENDAR3yearsto5yearsofagePDF_0.pdf

For yourself, search through the internet on Pi.  Go to the library and look for books about Pi and read them for yourself and for your children.  For Pi, it is not just about that one day our of the year to learn about it, it is most importantly about seeing how this relates to the world around you and your children.

The more you and your children can see how you interact and deal with mathematics in everyday life and in nature, the more comfortable you will become in learning mathematics.  Learning about math is for everyone.  Mathematics is not just for the ones who go to college, or because they are a certain gender, mathematics is something that is all around us and everyone can study it.

So we can we celebrate Pi Day? Of course! Celebrate math everyday! 🙂

Preparing for the Winged Visitors Coming Back from the Winter: Pouring, Measuring, Classifying, and Counting.

At this time of year, it might be snowing where you live, but not here.  The weather is slowly getting warmer and the birds are coming back from homes during the Winter time and they are hungry!  So why not prepare something for them and turn it into a mathematics lesson?

You can either make your own bird feeder and bird seed mix or purchase them from the store.  Get some measuring cups, a ruler/measuring tape, and go outside to have some fun!

First, take a look at the bird seed mix.  What shapes do you see?  Do you see some circles and ovals?  Do you see some triangles, spheres, or curvilinear triangles?  What colors do you see?  How many different types of seeds do you see?  Could you sort them out if I gave you a cup of that bird seed?  How would you sort them?

Next, have your child look at the measuring cup and estimate how many cups of bird seed it will take to fill up the feeder. Remember what your estimate is and now begin to count how many cups of birdseed it takes to fill up the feeder.

Then,  how many inches, or rulers tall, or building bricks tall, or hands tall is the bird feeder?  Where are we putting the feeder and how long of a string do we need?

Once you have your feeder up, let the fun begin by observing what birds come to use it.  It might take a day, or two before the birds come, but it will be a great experience to see how many birds a day visit the feeder.  What colors do the birds have?  How big are the birds?  How many different birds come visit the feeder?

This whole math lesson may take 5 to 15 minutes from start to finish and it is worth it.  Something very simple and so many mathematical ideas to explore!  Have fun with this and with your child(ren)!

This activity can be adapted for any age of child and learning stage for the child.  You know your child(ren) better than I do 🙂  So, you may want to not ask so many questions, maybe use three.  If you have older children, they can make charts to categorize and keep track of the kinds of birds they see.  They can also name the types of seeds and birds as well.

Whether or not the weather is right at the moment, the birds will still be hungry and you are inviting the birds to come to you 🙂  The kids and you can even practice different bird calls and whistles by listening to them as well!  Get yourself and your child(ren) outside to explore the Mathematics around you and have fun!

Enjoy!

Concentricity: Triangles, Circles, and Even More Shapes in Our Food, Life, and in Nature

Mount Lemmon, AZ

Concentricity is something that others would say is too early to teach the little ones about.  I strongly disagree on this note.  Basically, Concentricity happens when there is a common center shared among other circles or spheres.  What I have found are some other examples that go outside of the rule of circles.  With the kids, we have found examples with triangles and ovals.

So by trying to keep this short and sweet for this month’s post, look at the examples below.  When Concentricity happens out in Nature, it is so easy to just point that moment out to our children, regardless of age.  This happens outside our home, inside the home, and in our food.  I hope this encourages you to go find more examples where you live. 🙂

Concentric Circles:

Tree rings are about the most common one that all of us can identify as they are concentric circles.  The sliced beets you see below are candy-striped beets and they taste delicious!

Concentric Triangles:

This Pine is a wonderful example of concentric triangles. So go out to the forest and see what the trees can teach you! 🙂 Let us not forget the strawberries too!

Strawberries 🙂

Concentric Ovals and More:

Kiwi is just as delicious and a great tool to show Concentricity.  This beautiful Agate can be debated on whether this shape is an oval, or an ellipse, or a five-sided figure.  Either way, I see the Concentricity here too 🙂 Do you?

How about squares? When do concentric squares happen?  How about other shapes? Where do you see them?  Think about it and start exploring!  That is the beauty about Mathematics as it is out there and there are so many opportunities for more than one answer because that is just how it is.  Just because a definition of Concentricity only includes circles, or spheres does not mean that there is no likelihood of an exception for that definition.  When we are able to discover and see the exceptions when they happen, that is where the heart and beauty of Mathematics exists.  These interesting surprises are the most important to point out to the children!  and to you!

Learning about Geometry, especially Concentricity, at such an early stage in life gives them the opportunity to see it everywhere.  Once a child, or any person of any age, is able to see the Geometry, it becomes more tangible when it is time to learn more in the classroom.  It then becomes more relevant and more important to them to learn because Mathematics is even more interesting than rules and procedures, it is about exploring and experiencing what happens outside your door.

Have fun learning and exploring together! 🙂

Hearts, Hearts, and More Hearts: A Shape We Can Find in Nature

Common Yellow Wood Sorrel

If you have good weather today, go take your child outside and look for hearts!  Hearts actually exist in Nature and are the shapes that will brighten any person’s eyes.  Find hearts in the Cacti, the Jasmine leaves, strawberries, Wood Sorrel, or your potatoes.  The potato is one that my mother found in her bag of potatoes.  It was exciting to have the kids receive this from her. 🙂  Hearts are certainly everywhere.

My children, including myself, have a new tradition of looking for heart rocks, rocks shaped like hearts.  We either keep them to remember our memory together, or give them to each other to show how much we care.  Heart rocks really rock in our family!

When exploring Mathematics in our world, it does not need to be anything formal when we are with our kids.  The purpose is to see, touch, experience, smell, and feel the Mathematics in our world.  Mathematics is everywhere and what better classroom than in the home and outside. 🙂

Remember, it is not about getting to the finish line first, it is about actually getting there.  Whether you are an adult, or a child, it is always a good day to learn the mathematics, especially if it means spending more quality time with your children. 🙂

There’s Math in Them There Mountains!  Spending Time Outside, Exploring Math, and Building Vocabulary

(On Mount Lemmon, Arizona )

Summer brings grandkids, our own kids, nieces, and nephews up to the mountain.  This is the greatest time for kids to explore and enjoy the mountain life. Even we can be kids at heart and enjoy what the mountain has to offer! But what’s that you say? There is math on these mountains?  Of course!

As a mother and a mathematics teacher, I take every opportunity to teach my children about math, even on Mount Lemmon.   Here are a few ideas of how to look at the natural landscape of our beloved sanctuary for the little ones:

Shape Watching on a Nature Walk

1. Small Pine trees are growing all over and some are the right height for young children to see the top of them.  Have them look at the top, looking down, and ask them what they see?  Do they see baby pine cones growing, they are called cones for a reason because cones are shapes.  Also, look at the way the needles are growing, they form a spiral!

2. While you are looking at the Pines, look down below because the Ferns are growing.  Did you know that they grow from unraveling from a spiral? When the leaves stretch out, they are little triangles too!

3. There are many tree stumps around, so take a closer look.  What shape do you see?  We see circles, tree rings. Together, they are concentric circles, like a bullseye.  What if you dropped a rock in the stream, would that make “tree rings”, or concentric circles in the water too?

4. What about when the Common Dandelions (Taraxacum officinale)come out?  The parts that we like to call Dandelion wishes are small spheres.  If you look closer, each little part of the white “Dandelion wish” are little parabolas.

Counting on Nature to Teach Us Numbers

1. Let us look at the Richard’s Geraniums (Geranium richardsonii) and Cranesbill (Geranium caespitosum) that will be growing soon.  Count the number of stamen of the flower and count the number of petals on the flower.  Is one double of the other? Is one half of the other? Are they the same?

2. Take a look at the Big Leaf Periwinkle (Vinca major).  Looking at the center, you see a pentagon, then out of that, another pentagon, and then the five petals.  This flower is all about the number five 🙂

3. When the Common Sunflowers (Helianthus annuus) start growing, count the number of petals they have.  Do you get an odd or even number of petals?  How many?  What about the flowers on the Common Mullein (Verbascum thapsus), count the number of petals on one little flower.  Do you get an odd or even number of petals?  How many?

These are simple things to open the mind of the child, and the child-like hearted ones we all are, to seeing the mathematics out in Nature.  Even if this takes five minutes to the whole entire day, everyone went outside, explored mathematics, and learned and used new vocabulary. This is a great way to show relevance of learning shapes and numbers because it is out there in our world.  🙂

Also, a many thanks to Frank S. Rose’s work on Mountain Wildflowers of Southern Arizona as it was a great resource to me to finally learn the names of the wonderful plant life we see on Mount Lemmon, AZ.

Spirals: Looking for Them in Nature and Creating Art with Them

The Summer season is approaching and we are at the moment between the end of Spring and the beginnings of Summer.  For most areas, it is time to go out and explore.  This would be a great time either go look for spirals, or create them with your children.

There are so many, many things that grow in spirals.  You can talk about the solar system that we live in to your child and show how the planets, starting from the center that is the Sun and show how the movement is in a spiral, while each planet does move around the Sun in an elliptical motion, the whole system moves inward, out.  Because we cannot take to the outskirts of our solar system, we can show them how living things in the world we live in also grow in a spiral fashion.  We can also make spirals for art. 🙂

FERNS:

Look at the Fern, in the picture above.  The way that this Fern grows is first starting in a Spiral and then opening up by unraveling itself.  If you look closely to the ends of this Fern, you can see little tiny spirals that are waiting to unravel.  I am sure there is a better scientific way to describe this, but I am here to show you how you can teach your child about different shapes, which includes spirals 🙂

SHELLS:

There are many shells that have circular spirals and are fun to look at and find on the beach.  There are also shells that are more conic, cones, that form in a spiral fashion.  So, if you live near a beach, or a craft store, or dollar store, go see what you can find.

We get a lot of things from the nearby dollar store for arts and crafts and such.  These glass beads are so beautiful to use to make art with, especially spirals.  This gives the child and you a chance to figure out how to space things out so that everything is symmetric, or balanced on both sides.  For children who are not able to draw spirals in the beginning, this gives them an opportunity to create one with stones.  Glass beads are not required, but you get the idea.  You can even print this one out and start from the first light blue glass bead from the center and start singing the ABCs.  You have enough light blue beads to complete the whole song. 🙂

LEAVES:

There are some leaves, that when they fall off the branch and begin to dry, they make spirals.  If you are living in the Southwest, you might be more familiar with these leaves.  They are all over our yard and they dry up in little beautiful spirals.

CAROLINA JASMINE VINES:

These vines have these yellow trumpet like flowers that hummingbirds, butterflies, and bees love when they are in bloom.  The interesting way that Carolina Jasmine grows is how the vines spiral out when they grow.  This is how the Carolina Jasmine grows in different directions, whether on a lattice, around a tree, or attaching to a bush.  The Carolina Jasmine does not have any “grippers” or “creepers” to attach to a wall or a tree, it actually grows in spirals, as you can see on the picture above.  All you need to do is just pay attention.  🙂

CABBAGE:

Cabbage!  Slice up your red/purple cabbage to reveal that not all spirals are formed by circles.  If you look at the center, you see a five-pointed star.  On the outer perimeter of the star is a pentagon.  This pentagon rotates and rotates and you see a spiral as well 🙂 Give this to your child to trace the spiral with their fingers.  If you don’t have cabbage, print this picture out, or show this to them on the screen!

SYCAMORE LEAVES SPIRAL ART:

This photo of the spiral made from Sycamore leaves is not a new addition to this blog.  This was a short activity to involve my children in when working on the idea of smallest to biggest.  Do this with dried leaves, fresh leaves, flowers, cereal, or rocks.  The kids really liked this one, but you may find that keeping this as few of leaves as possible will guarantee that the kids will finish it.

How will this prepare them for Kindergarten, or for a mathematics readiness test?  It does something even more important than that.  You showing them that the world they live in has mathematics gives them relevance and excitement.  Learning mathematics and exploring mathematics is not all about formulas, it is really about understanding how much our world lives in mathematics.  Whether it is how a plant spreads out in growth, the food we eat, or artwork that we create, the more involved we feel in something we are learning, the more we lead ourselves to a better understanding of it.

My oldest son might just say “Ya, ya, I know it’s a spiral,” but I will keep doing this over and over when I get the chance to just take a moment to point things out in his world.  It is like showing a child where vegetables come from and starting a garden, or picking from a garden.  It offers an opportunity to become more connected with the world.  So go outside and have some fun and take a few moments to point out the spirals that you see.  Enjoy the time you have with your children and make it fun. 🙂

Looking for Shapes in Rocks: Hearts, Trapezoids, Rectangles, Triangles, and Rhombi.

Rhombus-Shaped Rocks, or Diamonds

The kids wanted to go ride their bikes outside and while everyone took their water break, we took the opportunity to look for rocks.  It all started by asking the kids to look for rocks in the shape of triangles.  Those were put in a pile.  Then I asked them to look for rocks in the shape of rectangles.  Then one of them found a trapezoid shaped rock and the rest found more of those.  After that, it was time to look for rocks shaped like a rhombus, or diamond shaped.  It took all of five minutes and it was fun!  That’s all it has to take to see shapes in shapes because it is just that easy.  The best thing about this is that it is a scavenger hunt that is fun at any season of the year 🙂  So go outside and explore the shapes that rocks have to offer!

Rectangle-Shaped Rocks

Heart-Shaped Rocks

Trapezoid-Shaped Rocks

Triangle-Shaped Rocks

Go outside and search for the shapes because they do happen naturally, even hearts!  If you do not have a yard, or a place to look for rocks, then go look at the shapes you see on buildings, or the sidewalk.  The shapes are everywhere and it is free! No prepping, no spending, just walk outside and point these things out to your kids.  From time to time, ask them what shape this is, or ask them to find something in this shape.  It is so much fun!

Get excited about math and get them excited too! When you show interest, they will follow.  Change the way they see the world because it is so beautiful outside 🙂

copyright 2016 learning math with mom

Learning About Red, Green, Black, and Time. What’s in Your Garden?

A garden is just a garden, right?  What is so interesting about a garden?  Well, what you grow in the garden can teach your children many things like the fact that colors can have flavor, texture, and smell.  A garden can teach you about how time can be measured more than with days, weeks, and months.  So what’s in the garden?

For my current little one in the house, we were fortunate to pick some tomatoes and watermelon from a garden that we help at once a week during late summer and fall.  This was a perfect opportunity to teach my daughter about the color red, green, black.

Before giving the fruit, or vegetable to your child, describe the color.  Not all watermelons are red inside.  Not all tomatoes are red either.  Even on the same fruit, or vegetable there can be multiple colors.  Point those out 🙂

Learning about a color of a fruit, or vegetable is very important because they learn when it is ripe to eat, or best to eat it.  Talking about when a tomato gets red and what color is it when it begins to grow is very important to learn and it gives them the opportunity to understand why certain colors of food is so important to know before eating it.  Why do we not eat the tomato when it is green?  We eat celery when it is green, why not tomatoes?

To learn about flavor of a fruit or vegetable, it is easy to just have the child eat it.  For smell, have the child smell it and ask it the smell and taste are the same, or different.  For example, some people can tell if they are smelling cilantro, but the taste to them is like eating grass.

On another thought, what does the rind, which is green, taste like when you take a bite of it?  What anything green taste like and smell like?  How about the color black?  Black berries and black cherries are great examples of black fruit!  What about a banana that goes from green, to yellow, to brown, to black?  What does a banana taste like and smell like when it is those colors and when would we eat them, or use them to cook with?  In other words, give your child the experience to find out these certain characteristics of food that we sometimes take for granted.

For texture, I know people who might describe a tomato has mushy, slimy, or juicy.  It just depends on the person who is tasting that tomato at that moment.  The same can go for a the texture of watermelon.  🙂

So what does color, smell, texture, and taste have to do with learning about math?  When we take the little moments to help our children understand the relevance of color, smell, texture, and taste of what we eat, we are giving our children an opportunity to understand the world they are living in.  By also taking the time to explore the characteristics of fruit and vegetables we prepare the child to use more vocabulary in describing something.  In mathematics, exploration, understanding relevance, finding more ways to describe something, and looking for patterns is very important.

Think about time for a moment, time can be measured by seconds, minutes, hours, days, months, and years.  But when we look at vegetables and fruit, time can also be measured in the color that a vegetable turns.  Time can also be measured in terms of the texture and smell that a certain vegetable and fruit produces.  It is very important to understand time this way because it teaches us to understand when a certain vegetable, or fruit from our garden is ready to eat.

When we can think of different ways to describe what goes on in our world, like produce from the garden, the more interested we might become in exploring other situations around us.  The more different ways we can see a garden, the deeper the understanding we can develop about how a garden works and what goes on in a garden and this can all start with your little one.