# Cookie Cutters and Snow: A Winter Exploration with Shapes

There is snow outside, but what if there is not enough to make a snowman? Get out those cookie cutters and make some shapes!

It was still a cold day and the kids wanted to play with the snow. At this point, the snow was more like chunky ice, but still manageable.  So I gave my youngest cookie cutters to make shapes with the snow and it was a lot of fun!  This was one of those great explorations that took of little to no time for prepping and more time for exploring!

With using cookie cutters, the shapes become more 3-dimensional and is transformed from their 2-dimensional point of view.   For some eyes, going from 2-dimensional to 3-dimensional can be a challenge. The more explorations one can do with going from looking at a 2D heart to a 3D heart, the better. For those circle shapes, show how a circle in 3D looks like a snowball, a sphere! If you have some empty tissue boxes, or shoe boxes, fill those up as well with snow and see what they can build with them.

Would you like another exploration? Look up videos of people building igloos with snow/ice.  It might be amazing for the little ones to see how blocks of snow can create something that looks like a hemisphere shape. 🙂

Remember to make this a fun mathematical exploration. This is not only a time to learn about math, but a time to get together and make mathematical memories! Enjoy!

# However You Slice It, There is Always Something Mathematical to Learn From Watermelon: Shapes and Application

There is not enough to be said about the Watermelon.  When we think of summer, the Watermelon is the iconic fruit of sunshine and a carrier of water that so many of us treasure!  If you just take a moment to look at the Watermelon that you eat, it tells you a story through shapes.

Take a look at the picture above and look at the naval.  That navel is the center of a beautiful multi-pointed star that tells the story of how it began.  This watermelon started out as a flower, as most fruits do.  So as not to forget where the Watermelon came from, there is this beautiful light green and white star on it.  Also take a look at the “vein-like” features of the skin and compare this to the leaves of the plant from which it came from.

At this time, I am explaining this to my little one and telling her about the star and that this is an imprint of the flower that the Watermelon came from.  Her response was, “So this came from a flower?  So I eat flowers?”  Yes!  🙂

(Note:  This might be a good time for you to look up the blossoms of a watermelon plant right now and compare it with the picture above of the watermelon )

Take a look at the seeds in the picture above, which I have found to be a treasure hunt in itself to find watermelons with seeds in them still.  The shapes of the seeds are oval, but they also look like water droplets and remind us of how much this wonderful fruit needs so much water to grow and retains it too!

Now take a look at the Watermelon slice below. I sliced this width-wise and saw this beautiful result!  I see spirals and curves and this slice being partitioned in at least three parts.  What do you see?  What story does this Watermelon show you on how it grew?

Application:

Lastly, what if you have a small-sized Watermelon and many little hands to eat it?  How would you slice this up?  I learned this great way of slicing through someone on the internet.  This is a great way for little children to be able to hold the slice in one hand and be able to finish it before getting another piece.  What shape is the piece of Watermelon now?  A rectangle? A rectangular prism?  A rectangular prism with a curved edge?  I am always an advocate for trying out different names to call a certain shape or object.  There is a place for exact names of shapes of objects, but I like to give some opportunity for the eyes to explore beyond and see what other possibilities there are.  🙂  And all with a slice of Watermelon!  🙂

Something as much as a fruit can be looked upon with a Mathematical eye, not a Mathematical eye of analysis, but an eye of wonder!  Everything tells a story, however you slice it.  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

# When the Only Way Your Child Learns Shapes is if it’s Pink: Adapting to Our Children

It was that time to teach my daughter her shapes.  I tried the shape cards to show her what is a circle, a square, a triangle, and the rest of the shapes.  When we went to the grocery store, I pointed out items that were in the shape of a circle, a square, a rectangle, and such.  She did not seem interested, but I continued to do it.

The same went for colors.  The only color she wanted to learn was the color pink. It was a few months, but then she opened up to purple.  After that, she was interested in red, but her favorite color was pink.  So I went along with her favorite color and wanted to use that to help her get interested in learning her shapes.

One morning, I picked out the pink shapes for each different shape and she was so excited! From then on, we work on the pink shapes because for now, that is what works. As for counting  items from 1 through 10, they are the color pink.  🙂

Here is the link to the shape cards that are in color in both English and Spanish:

2 dimensional shape flash cards in English

Click to access 2dimensionalshapeflashcardswithellipse.pdf

2 dimensional shape flash cards in Spanish

Click to access 2dimensionalshapeflashcardsinspanish.pdf

Just because my daughter is a girl, did not automatically mean that she was going to like the color pink.  I am female and prefer the color blue.  Your son might like the color pink and your daughter might like orange.  The point being is that certain colors should not be assumed that a certain gender will like them.  We all , young and older, have different interests.  With that, use your child’s interest as a tool for learning.

Remember that we also learn at different times.  It is not about getting to the finish line first, it is about actually getting there.  Take the time to do a little bit each day, or each week to work with your child on mathematics.  If it becomes frustrating, take a breath and come back to it at another time.

The mathematics is already there, whether it is time to make a meal, play outside, or shop for groceries.  The more we make mathematics as a part of our life, the more relevant it will become to your child to learn and understand.

copyright 2016 learning math with mom