Taking a Closer Look at Nature’s Flower, the Carnation: Counting and Comparing

It was a very hot day of over 100 degrees outside and we needed something to do in the house.  After having carnations left over from a bouquet, I made the decision to use them to teach my children and my nephew about the parts of the flowers and counting.  For this, I gave each child a carnation, a piece of paper, tape, and glue sticks.

The question that I gave them was to find out if the number of petals for each flower were the same as the other carnations.  The other task I wanted them to answer was to count the number of stamen and compare it to the number of petals as well.

So the children began taking a part the flower petals and spreading them out.  All I have to say is how beautiful everything smelled in the room! As you look at the photos, some of them had 37 petals, while another had 36 petals.  The numbers were all within range of each other.  It was really interesting for them to work carefully in pulling apart the carnation flower from the stem and then finding out how difficult it was to pull the stamen and stigma apart from each other.

For the number of stamen and comparing this to the numbers of petals, I will have you figure this out with your own children at home.  This idea came from my time taking photos of the flowers on the mountain close to us.  Sometimes the comparison was equal, while other times it was double or half of the other.  The idea for doing this and observing is to acknowledge that there is a relationship here.

This activity took about 10-20 minutes to do.  Most of them could do this on their own, but sometimes needed help in taping, or glueing this onto the paper.  We did let the petals dry and we put the rest of the flowers into the compost.

On the photo above, you see the number 28 and then the number 36.  For this, I asked one of the them to guess the number of petals he had on his paper.  He guessed 28 and then we counted them together to get 36.  So his estimate was not too far off from what the actual count was.  Estimating is a wonderful skill to have, so even doing this is a great example of how to have your child practice estimation. When you go get blueberries, or raisins in a box, have the child estimate the number and then count them and eat them!

Remember, doing mathematics at home does not have to be fancy.  You can go outside and look at the flowers and count petals.  If you have cut flowers at home and would like to get some more use out of them, think about doing this activity.  You do not even need to have paper and glue handy.  Just have them take a part the flower and start counting.  🙂  Take a closer look around you and start counting and comparing.  🙂 Below are more examples of the work the children did that day!

Radials in Nature: Plant Life That Reflects the Starburst, Sunburst, and Nature’s Fireworks.

There are so many beautiful teachable moments up on the mountain and everywhere else, when it comes to plant life.  As children, we are taught about circles and squares and triangles, but what about radials-starbursts and sunbursts?

Radials are something that begin in the center and bursts out from there, like fireworks.  They capture our attention.  They make us stop and look and admire the beautiful way that it grows.  Some could be easily described as growing in a circular pattern, or like a globe.  This is true, but it could also be described as a radial pattern.

Look at the photo above of the Wheeler Thistle.  This flower is blooming at Rose Canyon Lake near Mount Lemmon, AZ.  From afar, it looks more like a globe, or a sphere.  When you look a little closer, it looks like fireworks!  Most of the grasses on Mount Lemmon also grow from the center and branch out as well. It is really amazing just how many radial forms are out there.

When you are walking through the desert, look at the Aloe Veras and Agaves.  Take a moment to look from above and look down to the center. They all begin from the center and grow outwards in a fireworks pattern.

Is it enough for my small child to just know what a triangle is, a square, a circle, a rectangle, a heart?  The answer is yes.  If you can show more shapes at an earlier age, then you can open their eyes to see a lot  more than just what we are normally taught.  In some cases, things do not necessarily belong just with circles, or just with triangles.  Depending on how you see the plant for that moment, it could be both, or something entirely different.  This is how mathematics is, observing the behavior and seeing for what it is for that one moment.

Take the Blue Globe Glow Thistle.  Once the petals have fallen off and I look from above the blossom, I could say that this is a radial pattern, something that looks like fireworks.  However, when the petals are still there, as shown below, I could say that this looks like a sphere, or little stars on a sphere.  It just depends on how you look at this flower.  Nature shows us how many different names and answers we can come up with by the way we look at things.  In many cases, problems in mathematics may have more than one answer, just like this Blue Globe Glow Thistle. 🙂

More Examples of Radials in Nature:

So there you go, radials are another shape, or growth pattern in plants that we can teach our children about and ourselves.  I will continue to say that Mathematics is everywhere.  The Mathematics out in Nature is free and teaches us that there is more out there than we are taught in the classroom and there is always more than one answer to something, it just depends on how we observe for that moment in time.  If you do not have plants growing where you live, print these out, or point them out to your children.  Have fun with your kids outside as much as you can!

P.S

Math on the Mountain: The Geometry of Streams, Bubbles, and Chocolate Milk

Mount Lemmon has been getting a lot of rain. With rain, comes running streams. Running streams bring a great lesson in geometry…..bubbles!

Take a walk and listen to the running water. Ask the kids to go find the water and see if there are any bubbles forming. Look at the bubbles and ask the kids to name the shapes they see. Do they see Spheres? Do they see Circles? What happens when the Spheres get pushed together, what other shapes do they form? Do they see Pentagons, or Hexagons (five-sided or six-sided shapes)? How would you be able to recreate these shapes at home? How about with milk?

If it raining outside, or you need to take a snack break, give the kids some milk….chocolate milk if you have it.  Get a straw and have them blow bubbles in the milk.  What happens?  Do Spheres take shape? What happens if they get pushed together?  Do you see the same shapes as from the stream?  Do you see a rounded triangle?  Well, that is called a curvilinear triangle!

Look Closer.  You will see a Curvilinear Triangle to the left of the center of the picture.  Copyright 2016 Christina Grossman All Rights Reserved

Take a look at the size of the shapes when looking at the bubbles in streams, or in the milk.  Are all the bubbles the same size?  What do you notice when big bubbles are pushed together?  Do you notice a pattern in the bubble formations?  These are great questions to ask, even if asking just one or two of these questions.  It creates another way of looking at something that we might have taken for granted, especially up on the mountain. For instance, blowing bubbles and why are they always spherical….this is something to think about.

The next time you have some bubble solution, bubble wands, and/or a bubble machine, ask this question:  Does the bubble always come out as a sphere regardless of the shape of the bubble wand?  Why do think that happens?

Here is a website that has a brief description about that:  http://bubbles.org/html/questions/round.htm

Remember, these small lessons are to help the child and ourselves to begin seeing and thinking about the world for what it is.  The mathematics is there, it is free for everyone to learn, and there is an abundance of math to explore inside your home and outside, on the mountain, on a desert, and everywhere else.  🙂

If you would like a recipe to make bubble solution, here is a link for you (I am not paid to show support for this site, as well as the one above regarding the spherical shape of bubbles).  Enjoy!

http://www.wikihow.com/Make-Bubble-Solution

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.

Learning Math with Mom is on Facebook

The hope for putting Mom on Facebook is to build a community that interacts more frequently than just once a month.  You will still get the updates via email, if you are following this blog.  New posts will still be on this blog, so keep connected!

In addition to this, my hope is that you can share out which Learning Math with Mom activities and ideas you have been using at home.  What has worked?  What do you and your child need more help with?  How has your child’s view of the world changed from being more open to math?  How have you changed since having used, or just keeping up with the reads from Learning Math with Mom?

Remember, all of this is free and will remain free online.  The mission of Learning Math with Mom is to spread the message of opening the world of mathematics to the little ones in our world, wherever you are. Keep in mind that whatever you share on Facebook with Learning Math with Mom will not be sold, or printed for profit.  So go to http://www.facebook.com/learningmathwithmom and like it, share it, and send it out to day cares, preschools, neighbors, and friends!

Thank you for the followers of Learning Math with Mom since the beginning and I look forward to chatting with you and learning how you are helping your child learn math in your part of the world!

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.

Mathematics becomes more interesting when we think it is connected to things in our life because it really is.  When we give our children the opportunity to see it in their early years, the less of a struggle it will be when they get older.  We all, at some point, need to know why we need to learn something and that, my friend, is called relevance.

I have come across this need for relevance many times when I taught students in the classroom, also other teachers in mathematics, with my own learning, and with my children. We all want to know why we need to learn something and that is a good thing.   When we see that it is part of our everyday life, then we are more open to learning about it.  All this, from a garden.  So what’s in your garden?

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