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

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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!

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Palisades on Mount Lemmon, AZ

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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?

 

 

Something To Think About:

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! 🙂

copyright 2016 Christina Grossman. All Rights Reserved

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

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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!

 

 

Something to Think About:

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. 🙂

Copyright 2016 Christina Grossman.  All Rights Reserved

 

 

 

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

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Fern on the mountain that grows out from a spiral. © Christina Grossman. All Rights Reserved

 

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 🙂

 

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Sea Shell from the ocean that I used for a Mandala for water ©Christina Grossman All Rights Reserved

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.

 

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Fern on the mountain that grows out from a spiral. © Christina Grossman. All Rights Reserved

GLASS BEAD SPIRAl ART: 

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. 🙂

 

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Fern on the mountain that grows out from a spiral. © Christina Grossman. All Rights Reserved

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.

 

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A vine from our Carolina Jasmine in our yard.  ©Christina Grossman. All Rights Reserved

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.  🙂

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Fern on the mountain that grows out from a spiral. © Christina Grossman. All Rights Reserved

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!

 

Spiral art made from Sycamore leaves from smallest to biggest. © Christina Grossman. All Rights Reserved

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.

 

Something To Think About:  

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. 🙂

 

copyright 2016 Christina Grossman. All Rights Reserved

 

 

 

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

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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.

Something to Think About:

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

copyright 2016 learning math with mom

 

Activity Calendars From Learning Math with Mom

copyright 2016 christina grossman

copyright 2016 Christina Grossman

 

As a new mom years ago, I could  not think straight from all the lack of sleep.  I still wanted to see how I could teach my firstborn math, but needed a reminder to keep track.  As time passed, two more calendars were posted up on the refrigerator to remind me now and then of what we could focus on that day.  These have been shared throughout this blog as the “Schedule of Activities”.

At first glance, it looks like a rigid schedule to follow and leaves one to question when there was time to do anything else.  The calendars are there to serve as reminders of what could be done that day.  The calendar can be followed just as it is, or adjusted to what works for you in your household. Either way, it is to be a resource for you and your family.  🙂

Remember, it is not about following a strict schedule of teaching math to your child(ren) at home.  It is about actually finding ways to incorporate it into your family life in things that we already do because the math is and was already there to begin with.  🙂

Please enjoy this as a resource and friendly reminder for ages newborn-5 years of age.

Schedule of Activities for 0-18 months

Click to access Schedule%20for%20the%20Week_zerotoeighteenmonths.pdf

 

Schedule of Activities for 18 months-3 years of age

Click to access ScheduleofActivitiesfor18mosto3yrsofage_0.pdf

 

Schedule of Activities for 3 years – 5 years of age (with go through a revision soon)

Click to access CALENDAR3yearsto5yearsofagePDF_0.pdf

copyright 2016 learning math with mom

copyright 2016 Christina Grossman

What Books Does Mom Have About Math? Here are just a few….

 

At our home, we have a lot of books about math.  I have been asked what books I have read or the kids used since they were little ones and even to this present day.  The best way I can do this is through photos and there will be repeats as I have taken these photos at different times.

As a note, none of the publishers, nor the authors have paid me or asked me to post these books on this blog.  These are books that we actually own, or have owned.  You do not need to get all of these books, just choose a one or a few and go from there.  Remember, checking them out in the library, borrowing them from a friend, or buying them are options.  The important thing to remember is to begin reading to your child, especially in mathematics. 🙂

 

copyright 2015 Learning Math with Mom All Rights Reserved

copyright 2015 Learning Math with Mom
All Rights Reserved

 

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Do You want a Half of a Banana, or a Whole Banana? Starting Fractions Early

When it is time for a snack or dessert, a banana is so nice and sweet for the little ones.  At first, when I have asked each of my kids whether they want a half of a banana, or a whole banana, they look at me like I am crazy.  So I take out a banana and show them a whole banana, then I take that banana and show them half.  Usually, they will say that they want a whole banana and then go eat because of course they want a whole banana.  It was not to test them on the idea of whole, or half.  It was giving them the vocabulary to use to describe how much of something they wanted.

One whole banana

Why would anyone want half a banana?

With my two boys being so little and close in age, sometimes there would be only one banana left.  If both were to get a banana, we would need to cut this in half.  This is the moment to now see half as equal parts because for kids, each person should get the same as the other, right?

Taking the knife to cut the banana, I placed the knife at different parts of the banana, asking them each time if this was cutting the banana in half.  “Would the both of you get the same amount if I cut it here?” “Would he get more or less of the banana, if I cut it here?” “Where would I cut the banana so that both of you get the same amount?”

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After cutting the banana in half, I put the two pieces, one over the other, to have the boys see if both pieces were equal.

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So, there it is.  It took me longer to type this out, than it did to show my kids in real time about half and whole.

Where is this in the Schedule of Activities for ages 18 months to 3 years?

Click to access ScheduleofActivitiesfor18mosto3yrsofage_0.pdf

Answer:

1. Tuesday-Numbers

2. Wednesday-Big and Small

3. Thursday- More and Less

 

Something to Think About:

Start asking your little one about whole and half. This does not need to happen each and every time someone asks for a banana because then it starts to sound scripted. Once in a while, bring it up as this lesson should only take no more than five minutes.

Teaching math to the little ones should be a part of life so that they can see early on how math relates to their world. The more we do this, the less foreign it will be when they begin school. Math is a part of life, just as it is with sharing a banana.

copyright 2015 learning math with mom

copyright 2015 learning math with mom

The Power of One, Two, Three…

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The power of 1,2,and 3 is quite powerful, especially for a baby or toddler.  When you begin counting one, or two of something, you are giving the child a sense of numbers. It is not the sake of counting, it is the sense of showing quantity.  The ways to offer your child a lesson in quantity is to:

1.  Count the number of pieces of fruit or cereal you are giving them;

2.  Count out loud and with fingers the number of rocks, trees, or plants outside; and

3. Read them books that focus on counting to three, ones that I have are in the picture above.

Counting to one, two, and or three does not seem like a big deal for us, but it is for a baby and toddler. To them, having one nose is a big deal. What do you mean we have two eyes and two ears? But what about one more? What happens in threes? These are all questions to show how to count, point them out, and read about.

Where is this in the Schedule of Activities for 0-18 mos?

Answer:

1. Wednesday -numbers(counting)

http://www.learningmathwithmom.com/sites/default/files/Schedule%20for%20the%20Week_zerotoeighteenmonths.pdf

Where is this in the Schedule of Activities for 18mos to 3 years?

1. Tuesday-numbers

http://www.learningmathwithmom.com/sites/default/files/ScheduleofActivitiesfor18mosto3yrsofage_0.pdf

Something to Think About:

With our babies, there is so much to learn as this is a  great time to get to know the world around them in new ways, especially in number sense.  As a parent, though, we might think we need to hurry up on teaching certain things to our children so that they won’t fall behind.  This allows us to become more stressed or pressured if our children are not learning at the rate we think they should.  No worries….just breathe.  Just start counting in front of the babies and be more transparent in your thinking.  Say the numbers aloud, the colors aloud, and the shapes aloud.  Doing this broadens their bank of vocabulary.  Remember that it is that important to know that you are doing a great job!

 

 

copyright 2015 learning math with mom

copyright 2015 learning math with mom

 

You Deserve to Understand Mathematics

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In talking and listening to my colleagues at work, it dawned on me that many reasons why some of us might not be open in learning math, or even teaching others math for that matter, stems from the question of “Do you believe those you teach deserve to learn and understand the math?” and “Do you believe you are deserving to learn and understand math?”

Your answer and my answer might be, “well, of course!” Really think about this for a moment. You believe that you and your child deserve to read, so you find out tools to use and what things to do with your child to help him/her to read. You believe that you and your child deserve to have a healthy eating lifestyle, so you do what you can to achieve that. I am wondering if we truly believe that we deserve to learn mathematics.

From my teaching years in the classroom, the meet-ups with parents and even other adults throughout the day would freely share how their parents were not great at mathematics and so they believed this was the reason why they are not good in math. Some parents would also freely share that they were not great in math and so they do not expect their child to be great in math, as if this was connected to genetics. If you really want a gene, a math gene, then go to http://www.learningmathwithmom.com/index.php?q=img_assist/popup/31 and get your math gene. Make this yours and pass it on to others so that we can stop the thinking that the math gene is out of reach.

On behalf of anyone who has told you that you cannot learn math, or anything for that matter, I apologize. I am so sorry that happened to you or to your child. We are all capable of learning. We all have our strengths and we all have our desire to learn.

At least learn one new thing a week, or even every two weeks. Begin telling yourself and your children that the both of you deserve to learn the math and understand it. Keep telling yourself that you can do it and spread the message to your child. If you want to learn more about how to help yourself and/or your children to understand math, keep reading the blogs, subscribe, and feel free to e-mail me at mom@learningmathwithmom.com .

copyright 2014 learning math with mom

copyright 2014 learning math with mom

Taking a Break to Breathe :) Why I Do This for My Kids and For You!

It has been two months since I last posted an activity and all I can say is that it was time to take a break to breathe. I hope you were able to do the same, whether it was for five minutes or all summer. Sometimes it is okay to not try to schedule everything all at once, to have your life planned for every single second, and meet every single deadline. Bottom line, when you feel rushed, so do you kids. So take the time to breathe and enjoy the time you have with your little ones, especially before they go off to school…if they haven’t done so already.

 

Something to Think About:

My two cents worth of being part of this movement to incorporate more math in the early years is not just about teaching shapes and how to count before a child begins school. It is also about changing the way we think and do mathematics in our lives. I have been trying to show you how simple, less complex, and how easy it is to teach your child about math before he/she starts school for the first time.

For the past five years, I have been asked if I am homeschooling my kids. At first, my thoughts were that I was not homeschooling them because they were eventually going to school when they are of age. Then I thought more about what people were really asking me. Many people need to label what they do or others do to try to wrap their minds around something that is not the norm. All I was trying to do was create an environment where my kids did not feel bombarded or bored about learning math. My goal was to just make it a normal part of their life and not a chore or another extra thing they needed to do. In a way, I am homeschooling my kids. In one way or another, we all do that with just about anything we teach our kids. We teach our kids certain things we think and feel are important for them to understand. The important thought I want you to understand is that it is really important to surround your child or children with the knowing that learning in not just at school; learning happens at home, on the playground, at lunchtime, outside, and as a family.

Whatever subject or skill, or just about anything you want your child to learn from you, you need to understand and feel that it is important or your children will not see the purpose in learning it. Although I am teaching my kids math, I also am expanding to other areas that I was not very strong in. To be a supporter of the arts, I needed to do things in art to feel empowered and confident so that my children can also know that they can feel that way to. Whatever it is, become their teacher of making a success and a teacher of making mistakes 🙂

Throughout all these years, I love every minute I was able to be with my kids, especially showing them that there is nothing to fear in math, or in any subject. You fall, so dust yourself off and try again. You make a mistake on the canvas for art, there is always white paint. Remember to have an eraser at the end of your pencil. It is not how fast you get there, it is the fact that you got there!

So stop and take a breather with your kids and let us get back to learning math 🙂

copyright 2014 learning math with mom

copyright 2014 learning math with mom