Look Up to the Clouds and Name What You See: Harnessing Imagination to Build Stronger Thinking in Mathematics

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I see a dragon on his back, a troll, a moose head/reindeer head, and some kind of duck doing the back stroke. Ha! ūüôā What do you see?

With Spring and Summer bringing beautiful clouds, this is a great time to plop on the ground and look up at the sky!  Have you ever played the game of naming clouds?  Do you know that this might be great for your creative eyes to stretch and have some fun?

Just go outside and take a few minutes to look at some clouds and take turns with your child as to what they see and you see.  Name some shapes too!  Have lots of giggles and smiles!  Your child might be able to see their favorite cartoon character, or a favorite animal.  Here are some clouds that I thought were fun look at:

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To me, these clouds look like sun glasses.  My sons sees stretched out silly putty!  What do you see?

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A little later in the morning, the same cloud from above transformed to this!  I see two space ships.  My older son sees two eyes.  What do you see?

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These are special clouds as you may be able to see a fairy or two up in the sky ūüôā

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The bigger cloud may look like a seahorse or dragon looking down.  What do you see?

 

Something To Think About:

In Mathematics, the patterns, or solutions that we need to find are not always going to pop up at you and say “Here I am!”. ¬†I have used a lot of creativity and imagination to solve some mathematical problems. ¬†The more opportunities we take time to be creative in what we see, the easier it will be to see even the hardest patterns and solutions. ¬†It is helping yourself and your child to see and think outside of the box. ¬†It will also make it easier to explain it to someone else. ¬†We also need to remember that some of the most innovative advances in science have also come from authors of science-fiction. ¬†Creativity inspires! ¬†ūüôā

There is always more than one way to add, there is always more than one way to multiply, and there is always more than one way to approach a problem.  Being an example to our children in this way can really help them adapt to challenges, seeing things differently, and knowing it is great to try another approach.

Remember, creativity and imagination go hand in hand with Mathematics!  Having this attitude and belief will help us see just how attainable Mathematics really is to all of us.  Enjoy being with the clouds!

copyright 2018 Christina Grossman. All Rights Reserved

 

 

Cookie Cutters and Snow: A Winter Exploration with Shapes

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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!

Something To Think About:

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. ūüôā

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!

 

copyright 2018 Christina Grossman. All Rights Reserved

 

 

 

 

 

 

 

Symmetry, the Bilateral Kind: Looking into Nature to Find the Balance

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As we approach Autumn, things will be slowing down for us on the mountain and in the desert.  This is a very important time to still be able to go outside into Nature and find the balance.  Take pictures, enjoy the time outside and when it starts to cool down.  Notice what the plants are showing you in terms of symmetry, especially the bilateral kind.

Yes, there are different types the symmetry, but what we are all familiar with is the type that we know when we can ‚Äúcut‚ÄĚ something in half, or see the same image reflected on the other side, or even think of it as the mirror image.¬† However young or young-at-heart we are, this is something that we can all enjoy learning about!

Go for a walk soon and figure out what is symmetrical.¬† This would be also a great time to put together a math nature journal too!¬† Take this mushroom above, where would you place the mirror to reflect the same image?¬† The place that you have the mirror is called the line of symmetry.¬† How many lines of symmetry could this mushroom have?¬† One? Two? More?¬† Go with those questions when you go for a walk outside.¬† Don‚Äôt have a mirror? Take a pencil or a straight stick with you.¬† Place the stick where you would a mirror and eyeball it.¬† Where‚Äôs the line of symmetry? ¬†ūüôā

If you are not able to go outside right now and explore, print out the pictures from the website, or place them up on the screen.  Get out a mirror and see where the mirror can be placed so that the same image can be seen.  Play with it!  In some cases, it might not be exactly symmetrical, but close enough.

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Something To Think About:

Have a conversation with your child, or with someone else about what it means in Nature to be symmetric.  What does a symmetric plant tell the pollinators: the bees, the hummingbirds, and the butterflies?  Is it still alright for something to be not symmetrical?  Yes! There are many beautiful examples of what is not symmetrical, or what we call asymmetrical.  Everything in the Mathematical world has a place and importance, so asymmetrical is also wonderful and tells us a great many stories too!  Hmmmmm, I think I see a future post here!

Learning about Mathematics is not about getting to the finish line first, it is actually getting there and having an understanding and an appreciation for it.  The more we can connect with how our world is tied to Mathematics, the more we can see the patterns unfolding and even the importance of balance. Also remember that a good rule when we go out to explore is that the only thing we take are pictures, drawings, notes, and memories.  It is best to leave the plant in the natural habitat.

copyright 2017 Christina Grossman. All Rights Reserved

 

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

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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! ¬†ūüôā

(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?

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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. ¬†ūüôā ¬†And all with a slice of Watermelon! ¬†ūüôā

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Something To Think About: 

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!

 

Getting Our Child Ready for Kindergarten: The Count Down Begins

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Copyright 2017 Christina Grossman. All Rights Reserved

 

If you need some ideas of what math activities to do with your child(ren) at home, go to the header above on this blog and select an age, or topic!  If you have any questions, feel free to contact me on the comment section or email me at momatlearningmathwithmomdotcom (spelling this all out because of spammers).

If you would like to have a checklist handy for the summer, here are two resources for you to use:

  1.  Summertime Tips for Preparing Kids to Enter Kindergarten from AZ First Thing First http://www.azftf.gov/WhatWeDo/Impacting/Documents/Preparing%20Kids%20to%20Enter%20Kindergarten.pdf
  2. Getting Kids Ready For School With PBS KIDS from PBS.org http://www.pbs.org/parents/education/going-to-school/starting-school/getting-kids-ready-for-school/

Do you also want a chart, or schedule, as a friendly reminder during the summer?  Go to this link to see charts to set up your day by topic for different age ranges!

https://learningmathwithmom.wordpress.com/category/schedule-of-activities/

Something To Think About:  

There are plenty of things at the stores and online that you can buy and do with your child at home.  This blog focuses on things that you might already have at home that you can use, so learning at home does not need to be expensive. From the checklists though, I hope you see that just talking to your children and pointing things out to them about numbers, colors, shapes, letters, and reading to them are just the fundamentals of getting your child(ren) ready for learning.

Remember, learning should not be a race to see who gets there first, it is actually about getting there. ¬†Learning should be enjoyable and relevant to the child’s world. ¬†Once the child sees how math is a part of his/her world, the mathematics becomes that more interesting to learn.

Copyright 2017 Christina Grossman. All Rights Reserved

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

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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.

 

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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! ¬†ūüôā

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Something To Think About:

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/

copyright 2017 Christina Grossman. All Rights Reserved

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

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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?

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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)!

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Something to Think About:  

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 ūüôā ¬†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 ūüôā ¬†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!

 

copyright 2017 Christina Grossman. All Rights Reserved

 

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. ūüôā

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! ūüôā Let us not forget the strawberries too!

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Palisades on Mount Lemmon, AZ

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Strawberries ūüôā

 

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 ūüôā 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! ūüôā

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. ūüôā ¬†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. ūüôā

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. ūüôā

Copyright 2016 Christina Grossman.  All Rights Reserved

 

 

 

There‚Äôs Math in Them There Mountains!¬† Spending Time Outside, Exploring Math, and Building Vocabulary

 

 

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Mount Lemmon, AZ . Copyright 2016 Christina Grossman. All Rights Reserved

(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!

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      Pine. Copyright 2016 Christina Grossman. All rights Reserved

    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!

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      Fern. Copyright 2016 Christina Grossman. All Rights Reserved

    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 ‚Äútree rings‚ÄĚ, or concentric circles in the water too?

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      Tree Stump Showing Tree Rings. Copyright 2016 Christina Grossman. All Rights Reserved

    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 ‚ÄúDandelion wish‚ÄĚ are little parabolas.

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      Common Dandelion . Copyright 2016 Christina Grossman. All Rights Reserved

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?
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      Cranesbill. Copyright 2016 Christina Grossman.All Rights Reserved

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      Richard’s Geranium. Copyright 2016 Christina Grossman. All Rights Reserved

    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 ūüôā

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      Big Leaf Periwinkle. Copyright 2016 Christina Grossman. All Rights Reserved

    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?

       

       

Something to Think About:

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. ¬†ūüôā

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.

copyright 2016 Christina Grossman. All Rights Reserved